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⚡ Chapter 8 · NCERT Science IX

FORCE AND LAWS
OF MOTION

Newton's three immortal laws of motion — inertia, F = ma, and action-reaction — form the unshakeable foundation of classical mechanics.

ILaw of Inertia
IIF = ma
IIIAction–Reaction
p = mvMomentum
3Newton's Laws
★★★★★Exam Weight
📍 Chapter Snapshot — Newton's Three Laws
I
Law of Inertia
A body at rest or in uniform motion continues its state unless acted upon by a net force.
II
F = ma
The rate of change of momentum is proportional to net applied force.
III
Action-Reaction
Every action has an equal and opposite reaction — acting on different bodies.
🎯 Why This Chapter Matters for Exams
📌 Newton's 2nd Law derivation (F = ma from momentum) is a standard 5-mark question.
📌 Conservation of momentum numericals — especially for collisions — appear every year.
📌 Inertia examples (seatbelt, coin on card) are favourite MCQ contexts in board exams.
📌 3rd Law applications — rocket, swimming, recoil of gun — tested in both theory and MCQ.
⚗️ Important Formula Capsules
Newton's 2nd LawF = maN (kg·m/s²)
Momentump = mvkg·m/s
ImpulseJ = F × t = ΔpN·s
Conservation of Momentumm₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
💡 Key Concept Highlights
InertiaMomentumImpulseNewton's LawsConservation of MomentumBalanced ForcesUnbalanced ForcesMass vs WeightFrictionRecoil Velocity
📚 What You Will Learn
  • 1Balanced and unbalanced forces — when and why objects accelerate
  • 2Newton's three laws of motion with real-life examples and derivations
  • 3Concept of momentum and impulse with numerical problems
  • 4Conservation of linear momentum in collisions
  • 5Applications — rocket propulsion, gun recoil, friction, seatbelts
🔗 Navigate to Chapter Resources
📄
Full Notes
🧩
MCQs Practice
✅
True / False
📝
NCERT Exercises
🏆 Exam Strategy & Preparation Tips
01
Derive F = ma
Derive the second law from the rate of change of momentum — mandatory 3-marker.
02
Examples for Each Law
Keep 3 daily-life examples for each Newton's law memorised and ready.
03
Collision Problems
For momentum problems: list m₁, u₁, m₂, u₂ first — then apply the conservation formula.
04
Recoil Calculations
Gun-bullet recoil problems are a popular numerical — remember v_gun is negative (opposite).
Chapter 8 · CBSE · Class IX
💥

Introduction to Force

Force Laws of Motion Newton's Laws of Motion First Law of Motion Second Law of Motion Third Law of Motion Inertia Mass Momentum Force and Momentum Change in Momentum Rate of Change of Momentum Linear Momentum Balanced Forces Unbalanced Forces Action and Reaction Conservation of Momentum Impulse Net Force SI Unit of Force Free Body Diagram Applications of Newton's Laws Numericals
📋
Table of Contents
14 sections
🗺️ Overview
Force is one of the most fundamental concepts in Physics. Every movement around us, whether it is walking, writing, lifting a bag, kicking a football, opening a door, or launching a rocket, involves the application of force. In daily life, we constantly push, pull, lift, twist, stretch, or compress objects. All these actions are different ways of applying force.

In this chapter, we shall study what force is, how it changes the state of motion of an object, and how it is related to Newton's Laws of Motion.
📘 Definition of Force
🔎 Force Around Us
🔷 Characteristics of Force
🔷 Characteristics
  • Force is a vector quantity.
  • It possesses both magnitude and direction.
  • Force can increase or decrease the speed of an object.
  • Force can change the direction of motion.
  • Force may change the shape or size of an object.
  • Force can act only when there is interaction between two objects.
  • A single force may or may not produce motion depending upon the balanced or unbalanced nature of the forces.
📌 Interaction is Necessary for Force
📌 Note
Properties
Force is a Vector Quantity
Since force has both magnitude and direction, it is classified as a vector quantity.

Examples

  • 20 N towards East
  • 50 N vertically upward
  • 120 N downward
Writing only "20 N" is incomplete unless the direction is also specified whenever direction matters.
SI Unit of Force
Physical Quantity Unit
Force Newton (N)
Symbol N
CGS Unit Dyne
Dimension \([MLT^{-2}]\)
The SI unit of force is named after the famous English scientist Sir Isaac Newton for his extraordinary contribution to the study of mechanics.
📘 Definition
What is One Newton?
🔢 Formula
Formula of Force (Preview)
🌟 Why is Force Important?
🛠️ Applications of Force in Daily Life
Situation Role of Force
Walking Feet push the ground backward.
Playing Cricket Bat changes speed and direction of ball.
Applying Brakes Frictional force slows down the vehicle.
Lifting Objects Muscular force works against gravity.
Opening Bottle Cap Twisting force is applied.
🎨 SVG Diagram
Concept Diagram
Concept of Force Infographic A high-fidelity physical science infographic explaining the Concept of Force and its effects (motion and shape changes) in a deep sea blue design system. THE CONCEPT OF FORCE VECTOR QUANTITY (F = m · a) • PUSH OR PULL ACTING ON AN OBJECT FORCE (F) Push or Pull Interaction Changes Motion Alters State of Velocity Changes Shape Deforms Structural Matter Speed F v₁ v₂ Acceleration / Deceleration e.g., Pressing Accelerator Direction F v₁ v₂ Changes Trajectory Path e.g., Striking a Tennis Ball Elastic Change F Temporary Deformation e.g., Compressing a Spring Plastic Change F Permanent Deformation e.g., Crushing a Metal Can CONTACT: Friction, Tension, Applied SI UNIT: Newton (1 N = 1 kg·m/s²) NON-CONTACT: Gravity, Magnetic PHYSICS INFOGRAPHIC V2.0
✏️ Example
Solved Example
A football lying on the ground is kicked by a player. What changes are produced due to the applied force?
Force can change the state of rest, speed and direction of an object.
  1. 1
    Identify the initial state.
  2. 2
    Observe the effect after force.
  3. 3
    State the change.
Initially the football is at rest. When the player kicks it, muscular force acts on the ball and changes its state of rest into motion. Therefore, force makes the football move.
A clay ball becomes flat when pressed between the hands. Which effect of force is observed?

The applied force changes the shape of the clay. Hence, force can deform objects.
⚡ Exam Tip
❌ Common Mistakes
  • Writing force as a scalar quantity.
  • Confusing force with energy.
  • Forgetting that interaction between two bodies is necessary.
  • Ignoring the direction of force.
  • Writing the unit as "newton" without symbol N in numerical answers.
📋 CBSE Competency Based Question (HOTS)

Question

Two students push a stationary cupboard from opposite sides with equal force. The cupboard does not move. Does this mean no force is acting on it? Explain.

Answer

No. Force is acting from both sides, but the two forces are equal and opposite. Their resultant becomes zero, so the cupboard remains at rest. Such forces are called balanced forces.

⚡ Quick Revision
  • Force is a push or pull.
  • Force is a vector quantity.
  • Interaction between two objects is essential.
  • SI unit of force is Newton (N).
  • \(1N=1kg\,m\,s^{-2}\).
  • Force can change speed, direction, shape and state of motion.
  • Mathematical expression (to be derived later): \[F=ma\]
💥

Effects of Force

📋
Table of Contents
7 sections
🗺️ Overview
Force is responsible for producing various changes in an object. When a force acts on a body, it may or may not produce motion depending upon whether the forces acting on the body are balanced or unbalanced. In general, force changes the state of rest, state of motion, speed, direction, shape, or size of an object.

The effect produced by a force depends upon:
  • The magnitude of the applied force.
  • The direction in which the force is applied.
  • The duration for which the force acts.
  • The mass and physical properties of the object.
📌 Major Effects of Force
  • Force can move a stationary object.
  • Force can stop a moving object.
  • Force can increase or decrease the speed of an object.
  • Force can change the direction of motion.
  • Force can change the shape and size of an object.
  • Force can produce rotation in an object.
Force Moves a Stationary Object
Definition
When an object is at rest, an external unbalanced force can make it start moving.
Concept
According to Newton's First Law of Motion, an object at rest remains at rest unless acted upon by an unbalanced external force. Rest → External Force → Motion
Examples
  • Kicking a football lying on the ground.
  • Pushing a parked bicycle.
  • Moving a shopping trolley.
  • Pushing a chair across the classroom.
  • Starting a toy car by pushing it.
Force Stops a Moving Object
Definition
A force applied opposite to the direction of motion can reduce the speed of an object and eventually bring it to rest.
Concept
Stopping an object requires an unbalanced force acting opposite to its motion.
Examples
  • Applying brakes to a bicycle.
  • A goalkeeper stopping a football.
  • Catching a moving cricket ball.
  • Stopping a moving shopping cart.
  • Holding a swinging door.
Force Changes the Speed of an Object
Definition
Force can either increase or decrease the speed of a moving object.
Concept
If the applied force acts in the direction of motion, speed generally increases. If it acts opposite to the motion, speed decreases.
Direction of Force Effect on Speed
Same as motion Speed increases
Opposite to motion Speed decreases
Examples
  • Pushing a moving trolley increases its speed.
  • Applying brakes decreases speed.
  • A cyclist pedals harder to increase speed.
  • Air resistance slows down a parachutist.
Force Changes the Direction of Motion
Definition
A force acting sideways or at an angle can change the direction in which an object moves.
Concept
The speed may remain almost the same, but the path of motion changes due to the applied force.
Examples
  • A batsman hits a cricket ball.
  • A football rebounds after striking a goalpost.
  • A tennis player returns a serve.
  • A hockey stick changes the direction of the ball.
Important: Circular motion is possible because a force continuously changes the direction of velocity.
Force Changes the Shape or Size of an Object
Definition
Force may deform an object by stretching, compressing, bending or twisting it.
Examples
  • Stretching a rubber band.
  • Squeezing a sponge.
  • Compressing a spring.
  • Kneading dough.
  • Bending a plastic scale.
Soft materials change shape more easily than rigid materials.
Force Produces Rotation
When force is applied away from the axis of rotation, the object starts rotating instead of moving in a straight line.
Examples
  • Opening a door.
  • Turning a screwdriver.
  • Rotating a ceiling fan.
  • Turning a steering wheel.
  • Using a spanner to loosen a nut.
This rotational effect of force is called torque, which will be studied in higher classes.
🌟 Important Note
🔢 Formula
Formula Box
⚡ Exam Tip
❌ Common Mistakes
  • Writing that every force produces motion.
  • Ignoring balanced forces.
  • Confusing speed with velocity.
  • Thinking shape changes only in soft materials.
  • Forgetting that direction can change even when speed remains constant.
📋 CBSE Competency Based Question (HOTS)

Question

A cricketer catches a fast-moving ball and gradually moves his hands backward instead of stopping the ball suddenly. Which effects of force are involved?

Concept

Force stops the moving ball, but increasing the time of contact reduces the impact force (Impulse concept).

Answer

The applied force changes the state of motion of the ball by bringing it to rest. By moving the hands backward, the stopping time increases, reducing the impact force and preventing injury.
💥

Push

📋
Table of Contents
12 sections
🗺️ Overview
Push is one of the most common ways of applying force. In a push, the force is applied to move an object away from the source of the force. Whenever we push an object, our muscles exert a contact force on it. Depending on the magnitude and direction of the applied force, the object may start moving, stop, speed up, slow down, change its direction, or change its shape.
📘 Definition
💡 Concept
🔷 Characteristics
Characteristics of Push
🔷 Characteristics of Push
  • Push is a type of contact force.
  • It acts away from the source applying the force.
  • It can start the motion of a stationary object.
  • It can increase or decrease the speed of an object.
  • It can change the direction of motion.
  • It may change the shape or size of an object.
  • Its effect depends upon the magnitude and direction of the applied force.
✏️ Example
Examples of Push
  • Opening a door by pushing it.
  • Closing a door by pushing it.
  • Pushing a table across the floor.
  • Pushing a stalled car.
  • Pressing a doorbell switch.
  • Pushing a shopping trolley.
  • Pushing thumb pins into a notice board.
  • Pressing computer keyboard keys.
  • Kicking a football.
  • Walking, where our feet push the ground backward and the ground pushes us forward.
ℹ️ Science Behind Walking
Walking appears to be a forward motion, but the actual force applied by our feet is directed backward on the ground. According to Newton's Third Law of Motion, the ground exerts an equal and opposite force on our feet, which pushes us forward.
Walking is an excellent example of push and Newton's Third Law working together.
🛠️ Application
Applications of Push in Daily Life
Activity Purpose of Push
Pushing a trolley To transport goods.
Closing a gate To move the gate away.
Pressing toothpaste tube To squeeze toothpaste out.
Pushing elevator button To operate the switch.
Pushing furniture To change its position.
🎨 SVG Diagram
Concept Diagram
Push Force Vector Infographic A high-fidelity physical science infographic explaining the Applied Push Force and friction interaction in a deep sea blue design system. APPLIED PUSH FORCE FREE BODY DIAGRAM (FBD) • CONTACT INTERACTION AGAINST FRICTION CARGO-ID: 77A-P1 MASS: 120 kg SURFACE: STEEL F_applied (Push) F_friction F_normal F_gravity (W = m·g) Static Friction (F_s) • Resists the initial startup of motion of the object. • Increases dynamically to balance the applied force. • Max limit: F_s,max = μ_s · F_normal (threshold of slip) Kinetic Friction (F_k) • Opposes sliding motion once the object is moving. • Remains nearly constant regardless of push velocity. • Formula: F_k = μ_k · F_normal (typically F_k < F_s,max) NET FORCE: F_net = F_push - F_friction WORK: W = F_applied · d · cos(θ) SURFACE RELATION: μ_s > μ_k PHYSICS INFOGRAPHIC V2.0
✏️ Example
Solved Example
Ravi pushes a wooden box lying on the floor. Initially the box does not move, but after applying greater force it starts moving. Why?
An object begins to move only when the applied force becomes greater than the opposing frictional force.
  1. 1
    Identify the opposing force.
  2. 2
    Compare applied force with friction.
  3. 3
    State the condition for motion.
Initially, the push applied by Ravi is smaller than the frictional force, so the box remains at rest. When Ravi increases the applied force, it becomes greater than friction. The forces become unbalanced, and the box starts moving.
📌 Important Note
⚡ Exam Tip
❌ Common Mistakes
  • Writing that push always produces motion.
  • Ignoring friction while explaining push.
  • Confusing push with pull.
  • Writing walking as only a pull action.
📋 CBSE Competency Based Question (HOTS)

Question

Two students push a heavy cupboard from opposite sides with equal forces. The cupboard does not move. Explain why.

Answer

The two pushes are equal in magnitude and opposite in direction. Their resultant force becomes zero. Since the forces are balanced, the cupboard remains at rest despite both students applying force.

💥

Pull

📋
Table of Contents
13 sections
🗺️ Overview
Pull is another common way of applying force. In a pull, the force is applied to move an object towards the source of the force. Pulling is a type of contact force because the object must be in physical contact with the person or object applying the force. Pull plays an important role in our daily activities, from opening drawers and lifting buckets from wells to playing sports and operating machines.
📘 Definition
💡 Concept
🔷 Characteristics of Pull
🔷 Characteristics
  • Pull is a type of contact force.
  • It acts towards the source applying the force.
  • It can set a stationary object into motion.
  • It can stop or slow down a moving object.
  • It can change the direction of motion.
  • It may change the shape of soft or elastic objects.
  • The effect of pull depends upon the magnitude and direction of the applied force.
✏️ Examples of Pull
  • Plucking the string of a guitar.
  • Pulling a rope during a tug of war.
  • Opening a drawer.
  • Pulling a window curtain.
  • Opening a refrigerator door.
  • Drawing water from a well using a rope.
  • Pulling a suitcase with wheels.
  • Pulling a chair towards yourself.
  • Lifting a bucket with a rope.
  • Pulling the zipper of a school bag.
ℹ️ Information
In a tug of war, each team pulls the rope in opposite directions. The team that applies the greater unbalanced force wins because the rope and the opposing team move towards the stronger pulling force.>br>
Tug of war is one of the best real-life examples of balanced and unbalanced forces.

🛠️ Applications of Pull in Daily Life
Activity Purpose of Pull
Opening a drawer To bring the drawer towards you.
Pulling luggage To transport goods conveniently.
Drawing water from a well To lift the bucket upward.
Opening curtains To uncover the window.
Operating gym equipment To perform physical exercise.
🎨 SVG Diagram
Concept Diagram
Pull Force Vector Infographic A high-fidelity physical science infographic explaining the Tension Pull Force, vector components, and normal force reduction in a deep sea blue design system. APPLIED PULL FORCE ANGLED TENSION VECTOR • OVERCOMING FRICTION BY LIGHTENING NORMAL FORCE CARGO-ID: 99B-T2 MASS: 120 kg COEFF (μ_k): 0.35 T (Tension Force) T_x = T · cos(θ) T_y = T · sin(θ) θ F_friction F_normal F_gravity (W = m·g) Tensile Pull Force (T) • Transmitted continuously through a string, rope, or cable. • Directed strictly along the axis of the pulling medium. • Horizontal Component: T_x = T · cos(θ) (active slider) Angled Lift Benefit • Vertical component (T_y) acts upward, opposing gravity. • Lightens Normal Force: F_n = m·g - T·sin(θ) • Less Normal Force directly reduces friction resistance! MOTION CRITERIA: T · cos(θ) > F_friction REDUCED FRICTION: F_f = μ_k · (m·g - T·sinθ) PULL ADVANTAGE: F_pull < F_push
⚖️ Comparison
Difference Between Push and Pull
Push Pull
Moves an object away from the source. Moves an object towards the source.
Example: Pushing a trolley. Example: Pulling a suitcase.
Force acts forward. Force acts backward towards the source.
Both are contact forces. Both are contact forces.
✏️ Example
Solved Example
A student tries to pull a heavy desk towards himself, but it does not move. After another student helps him, the desk starts moving. Explain why.
Motion begins only when the applied force becomes greater than the opposing frictional force.
  1. 1
    Identify the opposing force.
  2. 2
    Compare it with the pulling force.
  3. 3
    Explain why the desk starts moving.
Initially, the pulling force is less than the frictional force acting between the desk and the floor. Therefore, the desk remains at rest. When another student helps, the total pulling force becomes greater than friction, producing an unbalanced force and causing the desk to move.
📌 Important Notes
⚡ Exam Tip
❌ Common Mistakes
  • Confusing pull with push.
  • Writing that pull always causes motion.
  • Ignoring the effect of friction.
  • Forgetting that pull is a contact force.
📋 CBSE Competency Based Question (HOTS)

Question

During a tug of war, both teams pull the rope with equal force, but the rope does not move. Explain the reason.

Answer

The forces applied by both teams are equal in magnitude and opposite in direction. The resultant force is zero, so the forces are balanced. Therefore, the rope remains stationary until one team applies a greater force than the other.

💥

Hit

📋
Table of Contents
13 sections
🗺️ Overview
A hit is a special type of contact force in which one object exerts a large force on another object for a very short interval of time. Although the duration of contact is extremely small, the force is often large enough to produce a significant change in the object's state of motion, speed, direction, momentum, or shape.

Many sports and everyday activities involve hitting objects, such as batting in cricket, hammering a nail, striking a billiard ball, or kicking a football. The concept of a hit forms the basis for understanding Impulse and Newton's Second Law of Motion, which are discussed later in this chapter.
📘 Definition
💡 Concept
🔷 Characteristics of Hit
🔷 Characteristics
  • It is a contact force.
  • The force acts for a very short duration.
  • The magnitude of force is generally very large.
  • It produces a sudden change in motion.
  • It is closely related to the concept of impulse.
  • It is common in sports, machines and construction work.
✏️ Examples of Hit
  • A cricket bat striking a moving ball.
  • A hammer driving a nail into wood.
  • A cue striking a billiard ball.
  • A tennis racket hitting a tennis ball.
  • A golfer hitting a golf ball.
  • A football being kicked by a player.
  • A boxer punching a punching bag.
  • A carpenter striking a chisel with a hammer.
🔗 Relation Between Hit and Impulse
A hit is one of the best examples of Impulse. During a collision, a large force acts for a very small interval of time. The product of force and time is called Impulse. \[ \boxed{Impulse = Force \times Time} \] \[ J = F \Delta t \] where,
  • \(J\) = Impulse
  • \(F\) = Applied force
  • \(\Delta t\) = Time for which the force acts
This relation will be derived in detail after studying Newton's Second Law of Motion.
🌟 Importance of Contact Time
🛠️ Applications in Daily Life
Situation Purpose
Hammer and Nail Drive the nail into wood.
Cricket Bat Change the speed and direction of the ball.
Golf Club Send the golf ball over a long distance.
Tennis Racket Return the ball to the opponent.
Boxing Gloves Increase contact time and reduce injury.
🎨 SVG Diagram
Concept Diagram
Force and Laws of Motion: Hit and Impulse A high-fidelity physical science infographic demonstrating the mechanics of a 'Hit' leading to Impulse and Momentum Change, using a bat-and-ball collision model in a deep sea blue design system. FORCE & LAWS OF MOTION: HIT & IMPULSE NCERT CLASS 9 SCIENCE • UNDERSTANDING IMPULSIVE FORCES & MOMENTUM CHANGE CRICKET PITCH SURFACE (REFERENCE) u = -25 m/s Initial Momentum p_i = m·u IMPACT: Δt = 0.005s F_avg (Hit Force) v = +35 m/s Final Momentum p_f = m·v Time (t) Force (F) F_max F_avg AREA = IMPULSE (J) J = F_avg · Δt = Δp Change in Momentum Contact Time Δt NCERT Class-9: Physics of a 'Hit' • Impulsive Force: Large force in a short duration. • Impact Time: Shorter duration yields larger force. • Application: Karate strikes maximize impact force. Impulse-Momentum Theorem • Impulse (J): Force applied over a duration (F · Δt). • Momentum Link: Impulse equals momentum change (Δp). • Catching: Pulling hands back reduces impact force. IMPULSE DEFINITION: J = F_avg · Δt MOMENTUM CHANGE: Δp = m·(v - u) NEWTON'S 2ND LAW: F_avg = Δp / Δt
✏️ Example
Solved Example
Why does a cricket ball change its direction immediately after being struck by a bat?
A large force acts on the ball for a very short time, changing its momentum.
  1. 1
    Identify the type of force.
  2. 2
    Recognize the short contact time.
  3. 3
    Explain the change in momentum.
When the bat strikes the cricket ball, it exerts a large force for a very short duration. This force changes the momentum of the ball, thereby changing its speed and direction. Hence, the ball moves in a new direction.
⚡ Exam Tip
❌ Common Mistakes
  • Writing that hit acts for a long duration.
  • Confusing hit with continuous push or pull.
  • Ignoring the concept of impulse.
  • Assuming every hit changes only speed and not direction.
📋 CBSE Competency Based Question (HOTS)

Question

A cricketer moves his hands backward while catching a fast-moving ball. Explain this action using the concept of hit and impulse.

Concept

Increasing the time of contact reduces the force of impact for the same change in momentum.

Answer

While catching the ball, the player's hands move backward, increasing the stopping time. Since impulse remains the same, increasing the contact time decreases the impact force. This reduces the chances of injury and makes catching easier.

⚡ Quick Revision
  • Hit is a contact force.
  • It acts for a very short duration.
  • The force is usually very large.
  • Hit changes momentum, speed or direction.
  • Hit is the most common example of impulse.
  • \[ J = F\Delta t \]
💥

Balanced and Unbalanced Forces

📋
Table of Contents
16 sections
🗺️ Overview
In our daily life, an object is often acted upon by more than one force simultaneously. These forces may act in the same direction or in opposite directions. The overall effect depends upon the resultant (net) force acting on the object.

If all the forces acting on an object cancel one another, they are called balanced forces. If they do not cancel one another, they are called unbalanced forces.

Resultant Force (Net Force) is the vector sum of all the forces acting on an object.
📘 Definition
Resultant (Net) Force
📘 Balanced Forces<
💡 Concept
🔷 Characteristics of Balanced Forces
🔷 Characteristics
  • Equal in magnitude.
  • Opposite in direction.
  • Resultant force is zero.
  • No acceleration is produced.
  • No change in the state of motion.
  • May change the shape of soft objects.
🎨 SVG Diagram
Balanced Force
Force and Laws of Motion: Balanced Forces A high-fidelity physical science infographic demonstrating the Concept of Balanced Force using a wooden block on a table pulled by equal and opposite forces, styled in a deep sea blue design system. FORCE & LAWS OF MOTION: BALANCED FORCES NCERT CLASS 9 SCIENCE • EQUAL & OPPOSITE FORCES RESULTING IN ZERO NET FORCE TABLE SURFACE (HORIZONTAL REFERENCE) WOODEN BLOCK Mass m = 5.0 kg STATE: AT REST Pull Force F_1 = 50 N Pull Force F_2 = 50 N Normal Force F_N = 49 N Gravity Force F_g = m·g = 49 N FREE BODY DIAGRAM (FBD) F_1 F_2 F_N F_g F_net = 0 N Static Equilibrium (a = 0) NCERT Class-9: Balanced Forces • Net Force: Sum of all forces is zero (F_net = 0). • State: Resting or moving state remains unchanged. • Acceleration: No acceleration occurs (a = 0). Equilibrium Conditions • Horizontal Balance: Left and right forces are equal. • Vertical Balance: Normal force equals gravity force. • Deformation: Can change shape, but cannot accelerate. NET FORCE: F_net = ΣF = 0 VELOCITY: v = constant (a = 0) EQUILIBRIUM: Balanced State NCERT MECHANICS DIAGRAM V1.0
✏️ Examples of Balanced Forces
  • A book resting on a table.
  • A person standing on the floor.
  • A picture hanging on a wall.
  • Two people pushing a wall with equal force from opposite sides.
  • Two teams pulling a rope with equal force during tug of war.
✏️ Example
Solved Example
Two students push a cupboard from opposite sides with forces of 80 N each. Will the cupboard move?
Equal and opposite forces produce zero resultant force.
\[ F_{net}=80N-80N=0N \] Since the resultant force is zero, the forces are balanced. Therefore, the cupboard does not move.
📘 Unbalanced Forces
💡 Concept
🔷 Characteristics of Unbalanced Forces
🔷 Characteristics
  • Resultant force is not zero.
  • Produces acceleration.
  • Changes the state of rest or motion.
  • May change speed or direction.
  • Responsible for almost all observable motions around us.
🎨 SVG Diagram
Unbalanced Forces
Force and Laws of Motion: Unbalanced Forces A high-fidelity physical science infographic demonstrating the Concept of Unbalanced Force using a wooden block on a table pulled by unequal and opposite forces, styled in a deep sea blue design system. FORCE & LAWS OF MOTION: UNBALANCED FORCES NCERT CLASS 9 SCIENCE • UNEQUAL FORCES RESULTING IN A NET ACCELERATING FORCE TABLE SURFACE (HORIZONTAL REFERENCE) WOODEN BLOCK Mass m = 5.0 kg STATE: MOVING RIGHT Pull F_1 = 30 N Pull F_2 = 80 N F_net = 50 N Normal Force F_N = 49 N Gravity Force F_g = 49 N FREE BODY DIAGRAM (FBD) F_1 F_2 F_N F_g F_net = 50 N F_net = 50 N (Right) Accelerating (a = 10 m/s²) NCERT Class-9: Unbalanced Forces • Net Force: Sum of forces is not zero (F_net ≠ 0). • State Change: Alters the resting state or velocity. • Acceleration: Causes direct acceleration (a ≠ 0). Non-Equilibrium Dynamics • Horizontal Asymmetry: Unequal left and right forces. • Direction: Motion follows the larger force vector. • Deformation: Can change shape, but cannot accelerate. NET FORCE: F_net = F_2 - F_1 ≠ 0 VELOCITY: v is changing (a ≠ 0) MOTION STATE: Acceleration NCERT MECHANICS DIAGRAM V1.0
✏️ Examples of Unbalanced Forces
  • Kicking a football.
  • A fruit falling from a tree.
  • A car accelerating.
  • Applying brakes to stop a vehicle.
  • A cyclist starting to pedal.
  • A moving cricket ball struck by a bat.
  • Pushing a trolley so that it starts moving.
✏️ Example
Solved Example
A person pushes a box with a force of 60 N while friction opposes the motion with a force of 20 N. Find the resultant force.
  1. 1
    Identify the forces.
  2. 2
    Subtract the opposing force.
  3. 3
    State the effect.
\[ F_{net}=60N-20N=40N \] Since the resultant force is 40 N, the forces are unbalanced. Hence, the box accelerates in the direction of the applied force.
⚖️ Difference Between Balanced and Unbalanced Forces
Balanced Forces Unbalanced Forces
Resultant force is zero. Resultant force is not zero.
No acceleration is produced. Acceleration is produced.
No change in state of motion. Changes the state of motion.
May change only the shape of an object. May change speed, direction and shape.
Example: Book resting on a table. Example: Kicking a football.
⚡ Exam Tip
❌ Common Mistakes
  • Thinking balanced forces mean that no force is acting.
  • Assuming every applied force causes motion.
  • Ignoring the concept of resultant force.
  • Confusing balanced forces with equal forces acting in the same direction.
  • Forgetting that balanced forces can deform soft objects.
📋 CBSE Competency Based Question (HOTS)

Question

During a tug of war, both teams initially pull the rope with equal force. Suddenly, one team starts pulling harder. Explain the motion of the rope using the concept of balanced and unbalanced forces.

Concept

Motion depends on the resultant (net) force acting on the object.

Answer

Initially, both teams apply equal and opposite forces, so the resultant force is zero. The forces are balanced, and the rope remains stationary. When one team pulls harder, the resultant force becomes non-zero. The forces become unbalanced, and the rope moves toward the team applying the greater force.

💥

Newton's First Law of Motion (Law of Inertia)

📋
Table of Contents
12 sections
🗺️ Overview
Newton's First Law of Motion was proposed by the English scientist Sir Isaac Newton in 1687. It explains why an object does not change its state of motion unless an external unbalanced force acts on it. This law introduced the concept of inertia and therefore is also known as the Law of Inertia.
📘 Statement of Newton's First Law
📌 Explanation
📘 External Unbalanced Force
💡 Mathematical Concept
📌 Understanding the Law
✏️ Real-Life Examples
  1. Passenger in a Bus
    When a stationary bus suddenly starts moving, passengers tend to fall backward because their bodies resist the change in motion.
  2. Sudden Braking
    When a moving bus stops suddenly, passengers move forward due to inertia of motion.
  3. Dusting a Carpet
    Dust particles fall because they tend to remain at rest while the carpet is suddenly moved.
  4. Coin and Card Experiment
    A coin placed on a card falls straight into the glass when the card is pulled quickly.
  5. Seat Belts in Cars
    Seat belts prevent passengers from moving forward when a car stops suddenly.
  6. Hockey Puck
    A hockey puck keeps sliding on smooth ice because friction is very small.
🌟 Important Points
🗒️ 
Force and Laws of Motion: Newton's First Law (Inertia) A high-fidelity physical science infographic demonstrating Newton's First Law of Motion (Inertia) using the glass, card, and coin experiment, styled in a deep sea blue design system. NEWTON'S FIRST LAW OF MOTION NCERT CLASS 9 SCIENCE • THE LAW OF INERTIA: OBJECTS RESIST CHANGES IN STATE EXPERIMENTAL STAND REFERENCE Card flies away Flick Force F_ext Coin falls vertically Inertia of Rest (keeps coin over glass) Mass & Inertia Relationship 100 kg F = 10 N HIGH MASS High Inertia (Resists motion) a ≈ 0 (Stationary) 2 kg F = 10 N LOW MASS Low Inertia (Easy to move) a >> 0 (Accelerates) Newton's First Law (Inertia) • Definition: Objects resist changes to their motion. • Inertia of Rest: Stationary objects remain at rest. • Inertia of Motion: Moving objects maintain speed. Inertia and Mass • Measure: Mass is the direct measure of inertia. • High Mass: Higher mass creates higher inertia. • Low Mass: Lower mass creates lower inertia. FIRST LAW: State remains constant NET FORCE: ΣF_ext = 0 ⇒ a = 0 INERTIA MEASURE: Inertia ∝ Mass NCERT MECHANICS DIAGRAM V1.0
✏️ Example
Solved Example
Why do passengers bend backward when a bus starts suddenly?
Inertia of rest.
  1. 1
    Inertia of rest.
  2. 2
    Apply Newton's First Law.
  3. 3
    Explain the observed motion.
Initially the passenger's body is at rest. When the bus starts suddenly, the lower part of the body moves with the bus while the upper part tends to remain at rest due to inertia. Hence, the passenger appears to fall backward.
Why does a hockey puck continue to slide on smooth ice?
Since friction on ice is very small, there is almost no external unbalanced force acting on the puck. Therefore, according to Newton's First Law, it continues moving with nearly uniform velocity.
⚡ Exam Tip
❌ Common Mistakes
  • Writing "force" instead of "external unbalanced force."
  • Ignoring the words "uniform motion in a straight line."
  • Confusing inertia with force.
  • Assuming balanced forces mean no forces are acting.
  • Writing that motion changes without an external force.
📋 CBSE Competency-Based Question (HOTS)

Question

A coin is placed on a card resting over the mouth of a glass. When the card is pulled quickly, the coin falls straight into the glass. Explain this observation using Newton's First Law of Motion.

Concept

Inertia of rest.

Answer

The coin tends to remain at rest due to inertia. When the card is pulled quickly, very little horizontal force acts on the coin. Gravity then causes the coin to fall vertically into the glass. This demonstrates Newton's First Law of Motion.

💥

Types of Inertia

📋
Table of Contents
6 sections
🗺️ Overview
Inertia is the natural property of every object by which it resists any change in its state of rest, state of uniform motion, or direction of motion. Depending on the type of change being resisted, inertia is classified into three types:
🗂️ Types of Inertia
Inertia of Rest
Definition
Inertia of Rest is the property of a body by virtue of which it resists any change in its state of rest. An object at rest continues to remain at rest unless acted upon by an external unbalanced force.
Concept
Every stationary object prefers to remain stationary. It does not begin to move by itself. Only an external unbalanced force can change its state of rest.

Object at Rest → Remains at Rest → External Unbalanced Force Required
Daily Life Examples
  • Passengers fall backward when a stationary bus starts suddenly.
  • A book placed on a table remains at rest until someone moves it.
  • Dust particles come out when a carpet is beaten.
  • A coin falls into a glass when the card beneath it is pulled quickly.
  • Fruit remains attached to the branch until an external force acts.
Inertia of Motion
Definition
Inertia of Motion is the property of a moving body by virtue of which it resists any change in its state of uniform motion.
Concept
A moving object continues moving with the same speed and in the same direction unless acted upon by an external unbalanced force.

Moving Object → Continues Moving → External Unbalanced Force Required to Stop or Change Motion
Daily Life Examples
  • Passengers move forward when a moving bus stops suddenly.
  • A hockey puck continues to slide on smooth ice.
  • A moving bicycle continues to move for some distance even after pedalling stops.
  • A rolling cricket ball continues moving until friction stops it.
  • A satellite keeps revolving around the Earth because of its inertia of motion.
Inertia of Direction
Definition
Inertia of Direction is the tendency of a body to resist any change in the direction of its motion.
Concept
A moving object prefers to continue moving in the same direction unless an external force changes its direction.
Examples
  • Passengers lean sideways when a car takes a sharp turn.
  • A stone tied to a string flies off tangentially when the string breaks.
  • A cyclist bends while taking a turn.
  • Water droplets fly outward when a wet umbrella is rotated.

Inertia of direction is responsible for passengers being pushed sideways when a vehicle turns.
⚖️ Comparison of the Three Types of Inertia
Type Resists Change In Example
Inertia of Rest State of Rest Passenger falls backward when bus starts.
Inertia of Motion State of Uniform Motion Passenger moves forward when bus stops.
Inertia of Direction Direction of Motion Passenger leans sideways while turning.
🎨 SVG Diagram
Types of Inertia
Force and Laws of Motion: Types of Inertia A high-fidelity physical science infographic demonstrating the three types of inertia (Inertia of Rest, Inertia of Motion, and Inertia of Direction) with experiments in a deep sea blue design system. FORCE & LAWS OF MOTION: TYPES OF INERTIA NCERT CLASS 9 SCIENCE • INERTIA OF REST, MOTION, & DIRECTION EXPLAINED 1. Inertia of Rest F (flick) Coin stays, falls in glass Resists horizontal movement 2. Inertia of Motion Frictionless Surface Block v = const. F_ext = 0 (no friction) Block slides indefinitely Resists slowing or stopping 3. Inertia of Direction pivot stone string snaps v (tangent) Stone flies off tangentially Resists change in direction NCERT Class-9: Types of Inertia • Rest: Object opposes the start of motion. • Motion: Object opposes change in uniform velocity. • Direction: Object opposes change in path direction. Real-World Examples • Rest: Dust on a shaken carpet falls off. • Motion: Passengers fall forward on sudden braking. • Direction: Mud flies off spinning cycle wheels. REST: Object resists start of motion MOTION: Object resists speed change DIRECTION: Tangential release path NCERT MECHANICS DIAGRAM V1.0
⚡ Exam Tip
❌ Common Mistakes
  • Writing only two types of inertia instead of three.
  • Confusing inertia with force.
  • Writing that heavier objects have less inertia.
  • Ignoring inertia of direction in descriptive answers.
📋 CBSE Competency-Based Question (HOTS)

Question

Explain why seat belts are compulsory in cars using Newton's First Law and inertia.

Answer

When a moving car stops suddenly, passengers tend to continue moving forward due to inertia of motion. Seat belts apply the necessary external force to stop the passenger along with the car, thereby preventing serious injuries.

💥

Momentum

📋
Table of Contents
10 sections
🗺️ Overview
To understand Newton's Second Law of Motion, we must first understand the concept of momentum. In everyday life, we observe that a fast-moving truck causes much more damage than a slowly moving bicycle. Similarly, a cricket ball moving at high speed is more difficult to stop than the same ball moving slowly. This happens because the impact produced by a moving object depends on both its mass and velocity. This combined effect is known as momentum.
📘 Definition of Momentum
💡 Concept of Momentum
📌 Factors Affecting Momentum
✏️ Examples of Momentum
  • A bullet fired from a gun has very high momentum because of its enormous velocity.
  • A fast-moving cricket ball has more momentum than a slowly moving cricket ball.
  • A loaded truck has greater momentum than a motorcycle moving at the same speed because its mass is much larger.
  • A baseball flying through the air possesses momentum.
  • A moving train has enormous momentum due to its large mass.
⚖️ Comparison of Momentum
Object Reason for Higher Momentum
Loaded Truck Very large mass.
Bullet Very high velocity.
Stationary Car Momentum is zero.
✏️ Example
Solved Example
Calculate the momentum of a body of mass \(5\,kg\) moving with a velocity of \(8\,m/s\).
  1. 1
    Write the given values.
  2. 2
    Apply \(p=mv\).
  3. 3
    Calculate the answer with SI unit.
Given,\[ m=5kg,\qquad v=8m/s \] Using,\[ p=mv \] \[ p=5\times8=40kg\,m/s \]
\(40\,kg\,m/s\)
A stationary football has a mass of \(0.5\,kg\). What is its momentum?
Since,\[ v=0 \] Therefore,\[ p=mv=0.5\times0=0 \] Hence, the momentum of the football is zero.
⚡ Exam Tip
❌ Common Mistakes
  • Writing momentum as a scalar quantity.
  • Using speed instead of velocity in the definition.
  • Writing incorrect SI unit.
  • Ignoring the direction of momentum.
  • Assuming a heavy stationary object has momentum.
📋 CBSE Competency-Based Question (HOTS)

Question

A truck and a motorcycle are moving with the same speed. Which one has greater momentum? Explain.

Concept

Momentum depends on both mass and velocity.

Answer

Since both vehicles have the same velocity, their momentum depends only on mass. The truck has a much larger mass than the motorcycle; therefore, it possesses greater momentum.

💥

Newton's Second Law of Motion

📋
Table of Contents
13 sections
🗺️ Overview
Newton's Second Law of Motion establishes a quantitative relationship between force, momentum, and acceleration. While the First Law tells us when the state of motion changes, the Second Law explains how much the motion changes when an external unbalanced force acts on an object.

This law forms the foundation of mechanics and is widely used in engineering, transportation, sports, robotics and space science.
📘 Statement of Newton's Second Law
📌 Explanation
🔗 Relations
Relation Between Force and Momentum
Momentum of an object is given by \[ p=mv \] Suppose an object of mass \(m\) changes its velocity from \(u\) to \(v\) in time \(t\).
Initial Momentum Final Momentum
\(p_1=mu\) \(p_2=mv\)
Therefore,\[ \Delta p=p_2-p_1 \] \[ \Delta p=mv-mu \] \[ \boxed{\Delta p=m(v-u)} \]
📐 Mathematical Derivation of \(F=ma\)
According to Newton's Second Law, \[ F\propto\frac{\Delta p}{\Delta t} \] Since,\[ \Delta p=m(v-u) \] Therefore,\[ F\propto\frac{m(v-u)}{t} \] As mass remains constant,\[ F\propto m\left(\frac{v-u}{t}\right) \] Since,\[ a=\frac{v-u}{t} \] Therefore,\[ F\propto ma \] Replacing proportionality by equality,\[ F=kma \] In the SI system,\[ k=1 \] Hence,\[ \boxed{F=ma} \]
📌 Meaning of the Equation \(F=ma\)
📘 Definition of One Newton
🛠️ Applications of Newton's Second Law
  • Designing automobiles and braking systems.
  • Launching rockets and satellites.
  • Playing cricket, football and tennis.
  • Construction machinery and cranes.
  • Calculating forces acting on bridges and buildings.
  • Airbags and seat belt safety systems.
🎨 SVG Diagram
Concept Diagram
Force and Laws of Motion: Newton's Second Law A high-fidelity physical science infographic demonstrating Newton's Second Law of Motion (F = ma) through the effect of force and mass on acceleration, styled in a deep sea blue design system. NEWTON'S SECOND LAW OF MOTION NCERT CLASS 9 SCIENCE • F = ma • FORCE, MASS & ACCELERATION RELATIONSHIP 1. Effect of Force — Small Force Applied — 5 kg F₁=10 N a₁ = 2 m/s² — Large Force Applied — 5 kg F₂=25 N a₂ = 5 m/s² a ∝ F (m = constant) Double force → double accel. 2. Newton's 2nd Law F = m × a F_net = Δp / Δt = m · a m 5 kg F a a ∝ F (m = const.) a ∝ 1/m (F = const.) F_net = m · a SI Unit: 1 N = 1 kg · m/s² 3. Effect of Mass — Small Mass (2 kg) — 2 kg F = 10 N a = 5 m/s² — Large Mass (10 kg) — 10 kg F = 10 N a = 1 m/s² a ∝ 1/m (F = constant) More mass → less accel. Newton's 2nd Law: F = ma • Rate of Momentum: F_net = Δp / Δt • Constant Mass: F_net = m × a • SI Unit: 1 N = 1 kg × 1 m/s² Proportionality Relations • Force ∝ Acceleration (m = constant) • Acceleration ∝ 1/Mass (F = constant) • Greater mass needs a greater force SECOND LAW: F_net = m × a MOMENTUM: p = m · v UNIT: 1 Newton = 1 kg·m/s² NCERT MECHANICS DIAGRAM V1.0
✏️ solved Example
A force of \(30\,N\) acts on a body of mass \(6\,kg\). Find its acceleration.
  1. 1
    Write the given values.
  2. 2
    Use \(F=ma\).
  3. 3
    Calculate acceleration.
Given, \[ F=30N,\qquad m=6kg \] Using, \[ F=ma \] \[ a=\frac{F}{m} \] \[ a=\frac{30}{6}=5m/s^2 \]
A body of mass \(4\,kg\) accelerates at \(3\,m/s^2\). Calculate the applied force.
\[ F=ma \] \[ F=4\times3=12N \] Answer: \(12\,N\)
⚡ Exam Tip
❌ Common Mistakes
  • Writing force proportional to velocity instead of momentum.
  • Skipping the proportionality constant \(k\) during derivation.
  • Confusing mass with weight.
  • Using speed instead of acceleration in \(F=ma\).
  • Writing incorrect SI unit of force.
📋 CBSE Competency-Based Question (HOTS)

Question

A loaded truck and an empty truck are pushed with the same force. Which truck will have greater acceleration? Explain using Newton's Second Law.

Concept

According to \(F=ma\), for the same force, acceleration is inversely proportional to mass.

Answer

The empty truck has smaller mass, so it experiences greater acceleration. The loaded truck has larger mass, therefore its acceleration is smaller even though the applied force is the same.

⚡ Quick Revision
  • Momentum: \(\boxed{p=mv}\)
  • Newton's Second Law: Force is the rate of change of momentum.
  • \(\boxed{F\propto\dfrac{\Delta p}{\Delta t}}\)
  • \(\boxed{F=ma}\)
  • \(\boxed{1N=1kg\,m\,s^{-2}}\)
  • Greater force produces greater acceleration.
💥

Law of Conservation of Momentum

📋
Table of Contents
13 sections
🗺️ Overview
The Law of Conservation of Momentum is one of the most important principles of mechanics. It states that when two or more bodies interact with one another, the total momentum of the system remains constant provided no external unbalanced force acts on the system.

This law is a direct consequence of Newton's Second Law and Newton's Third Law of Motion. It is widely used in the study of collisions, explosions, rocket propulsion, recoil of guns, and many engineering applications.
📘 Concept of a System
✏️ Example
Consider a moving car.
  • The car may be considered as the system.
  • The road, air, trees and everything outside the car form the environment.
  • Engine force acting inside the car is an internal force.
  • Air resistance and friction with the road are external forces.
📘 Isolated System
📘 Statement of the Law of Conservation of Momentum
📐 Derivation of the Law of Conservation of Momentum
Consider two bodies A and B of masses \(m_1\) and \(m_2\).

Initially, they move with velocities \(u_1\) and \(u_2\).

After collision, their velocities become \(v_1\) and \(v_2\).
Step 1: Apply Newton's Second Law
Force on body A, \[ F_{AB}=\frac{m_1(v_1-u_1)}{t} \] Force on body B, \[ F_{BA}=\frac{m_2(v_2-u_2)}{t} \]
Step 2: Apply Newton's Third Law
\[ F_{AB}=-F_{BA} \] Therefore, \[ \frac{m_1(v_1-u_1)}{t} = -\frac{m_2(v_2-u_2)}{t} \] Cancelling \(t\), \[ m_1(v_1-u_1) = -m_2(v_2-u_2) \] Rearranging, \[ \boxed{ m_1u_1+m_2u_2 = m_1v_1+m_2v_2 } \] Hence, the total momentum before collision equals the total momentum after collision.
🤔 Did You Know?
Why is Momentum Conserved?
During the interaction of two bodies, the force exerted by one body on the other is exactly equal and opposite to the force exerted by the second body on the first body.

According to Newton's Third Law,
\[ F_{AB}=-F_{BA} \] Therefore, one object loses exactly the same amount of momentum that the other object gains. As a result, the total momentum of the system remains unchanged.
🛠️ Applications of Conservation of Momentum
  • Collision between billiard balls.
  • Collision between vehicles.
  • Rocket propulsion.
  • Recoil of a gun.
  • Explosion of fireworks.
  • Jet aircraft propulsion.
  • Spacecraft manoeuvres.
✏️ Example
Real-Life Examples
Situation Application of Conservation of Momentum
Collision of two cricket balls Total momentum before and after collision remains constant.
Rocket launch Rocket moves upward while gases move downward.
Gun recoil Bullet moves forward and gun recoils backward.
Explosion Fragments move in different directions while conserving total momentum.
🎨 SVG Diagram
Conservation of Momentum
Force and Laws of Motion: Conservation of Momentum A high-fidelity physical science infographic demonstrating the Law of Conservation of Momentum, using a two-ball collision model (Before, During, and After collision states) in a premium deep sea blue design system conforming to NCERT Class-9 Chapter 8. CONSERVATION OF MOMENTUM NCERT CLASS 9 SCIENCE • CHAPTER 8: LAW & MATHEMATICAL DERIVATION EVENT SEQUENCE BEFORE COLLISION A mA uA uA > uB B mB uB DURING COLLISION A mA B mB FBA FAB FAB = -FBA AFTER COLLISION A mA vA vB > vA B mB vB Law of Conservation of Momentum • The total momentum of an isolated system remains constant. • Occurs provided there is no external unbalanced force acting. • The momentum lost by Object A is gained by Object B. Mathematical Derivation (Newton's 3rd Law) • Collision Forces: F_AB = -F_BA • Substitution: m_A(v_A - u_A) / t = -m_B(v_B - u_B) / t • Canceling time (t) & rearranging yields the conservation equation. mAuA + mBuB = mAvA + mBvB
✏️ Example
Solved Example
A ball of mass \(2\,kg\) moving with velocity \(5\,m/s\) collides with another ball of mass \(3\,kg\) at rest. After collision, the first ball moves with velocity \(2\,m/s\). Find the velocity of the second ball.
Total momentum before collision equals total momentum after collision.
  1. initial Momentum
    \[ (2)(5)+(3)(0)=10 \]
  2. Final momentum,
    \[ (2)(2)+(3)v=10 \]
  3. \[\begin{aligned} 4+3v&=10\\3v&=6\\v&=2\ \mathrm{m/s}\end{aligned} \]
⚡ Exam Tip
❌ Common Mistakes
  • Ignoring the condition of an isolated system.
  • Using speed instead of velocity in momentum calculations.
  • Applying conservation of momentum when external forces are significant.
  • Forgetting that momentum is a vector quantity.
📋 CBSE Competency-Based Question (HOTS)

Question

Explain why a gun recoils backward immediately after firing a bullet using the law of conservation of momentum.

Answer

Initially, both the gun and bullet are at rest, so the total momentum is zero. After firing, the bullet gains forward momentum. To keep the total momentum of the isolated gun-bullet system equal to zero, the gun acquires an equal amount of momentum in the opposite direction. Hence, the gun recoils backward.

💥

Newton's Third Law of Motion

📋
Table of Contents
11 sections
🗺️ Overview
Newton's Third Law of Motion explains how forces always occur in pairs. Whenever one object exerts a force on another object, the second object simultaneously exerts an equal force in the opposite direction on the first object. These two forces are known as the action-reaction pair.
Br> This law explains walking, swimming, rowing a boat, flying of birds, rocket propulsion, recoil of a gun and many other natural and technological phenomena.
📘 Statement of Newton's Third Law
📌 Action and Reaction Forces
🔷 Characteristics of Action and Reaction Forces
🔷 Characteristics
  • They are always equal in magnitude.
  • They act in opposite directions.
  • They act simultaneously.
  • They always act on two different bodies.
  • They never cancel each other because they act on different objects.
  • They may produce different accelerations because the masses of the bodies can be different.
✏️ Daily Life Examples
Action Reaction
Walking: Foot pushes the ground backward. Ground pushes the person forward.
Swimming: Swimmer pushes water backward. Water pushes the swimmer forward.
Bird flies by pushing air downward. Air pushes the bird upward.
Rocket throws gases downward. Gases push the rocket upward.
Gun pushes the bullet forward. Bullet pushes the gun backward (recoil).
Rowing a boat. Water pushes the boat forward.
🤔 Did You Know?
Why Can We Walk?
While walking, our feet push the ground backward. According to Newton's Third Law, the ground exerts an equal and opposite force on our feet. This reaction force pushes us forward, enabling us to walk.
📌 Rocket Propulsion
🎨 SVG Diagram
Newton's Third Law of Motion - Illustrations
NCERT SCIENCE · CLASS IX · CHAPTER 8 Newton's Third Law of Motion "To every action there is an equal and opposite reaction." — The forces act on two different objects simultaneously. Reaction Force Action Force ① Rocket Propulsion Action: Gases pushed backward Reaction: Rocket moves forward Hot gases are expelled backward (action). The rocket is propelled forward (reaction). ② Swimming (Swimmer Pushing Water) Action: Pushes water backward Reaction: Swimmer moves forward The swimmer pushes water backward (action). Water pushes the swimmer forward (reaction). Both forces are equal in magnitude and opposite in direction. ③ Gun and Bullet (Recoil) Action: Bullet fired forward Reaction: Gun recoils backward F_bullet = -F_gun | m x a_bullet = -M x A_gun The gun exerts force on bullet (action). Bullet exerts equal and opposite force on gun (recoil). ④ Walking on Ground G R O U N D Action: Foot pushes ground back Reaction: Ground pushes person forward Your foot pushes the ground backward (action). The ground pushes your foot forward (reaction). This enables us to walk! Without friction (ground reaction), walking would be impossible. F_AB = -F_BA Forces are equal in magnitude, opposite in direction, and act on different bodies.
✏️ Solved Example
Explain how a swimmer moves forward in water.
Newton's Third Law of Motion.
  1. 1
    Identify the action force.
  2. 2
    Identify the reaction force.
  3. 3
    Explain the resulting motion.
A swimmer pushes water backward with the hands and feet. According to Newton's Third Law, the water exerts an equal and opposite force on the swimmer, pushing the swimmer forward.
⚡ Exam Tip
❌ Common Mistakes
  • Writing that action and reaction act on the same object.
  • Stating that they cancel each other.
  • Ignoring that both forces occur simultaneously.
  • Confusing Newton's Third Law with conservation of momentum.
📋 CBSE Competency-Based Question (HOTS)

Question

Why does a gun recoil backward when a bullet is fired?

Answer

When the gun exerts a force on the bullet to move it forward, the bullet exerts an equal and opposite force on the gun. As a result, the gun moves backward. This backward motion is called recoil.

💥

Inertial and Non-Inertial Frames of Reference

📋
Table of Contents
8 sections
📌 Note
📘 Frame of Reference
📘 Inertial Frame of Reference
✏️ Example
  • A stationary classroom.
  • A train moving with constant velocity.
  • A spacecraft moving uniformly in deep space.
📘 Non-Inertial Frame of Reference
✏️ Example
  • An accelerating bus.
  • A braking car.
  • A rotating merry-go-round.
  • A lift moving with acceleration.
⚖️ Difference Between Inertial and Non-Inertial Frames
Inertial Frame Non-Inertial Frame
Newton's Laws are valid. Newton's Laws are not directly valid.
Acceleration is zero. Acceleration is non-zero.
Velocity remains constant. Velocity changes continuously.
No pseudo force is required. Pseudo force must be considered.
🎨 SVG Diagram
Illustration - Inertial/Non-Inertial frame of Reference
⚡ Exam Tip
💥

Example 1

📋
Table of Contents
9 sections
❓ Question
Calculate Linear Momentum
A body of mass \(5\,kg\) is moving with a velocity of \(2\,m/s\). Calculate its linear momentum.
💡 Concept
🗒️ Given
  • Mass of the body, \(\;m=5\,kg\)
  • Velocity of the body, \(\;v=2\,m/s\)
🔢 Formula
🗺️ Roadmap
  1. Write the given values.
  2. Use the formula \(p=mv\).
  3. Substitute the values.
  4. Write the answer with the correct SI unit.
🧩 Solution
  1. Given,
    \[ \begin{aligned} m&=5\,kg\\ v&=2\,m/s \end{aligned} \]
  2. Using the formula,
    \[ p=mv \]
  3. Substituting the given values,
    \[ \begin{aligned} p&=5\times2\\ &=10\,kg\,m/s \end{aligned} \]
✅ Answer
\[ \boxed{p=10\,kg\,m/s} \]
🔍 Interpretation
The body possesses a linear momentum of \(10\,kg\,m/s\) in the direction of its motion.
⚡ Exam Tip
💥

Example 2

📋
Table of Contents
7 sections
❓ Question
Force Acting on a Body Initially at Rest
A force of \(10\,N\) acts on a body of mass \(2\,kg\) for \(3\,s\). The body is initially at rest. Calculate:
  1. The velocity acquired by the body.
  2. The change in momentum of the body.
💡 Concept
🔢 Formula
Required formulae:
🗒️ Given
  • Force, \(\;F=10\,N\)
  • Mass, \(\;m=2\,kg\)
  • Time, \(\;t=3\,s\)
  • Initial velocity, \(\;u=0\,m/s\)
🗺️ Roadmap

  1. Calculate acceleration using \(F=ma\).

  2. Find the final velocity using the first equation of motion.

  3. Calculate the change in momentum using \(\Delta p=m(v-u)\).

🧩 Solution

(1) Velocity Acquired by the Body

  1. From Newton's Second Law,
    F=ma
  2. Since
    \[ a=\frac{v-u}{t} \]
  3. Therefore
    \[ \begin{aligned} F&=m\left(\frac{v-u}{t}\right)\\[4pt] 10&=2\left(\frac{v-0}{3}\right)\\[4pt] 10&=\frac{2v}{3}\\[4pt] 30&=2v\\[4pt] v&=15\,m/s \end{aligned} \]
  4. Velocity acquired by the body:
    \[ \boxed{v=15\,m/s} \]

(2) Change in Momentum of the Body

  1. Momentum is given by,
    \[ p=mv \]
  2. Therefore, the change in momentum is
    \[ \Delta p=m(v-u) \]
  3. Substituting the given values,
    \[ \begin{aligned} \Delta p &=2(15-0)\\[4pt] &=30\,kg\,m/s \end{aligned} \]
  4. Change in momentum:
    \[ \boxed{\Delta p=30\,kg\,m/s} \]
⚡ Exam Tip
💥

Example 3

📋
Table of Contents
10 sections
❓ Question
Force from a Velocity-Time Graph
The velocity-time graph of a particle of mass 100 g moving in a straight line is shown in the figure. Calculate the force acting on the particle.
0 5 20 (5, 20) v t
💡 Concept
Concept Used
🔢 Formula
Formulae Used
🗒️ Given
  • Mass of the particle, \[ m=100\,g=0.1\,kg \]
  • Initial velocity, \[ u=0\,m/s \]
  • Final velocity, \[ v=20\,m/s \]
  • Time taken, \[ t=5\,s \]
🗺️ Roadmap
  1. Convert mass into SI unit (kg).
  2. Calculate acceleration using the slope of the velocity-time graph.

  3. Apply Newton's Second Law, \[ F=ma \]

  4. Write the answer with the correct SI unit.
🧩 Solution
Part (i)
Convert the mass into SI unit
  1. \[ \begin{aligned} 100\,g &=\frac{100}{1000}\,kg\\ &=0.1\,kg \end{aligned} \]
Part (ii)
Calculate acceleration from the graph
  1. Since the graph starts from the origin,
    \[ u=0\,m/s \]
  2. Therefore,
    \[ \begin{aligned} a &=\frac{v-u}{t}\\[4pt] &=\frac{20-0}{5}\\[4pt] &=4\,m/s^2 \end{aligned} \]
Part (iii)
Calculate the force
  1. Using Newton's Second Law,
    \[ \begin{aligned} F &=ma\\[4pt] &=0.1\times4\\[4pt] &=0.4\,N \end{aligned} \]
✅ Answer
\[ \boxed{F=0.4\,N} \]
👁️ Important Observation
⚡ Exam Tip
❌ Common Mistakes
  • Using mass as \(100\,kg\) instead of \(0.1\,kg\).
  • Calculating acceleration as \(\frac{t}{v}\) instead of \(\frac{v-u}{t}\).
  • Forgetting that the initial velocity is zero.
  • Writing the answer without the SI unit.
💥

Example 4

📋
Table of Contents
9 sections
❓ Question
Force Applied by the Brakes
A car of mass \(480\,kg\) moving with a speed of \(54\,km/h\) is brought to rest by applying the brakes in \(10\,s\). Calculate the force applied by the brakes.
💡 Concept
Concept Used
🔢 Formula
Formula used
🗺️ Roadmap
  1. Convert the speed from km/h to m/s.
  2. Calculate the acceleration.
  3. Apply Newton's Second Law.
  4. Interpret the negative sign correctly.
🧩 Solution
Given:
  • Mass of the car, \[ m=480\,kg \]
  • Initial speed, \[ u=54\,km/h \]
  • Final speed, \[ v=0\,m/s \]
  • Time taken to stop, \[ t=10\,s \]
Convert the speed into SI unit
  1. Convert the speed into SI unit
    \[ \begin{aligned} u &=54\,km/h\\[4pt] &=54\times\frac{1000}{3600}\\[4pt] &=15\,m/s \end{aligned} \]
Calculate the acceleration
  1. Since the car comes to rest,
    \[ v=0\,m/s \]
  2. Therefore,
    \[ \begin{aligned} a &=\frac{v-u}{t}\\[4pt] &=\frac{0-15}{10}\\[4pt] &=-1.5\,m/s^2 \end{aligned} \]
The negative sign indicates that the car is decelerating (retarding).
Calculate the braking force
  1. Using Newton's Second Law,
    \[ \begin{aligned} F &=ma\\[4pt] &=480\times(-1.5)\\[4pt] &=-720\,N \end{aligned} \]
✅ Answer
\[ \boxed{F=-720\,N} \]
🔍 Interpretation
  • The magnitude of the braking force is \(720\,N\).
  • The negative sign indicates that the force acts opposite to the direction of motion.
  • In board examinations, if the question asks only for the magnitude of the force, the answer may be written as \(720\,N\).
⚡ Exam Tip
❌ Common Mistakes
  • Using \(54\,km/h\) directly instead of converting it to \(15\,m/s\).
  • Ignoring the negative sign of acceleration.
  • Writing \(F=720\,N\) without mentioning that the force acts opposite to the motion.
  • Using \(a=\frac{u-v}{t}\) without considering the sign convention.
💥

Exercise 5

📋
Table of Contents
7 sections
❓ Question
Bullet Striking a Wooden Block
A bullet of mass \(50\,g\) moving with an initial velocity of \(100\,m/s\) strikes a wooden block and comes to rest after penetrating a distance of \(2\,cm\) into it. Calculate:
  1. Initial momentum of the bullet.
  2. Final momentum of the bullet.
  3. Retardation caused by the wooden block.
  4. Resistive force exerted by the wooden block.
💡 Concept
Concept Used
🔢 Formula
Formula Used
🧩 Solution
Given:
  • Mass of the bullet, \[ m=50\,g=0.05\,kg \]
  • Initial velocity, \[ u=100\,m/s \]
  • Final velocity, \[ v=0\,m/s \]
  • Distance travelled inside the block, \[ s=2\,cm=0.02\,m \]
Part (a)
(a) Initial Momentum of the Bullet
  1. Initial Momentum of the Bullet
    \[ \begin{aligned} p_i &=mu\\[4pt] &=0.05\times100\\[4pt] &=5\,kg\,m/s \end{aligned} \]
  2. Answer
    \[\boxed{p_i=5\,kg\,m/s}\]
Part (b)
(b) Final Momentum of the Bullet
  1. Since the bullet comes to rest,
    \[v=0\]
  2. Therefore,
    \[ \begin{aligned} p_f &=mv\\[4pt] &=0.05\times0\\[4pt] &=0 \end{aligned} \]
  3. Answer
    \[\boxed{p_f=0}\]
Part (c)
(c) Retardation Caused by the Wooden Block
  1. Using the third equation of motion,
    \[v^2-u^2=2as\]
  2. Substituting the values,
    \[ \begin{aligned} 0^2-100^2 &=2\times a\times0.02\\[4pt] -10000 &=0.04a\\[4pt] a &=\frac{-10000}{0.04}\\[4pt] a &=-2.5\times10^5\,m/s^2 \end{aligned} \]
  3. Answer
    \boxed{a=-2.5\times10^5\,m/s^2}The negative sign indicates that the bullet is decelerating (retarding).
Part (d)
(d) Resistive Force Exerted by the Wooden Block
  1. Using Newton's Second Law,
    \[F=ma\]
  2. \[ \begin{aligned} F &=0.05\times(-2.5\times10^5)\\[4pt] &=-1.25\times10^4\,N \end{aligned} \]
  3. Answer
    Resistive Force: \[ \boxed{F=-1.25\times10^4\,N} \]
🔍 Interpretation
  • The magnitude of the resistive force is \(1.25\times10^4\,N\).
  • The negative sign indicates that the force acts opposite to the direction of motion of the bullet.
⚡ Exam Tip
❌ Common Mistakes
  • Using \(50\,g\) directly instead of \(0.05\,kg\).
  • Using \(2\,cm\) instead of \(0.02\,m\).
  • Ignoring the negative sign of retardation.
  • Using \(v=u+at\) even though time is not given.
  • Writing only the magnitude of force without explaining its direction.
💥

Chapter Summary: Points to Remember

📋
Table of Contents
3 sections
🗒️ Summary
The following points summarize the important concepts of Force and Laws of Motion. These points are highly useful for CBSE Board Examinations, school tests, competitive examinations and quick revision before the exam.
  • Force is a push or pull that changes or tends to change the state of rest, state of motion, direction of motion or shape of an object.
  • Force is a vector quantity; therefore, it has both magnitude and direction.
  • The SI unit of force is newton (N).
  • Balanced forces have zero resultant force and cannot change the state of motion of an object, although they may change its shape.
  • Unbalanced forces produce acceleration and change the state of motion of an object.
  • Newton's First Law of Motion states that an object continues to remain at rest or move with uniform velocity in a straight line unless acted upon by an external unbalanced force.
  • Newton's First Law is also known as the Law of Inertia.
  • Inertia is the natural tendency of an object to resist any change in its state of rest, state of motion or direction of motion.
  • The three types of inertia are: Inertia of Rest, Inertia of Motion and Inertia of Direction.
  • Mass is the measure of inertia. Greater the mass of an object, greater is its inertia.
  • The SI unit of mass is kilogram (kg).
  • Friction always acts in a direction opposite to the direction of relative motion.
  • Momentum is defined as the product of mass and velocity.
  • \[ p=mv \]
  • Momentum is a vector quantity, and its direction is always the same as the direction of velocity.
  • The SI unit of momentum is \(kg\,m\,s^{-1}\).
  • The dimensions of momentum are \([MLT^{-1}]\).
  • Newton's Second Law of Motion states that the rate of change of momentum of an object is directly proportional to the applied external unbalanced force and takes place in the direction of the applied force.
  • \[ F=\frac{\Delta p}{\Delta t} \]
  • For an object of constant mass,
  • \[ F=ma \]
  • One newton is the force required to produce an acceleration of \(1\,m/s^2\) in a body of mass \(1\,kg\).
  • \[ 1N=1kg\,m\,s^{-2} \]
  • Impulse is the product of force and the time for which it acts.
  • \[ \text{Impulse}=F\times t=\Delta p \]
  • The impulse acting on a body is equal to the change in its momentum.
  • The Law of Conservation of Momentum states that the total momentum of an isolated system remains constant provided no external unbalanced force acts on the system.
  • \[ m_1u_1+m_2u_2=m_1v_1+m_2v_2 \]
  • Newton's Third Law of Motion states that for every action there is an equal and opposite reaction.
  • Action and reaction forces:
    • Are equal in magnitude.
    • Act in opposite directions.
    • Act simultaneously.
    • Act on different bodies.
    • Do not cancel each other.
  • \[ F_{AB}=-F_{BA} \]
  • Walking, swimming, rowing, rocket propulsion, recoil of a gun and flying of birds are applications of Newton's Third Law.
  • An inertial frame of reference is a frame in which Newton's Laws of Motion are valid.
  • A non-inertial frame of reference is an accelerating frame in which pseudo forces must be considered for applying Newton's Laws.
⚡ Quick Revision
Concept Formula
Momentum \(\displaystyle p=mv\)
Newton's Second Law \(\displaystyle F=\frac{\Delta p}{\Delta t}\)
Force \(\displaystyle F=ma\)
Acceleration \(\displaystyle a=\frac{v-u}{t}\)
Impulse \(\displaystyle Ft=\Delta p\)
Conservation of Momentum \(\displaystyle m_1u_1+m_2u_2=m_1v_1+m_2v_2\)
Third Equation of Motion \(\displaystyle v^2-u^2=2as\)
⚡ Exam Tip
Last-Minute Board Revision Tips
· Updated

NCERT · Class IX · Science · Chapter 8

Force and Laws of Motion

Inertia, momentum, and Newton's three laws — explained, solved, and practised through a fully interactive engine.

3 CORE CONCEPTS AI-STYLE SOLVER 5 INTERACTIVE MODULES

What this chapter is really about

Chapter 7 told you how to describe motion — distance, speed, velocity, acceleration. Chapter 8 asks the deeper question: why does motion change at all? The answer, built up by Galileo and completed by Newton, is force.

Every idea in this chapter — a book staying still on a table, a bus jerking you forward when it brakes, a rocket lifting off in empty space — is a consequence of just three laws. Once you see the pattern, the "tricky" NCERT questions stop being tricky.

The three concepts in this engine

  1. Force, Inertia & Newton's First Law — why a moving object "wants" to keep moving and a resting object "wants" to keep resting, unless something pushes or pulls it.
  2. Newton's Second Law — the exact relationship between force, mass and acceleration: F = ma, derived from the rate of change of momentum.
  3. Newton's Third Law & Conservation of Momentum — why every force comes in a pair, and why the total momentum of an isolated system never changes.

How to use this engine

  • Read the three concept tabs in order — each builds on the last.
  • Use the AI Solver whenever a numerical doesn't make sense; it shows every step.
  • Keep the Formulas tab open as a quick-reference while solving.
  • Attempt Practice questions before reading their solutions.
  • Finish with the Interactive tab to lock in recall under quiz pressure.
01

Force and Inertia — Newton's First Law of Motion

The "law of laziness" that every object obeys

What is force?

A force is a push or a pull that can change, or try to change, the state of rest or motion of an object, its direction, or its shape. Force itself is invisible — we only recognise it by its effects:

  • Moving a stationary object (kicking a ball at rest).
  • Stopping or slowing a moving object (catching a thrown ball).
  • Changing the direction of motion (a fielder redirecting a ball).
  • Changing the shape or size of an object (squeezing a rubber ball, stretching a spring).

Balanced vs. unbalanced forces

When several forces act on an object, what matters is their net (resultant) effect. If the forces cancel out, they are balanced and the object's state of motion does not change. If they don't cancel out, they are unbalanced, and the object accelerates — it speeds up, slows down, or changes direction.

BLOCK F1 = 10N F2 = 10N Balanced → no change in motion

Equal and opposite forces → resultant force = 0 → balanced

Inertia — the reluctance to change

Inertia is the natural tendency of an object to resist any change in its state of rest or uniform motion. An object will not change its speed or direction on its own — only an external unbalanced force can do that.

Newton's First Law (Law of Inertia): an object stays at rest, or moves with constant velocity in a straight line, unless acted upon by a net external (unbalanced) force.
passenger jerks forward bus brakes

Bus stops suddenly — passenger's body keeps moving forward (inertia of motion)

Mass is the measure of inertia

A heavier (more massive) object has more inertia — it resists changes in motion more strongly. That is why pushing an empty cart is far easier than pushing a fully loaded one with the same force: the loaded cart has more mass, hence more inertia, hence less acceleration for the same force.

Two flavours of inertia

  • Inertia of rest: a stationary object resists being set in motion (a coin on a card flicked off the card stays behind, then falls into the glass).
  • Inertia of motion: a moving object resists being stopped (a person standing in a moving bus falls forward when the bus suddenly stops).
💡
Tip — spot the keyword "sudden"

Whenever a question says a vehicle "suddenly starts" or "suddenly stops", it is testing inertia, not the second law. Ask yourself: what was the body already doing, and what does it resist changing?

💡
Tip — "unbalanced" is the real trigger word

Forces can be balanced and still be large. It is the resultant (net) force that decides whether motion changes — never judge by the size of a single force alone.

⚠
Common mistake — "force is needed to keep something moving"

This is the pre-Newtonian (Aristotelian) error. In reality, a moving object with zero net force keeps moving forever at constant velocity. Force is needed only to change velocity, not to sustain it. Friction confuses students because it constantly opposes motion in daily life.

⚠
Common mistake — confusing mass with inertia as separate quantities

Mass is the numerical measure of inertia — they are not two different properties to compare; mass quantifies inertia.

02

Newton's Second Law of Motion

Putting a number on "how much" a force changes motion

Momentum — motion's "quantity"

The momentum of a moving object is the product of its mass and velocity. It captures both "how much stuff" is moving and "how fast" — a slow truck and a fast cricket ball can carry comparable momentum.

p = m × v p = momentum (kg·m/s), m = mass (kg), v = velocity (m/s)

Momentum is a vector — it has the same direction as velocity. A force changes an object's velocity, and therefore changes its momentum.

From momentum to F = ma

Newton's Second Law states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force, and takes place in the direction of that force.

F ∝ (mv − mu) / t

For a constant mass m, this becomes F ∝ m(v−u)/t = ma, since acceleration a = (v−u)/t. Choosing units so the constant of proportionality is exactly 1 gives the form you use in every numerical:

F = m × a 1 newton = the force that produces 1 m/s² acceleration in a 1 kg mass
m=2kg F = 10N a = F/m = 5 m/s² Bigger F or smaller m ⇒ bigger acceleration

a is directly proportional to F, inversely proportional to m

Everyday demonstrations

  • Catching a fast cricket ball: a fielder draws their hands backward, increasing the time t over which momentum changes to zero — this reduces the force on their palm (since F = Δp/t, larger t means smaller F).
  • Cushions, sand pits, crumple zones: all work by stretching out the stopping time, which lowers the force experienced.
  • Karate chop / hammer strike: here the goal is the opposite — momentum is changed in the smallest possible time, producing a very large force.
💡
Tip — always check units before substituting

F = ma only gives the force in newtons when m is in kilograms and a is in m/s². Convert grams to kilograms (÷1000) and km/h to m/s (×5/18) before you touch the formula.

💡
Tip — "time taken to stop" questions are momentum-change questions

Whenever a question gives an initial and final velocity and a time, compute F = m(v−u)/t directly — there is no need to separately find acceleration first, although you can.

⚠
Common mistake — forgetting the sign of deceleration

When an object slows down, v < u, so (v−u) is negative, and so is the force — meaning the force acts opposite to the direction of motion. Students often report the magnitude but drop the directional meaning needed in reasoning-based questions.

⚠
Common mistake — treating momentum and force as the same thing

Momentum (p = mv) describes a state of motion; force is what changes that state. Confusing the two leads to wrong formula choices in mixed numericals.

03

Newton's Third Law & Conservation of Momentum

Every action has an equal, opposite reaction — and momentum keeps the books balanced

Newton's Third Law

For every action there is an equal and opposite reaction, and the two forces act on two different objects, simultaneously. Action-reaction pairs never cancel each other for the system as a whole, because they act on different bodies — they only feel "balanced" if you wrongly apply both to one object.

BOAT YOU reaction action (push)

You push the boat backward (action) — the boat pushes you forward (reaction), so you can step off

Classic action-reaction examples

  • Walking: your foot pushes the ground backward; the ground pushes you forward.
  • Rocket propulsion: burnt gases are expelled downward at high speed; the rocket is pushed upward — works even in the vacuum of space, since no air is needed.
  • Gun recoil: the gun pushes the bullet forward; the bullet pushes the gun (and shoulder) backward.
  • Jumping off a boat: shown in the diagram above.

Conservation of momentum

The Third Law leads directly to one of the most powerful tools in mechanics. For two objects colliding and not acted on by any external force, the law of conservation of momentum says:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ total momentum before collision = total momentum after collision (isolated system)

Why it's true — a one-line derivation

During collision, object 1 exerts a force F on object 2 for time t; by the Third Law, object 2 exerts −F on object 1 for the same t. The momentum object 2 gains exactly equals the momentum object 1 loses, so the total is unchanged.

F₁₂ = −F₂₁  →  m₁(v₁−u₁)/t = −m₂(v₂−u₂)/t  →  m₁u₁+m₂u₂ = m₁v₁+m₂v₂
💡
Tip — pick one direction as positive and stick to it

In every collision/recoil problem, fix a positive direction first. Velocities opposite to it must be substituted as negative numbers — this single habit prevents most sign errors.

💡
Tip — "objects move together after collision" means v₁ = v₂

In a perfectly inelastic collision the two final velocities are equal — use a single unknown v and solve m₁u₁+m₂u₂ = (m₁+m₂)v.

⚠
Common mistake — applying conservation of momentum to a non-isolated system

If an external force (like friction from the ground, or a wall) acts during the event, total momentum of just the two objects need not be conserved. Always check the question says the surface is frictionless or the system is isolated.

⚠
Common mistake — thinking action and reaction act on the same body

This is the single most common conceptual slip. Action and reaction always act on two different objects — that is precisely why they never produce equilibrium for a single body and never cancel out for the system.

Step-by-step AI Solver

Choose a problem type, enter the known values, and the solver will reason through it exactly the way you should write it in your exam — formula, substitution, and final answer.

Quick formula reference

Momentum

p = m × v

Unit: kg·m/s. Vector — direction same as velocity.

Newton's Second Law

F = m × a

Unit of force: newton (N) = kg·m/s².

Force from momentum change

F = m(v−u) / t

Same as F = Δp / t — rate of change of momentum.

Acceleration (from Ch. 7)

a = (v − u) / t

Needed to connect kinematics to force questions.

Conservation of momentum

m₁u₁+m₂u₂ = m₁v₁+m₂v₂

Valid only for an isolated system (no external force).

Perfectly inelastic collision

m₁u₁+m₂u₂ = (m₁+m₂)v

Use when both objects move together after collision.

Recoil (gun & bullet)

m₁v₁ = −m₂v₂

System starts at rest; total momentum stays zero.

Unit conversions

km/h × 5/18 = m/s

1 g = 0.001 kg  |  1 N = 1 kg·m/s²

Concept-building practice (with full solutions)

Try to solve each problem yourself first — then tap a question to reveal the worked solution.

Concept 1 · Force & Inertia

Concept 2 · Newton's Second Law

Concept 3 · Third Law & Conservation of Momentum

MCQ Quiz

Score: 0 / 0

Flashcards

Tap the card to flip it

Matching Game — term to meaning

Tap a term, then tap its matching definition.

Fill in the Blanks

Momentum Collision Simulator

Set the mass and initial velocity of two objects, choose a collision type, and watch conservation of momentum play out.

Object 1
Object 2
m1 m2

ACADEMIA AETERNUM · NCERT CLASS IX SCIENCE · CHAPTER 8 — FORCE AND LAWS OF MOTION

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ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
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Force And Laws Of Motion | Science Class 9 | Academia Aeternum
Force And Laws Of Motion | Science Class 9 | Academia Aeternum — Complete Notes & Solutions · academia-aeternum.com
The chapter “Force and Laws of Motion” in Class 9 Physics is one of the most important topics of the NCERT Science curriculum. It explains how objects move, stop, or change direction when forces act on them. This chapter introduces the fundamental concepts of force, inertia, momentum, and Newton’s three laws of motion, which are the foundation of mechanics in physics. Students will learn about: Balanced and Unbalanced Forces – when forces cancel out or produce motion. Newton’s First…
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    ✔️ True / False
    📌 Exercise
    📝 Exercises
    Motion-Exercise

    Frequently Asked Questions

    Force is a push or pull on an object that can change its state of motion or shape.

    Balanced forces are equal in magnitude and opposite in direction, producing no change in motion.

    Unbalanced forces cause a change in the state of motion or shape of an object.

    Sir Isaac Newton formulated the three laws of motion.

    An object remains at rest or in uniform motion unless acted upon by an unbalanced external force.

    Inertia is the tendency of an object to resist any change in its state of motion or rest.

    The rate of change of momentum is directly proportional to the applied force and occurs in its direction.

    For every action, there is an equal and opposite reaction.

    Momentum is the product of an object’s mass and velocity, given byp=m×vp = m \times vp=m×v.

    The SI unit of force is the newton (N).

    Zero, as velocity is zero.

    Sand increases the time of impact, reducing the effect of the force on landing.

    Force equals the rate of change of momentum (F=?p?tF = \frac{?p}{?t}F=?t?p).

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