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Force and Laws of Motion

From auto-rickshaws lurching at traffic lights to rocket launches by ISRO, Newton's three laws of motion explain why things start, stop, and keep moving. This chapter covers force, inertia, momentum, and conservation of momentum.

ForceInertiaMomentumNewton's LawsConservation

Complete Chapter Roadmap — 10 Topics

01What is Force?02Balanced and Unbalanced Forces 03Newton's First Law and Inertia 04Types of Inertia 05Momentum 06Newton's Second Law 07Newton's Third Law 08Conservation of Momentum 09Applications of Momentum 10Chapter Summary

What is Force?

A push or pull that can change state of motion

Key Idea

Force can produce five effects: start motion, stop motion, increase speed, decrease speed, change direction, or change shape. A single force can produce one or more of these effects.

A force is a push or pull that acts on a body from outside. Force can start motion, stop motion, increase speed, decrease speed, change direction, or change the shape of an object.

When you kick a football in a local park or maidan, the ball starts moving because of the force your foot applied. When a goalkeeper stops the ball, a force again brings it to rest.

Force is a vector quantity — it has both magnitude and direction. The SI unit of force is the newton (N).

Balanced and Unbalanced Forces

Net force determines whether motion changes

When two or more forces act on a body and their net effect is zero, they are called balanced forces. Balanced forces do not change the state of rest or motion.

In a tug-of-war between two equally strong teams pulling a rope on a school sports day, the rope does not move because the forces on both sides cancel each other out.

Unbalanced forces have a net effect that is not zero. They cause a change in the state of motion. When one team is stronger in the tug-of-war, an unbalanced force acts on the rope and it moves toward the stronger team.

Quick Check

A book lies on a table. The table pushes up on the book and gravity pulls it down. Are these balanced?

Answer: Yes. The two forces are equal and opposite, so they are balanced and the book stays at rest.

Newton's First Law and Inertia

A body resists any change in its state of motion

Definition

Inertia is the tendency of a body to resist any change in its state of rest or of uniform motion in a straight line. A heavier object has greater inertia.

Newton's first law states that a body remains at rest or continues in uniform straight-line motion unless an unbalanced external force acts on it. This is also called the law of inertia.

You experience this law every day in Indian cities. When a DTC bus or an auto-rickshaw starts suddenly, passengers tend to fall backward — their upper bodies were at rest and resist the forward motion. When the same vehicle brakes suddenly, passengers lurch forward because their bodies resist the sudden stop.

Inertia is the natural resistance of a body to any change in its state. Mass is the measure of inertia. A loaded goods vehicle on a Delhi highway is harder to stop than an empty scooter because the truck has far more inertia.

Classic Demonstration

Coin on a card

Place a card on a glass and a coin on top of the card. Flick the card away sharply. The coin does not fly away — instead it falls into the glass because its inertia kept it at rest while the card moved away from under it.

Types of Inertia

Inertia of rest, motion, and direction

Exam Pointer

CBSE board questions often ask you to identify the type of inertia in a given situation and explain it using Newton's first law. Practise each type with at least two examples from daily life.

Inertia of rest: A body at rest tends to stay at rest. When a duster lying on a table is hit from below, the duster moves up but the chalk dust flies off because the dust tends to remain at rest.

Inertia of motion: A body in motion tends to stay in motion. When a moving bus stops suddenly, the passengers inside continue to move forward because their bodies were already in motion.

Inertia of direction: A body in motion tends to continue in the same direction. When a car turns a sharp curve on a mountain road, passengers tend to slide outward because their bodies try to continue in the original straight-line direction.

Momentum

The quantity of motion in a body

Formula

p = mv

where

m

= mass in kg and

v

= velocity in m/s.

Momentum is the product of the mass and velocity of a body. A body with more mass or more velocity has more momentum.

A slow-moving heavy truck and a fast-moving cricket ball can have similar momentum. The truck is dangerous on roads because of its large mass; the cricket ball is dangerous because of its high speed.

Momentum is a vector quantity. Its direction is the same as the direction of velocity. The SI unit is kilogram metre per second (kg m/s).

Solved Example

Comparing momentum

A 5 kg stone moves at 4 m/s and a 0.1 kg rubber ball moves at 30 m/s. Which has more momentum?

Stone:

p = 5 \times 4 = 20

kg m/s.
Ball:

p = 0.1 \times 30 = 3

kg m/s.
The stone has greater momentum.

Newton's Second Law

Force equals rate of change of momentum

Formula

F = ma

(for constant mass)

Also written as

F = \frac{\Delta p}{\Delta t}

in its more general form.

Newton's second law states that the rate of change of momentum of a body is directly proportional to the net force applied on it, and the change takes place in the direction of the applied force.

For a body of constant mass, the second law simplifies to

F = ma

where

F

is force in newtons,

m

is mass in kg, and

a

is acceleration in m/s².

A fast bowler in cricket delivers the ball at high speed. The batsman must apply a large force to reverse the ball's momentum. A skilled batsman playing a defensive stroke moves the bat backward slowly to increase the time of contact, which reduces the force on the bat and hands — a direct use of the second law.

Solved Example

Force needed to accelerate a vehicle

A 1200 kg car starts from rest and reaches 20 m/s in 10 s. Find the force applied.

a = \frac{v-u}{t} = \frac{20-0}{10} = 2 \text{ m/s}^2

F = ma = 1200 \times 2 = 2400 \text{ N}

Show a second-law numerical with impulse

A force of 50 N acts on a body of 10 kg for 4 seconds. Find the change in momentum.

Change in momentum = Force × time = $F \times t = 50 \times 4 = 200$ kg m/s.

This quantity $F \times t$ is called impulse and equals the change in momentum.

Quick Practice

A net force of 15 N acts on a body of mass 3 kg. Find the acceleration.

Answer:

a = F/m = 15/3 = 5 \text{ m/s}^2

Newton's Third Law

Every action has an equal and opposite reaction

Important Caution

Action and reaction are equal and opposite — but they act on different bodies. They are NOT a balanced force pair because balanced forces act on the same body.

Newton's third law states that for every action there is an equal and opposite reaction. These two forces always act on two different bodies and never on the same body, so they cannot cancel each other.

When you walk on a road or footpath, your foot pushes the ground backward and downward (action). The ground pushes your foot forward and upward with exactly the same force (reaction). The reaction force moves you forward.

On Diwali, a rocket pushes gases backward (action) and the gases push the rocket forward (reaction), launching it into the sky. A swimmer pushes water backward with their hands (action) and water pushes the swimmer forward (reaction).

Think About It

If a horse pulls a cart with force F, the cart also pulls the horse backward with force F. Why does the system move forward?

Answer: The horse pushes the ground backward; the ground pushes the horse forward with a reaction force. If this ground reaction exceeds friction on the cart's wheels, the horse-cart system moves forward.

Conservation of Momentum

Total momentum is constant when no external force acts

Formula

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

Total momentum before collision = total momentum after collision.

The law of conservation of momentum states that in an isolated system where no external unbalanced force acts, the total momentum of the system remains constant before and after any event such as collision or explosion.

This law follows directly from Newton's third law. When two bodies interact, their action-reaction forces are equal and opposite, so the total change in momentum is zero.

Consider two carom coins colliding on a carrom board. Before the collision, coin A moves and coin B is at rest. After the collision, some momentum is transferred from A to B. The total momentum of both coins together is the same before and after the collision.

Applications of Momentum Conservation

Recoil, rockets, and real-world events

Gun recoil: When a bullet of small mass is fired at high velocity, the gun of large mass moves backward at a smaller velocity so that total momentum remains zero (both were at rest before firing).

Rocket propulsion: A rocket expels gases backward at high speed. The gases gain momentum in the backward direction. By conservation of momentum, the rocket gains equal momentum in the forward direction. This is how ISRO launches satellites into orbit.

Jumping from a boat: When a person jumps off a boat at a river ghat, the person moves forward and the boat moves backward. The forward momentum gained by the person equals the backward momentum gained by the boat.

Solved Example

Recoil velocity of a gun

A gun of mass 3 kg fires a bullet of mass 0.03 kg at 400 m/s. Find the recoil velocity of the gun.

Initial momentum = 0 (both at rest).

0 = 0.03 \times 400 + 3 \times v_{gun}

3v_{gun} = -12

v_{gun} = -4 \text{ m/s}

The gun recoils at 4 m/s in the direction opposite to the bullet.

Show a collision conservation problem

A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley and they move together. Find the common velocity after collision.

Before: $p = 2 \times 3 + 1 \times 0 = 6$ kg m/s.

After: $p = (2+1) \times v = 3v$ .

By conservation: $3v = 6$ , so $v = 2$ m/s.

Complete Chapter Summary

Key laws, formulas, and ideas to revise before exams

Force: push or pull; can change state of motion or shape; SI unit = newton (N).

Newton's first law: body stays at rest or uniform motion unless external unbalanced force acts. Inertia is resistance to this change. Mass measures inertia.

Momentum:

p = mv

. Newton's second law:

F = ma

F = \Delta p / \Delta t

Newton's third law: equal and opposite forces act on different bodies.

Conservation of momentum:

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

in isolated systems.

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