Newton’s Laws of Motion | Formula, Examples and Questions

Newton’s Laws of Motion are the three fundamental laws given by famous English physicist Sir Issac Newton. He proposed them to explain the physics of motion of objects around us. This is an important chapter for the students of class 9 and 11.

There are three Laws of Motion by Newton, which are,

• Newton’s First Law of Motion
• Newton’s Second Law of Motion
• Newton’s Third Law of Motion

Newton’s Laws of Motion

Newton’s First Law of Motion

The first law of motion by Newton states that,

“For an object that is in the state of rest or state of motion remains in its state unless and until an external force is applied to the object.”

• Newton’s First Law of Motion also called the Law of Inertia. It is one of the fundamental laws of physics that deals with the inertia of any object.
• Inertia is the property of any material that is related to the mass and state of the object.
• For example, Suppose we see a man standing on a running bus and if the driver applies the brake then the man leans forward because his upper body is in a state of motion and no extra force is applied to it, and the man tends to lean forward.

First Law of Motion Examples

Various examples of Newton’s First Law of Motion observed are,

• Applying acceleration to the car, the passengers lean forward due to the presence of inertia. Inertia tries to keep the passenger moving. This is the reason why it is recommended to wear seat belts while traveling by car.
• Roller coaster uses the principle of inertia.
• If we kick a football it eventually stops due to the friction force on the ground, it continues to move infinitely.

• A book lying on the table remains at rest as long as no net force acts on it.
• If the branches of the tree are shaken vigorously, the fruits attached to it fall down as they continue to be in the state of rest and hence the sudden motion detaches the fruits from the branches and falls on the ground.

Newton’s Second Law of Motion

Newton’s Second Law of Motion states that,

“The rate of change of momentum of an object is proportional to the applied unbalanced force, in the direction of the force. The rate of change of momentum of an object is proportional to the applied force.”

Second Law of Motion Formula

Newton’s second law of motion provides a precise explanation of the changes that a force can make to a body’s motion.

Mathematically it is shown as,

Force ∝  (Change in Momentum) / (Time Taken)

F ∝ d(mv)/dt

F = kd(mv)/dt

F = k{v.dm/dt + m.dv/dt}

As mass is always constant, {dm/dt = 0}

F = km.dv/dt

Experimentally, k = 1

F = m.dv/dt

we know that, dv/dt = a

F = ma

where,

• F is the Force Applied
• m is the Mass of Object
• a is the Acceleration of Object

Second Law of Motion Examples

Various examples of Newton’s Second Law are:

• Catching a ball on the cricket field by a fielder is the best example of Newton’s second law of motion. When the fielder catches the ball it moves its hands backward to increase the time of the catch resulting in lowering the force by the ball.

• Airbags in a car increase the impact time of the accident and then reduce the impact of the accident, etc.

Newton’s Third Law of Motion

Newton’s Third Law of Motion states that ,

“For a pair of bodies every action has its equal and opposite reaction.”

Third Law of Motion Formula

This law is also explained as, when an object A applies a force of F₁ on object B then B applies a force of F₂ on the object such that,

F₁ = -F₂

Third Law of Motion by Newton is also called the Law of Action and Reaction.

Examples of Third Law of Motion

Various examples of Newton’s Third Law of Motion observed are,

• Recoil of the gun when a bullet is fired is an example of Newton’s Third Law of Motion.

• The launching of the rocket is also an example of the Third Law of Motion.

Laws of Motion Numericals

Here are some numericals on Newton’s Laws of Motion for you to practise and learn.

1. Find out how much net force will be needed to accelerate a 2500 kg truck at 5.50 m/s².

Solution:

Given,

• Acceleration (a) = 5.50 m/s²
• Mass of the Truck (m)= 2500 kg

Hence,

Force = Mass × Acceleration

F = 2500 × 5.5

F = 13750 N

Net force will be needed to accelerate a 2500 kg truck at 5.50 m/s² is 13750 N.

2. What will happen If a net force of 6 N is applied on 0.5 kg object. Calculate the acceleration of the material.

Solution:

Given,

• Force (F) = 6 N
• Mass (m) = 0.5 kg

Acceleration (a) = ?

Force = Mass × Acceleration

F = m × a

a = F/m

a = 6/0.5

a = 12 m/s²

The acceleration of the obhect is 12 m/s²

3. If a racing car driver is on the race track in order to overtake accelerates his racing car first at the rate of 8 m/s² and then at the rate of 16 m/s². Find the ratio of the forces exerted by the engine for the acceleration change.

Solution:

Given,

• a₁ = 8 m/s²
• a₂ = 16 m/s²

We have to find the ratio of F₁/F₂

F₁/F₂ = ma₁/ma₂

Mass of the racing car is same in both the cases,

F₁/F₂ = a₁/a₂

F₁/F₂ = 8/16

F₁/F₂ = 1/2 = 1:2

4. When a bullet of mass 20 gm is shot from a gun that has an initial velocity of 40 m/s the mass of the gun is 5 kg. What is the initial recoil velocity of the gun?

Solution:

Given,

• Mass of Bullet (m₁) = 20 gm or 0.02 kg
• Mass of Gun (m₂) = 5 kg
• Initial velocity = 40 m/s

Let final velocity is v m/s

By Law of Conservation of Momentum,

0 = 0.02 × 40 + 5 × v

5 × v = -0.8 

v =  -0.8 / 5

v = -0.16 m/s

Questions on Newton’s Laws

Here are some practice problems on Newton’s Laws of Motion for you to solve:

Problem 1: A book is placed on a table. Describe what happens to the book when:

a) No force is applied to it.

b) A gentle horizontal force is applied to the book.

c) A vertical force is applied to the book.

Problem 2: An object with a mass of 5 kg is subjected to a net force of 20 N. Calculate the acceleration of the object.

Problem 3: Two ice skaters, one with a mass of 60 kg and the other with a mass of 80 kg, push off each other on an ice rink. If the 60 kg skater exerts a force of 200 N on the 80 kg skater, what force does the 80 kg skater exert on the 60 kg skater?

Laws of Motion – FAQs

Who discovered 3 laws of Motion?

The 3 laws of Motion were discovered by Sir Issac Newton.

What are Newton’s Laws of Motion?

Netwon’s Laws of Motion in physcis are the fundamental laws of Physcis that are given by famous English scientist, Sir Issac Newton. There are three laws under Newton’s Law of Motion, that are,

• Newton’s First Law of Motion
• Newton’s Second Law of Motion
• Newton’s Third Law of Motion

All three laws are explained in detail in the article above.

What is Newton’s First Law of Motion?

Newton’s First Law of Motion is also called the Law of Inertia. It states that, “An object at the states of rest or motion states in its state of rest or motion until a a force is applied to it.”

What is Newton’s Second Law of Motion?

Newton’s Second Law of Motion states that, “Rate of change of momentum is the force applied to the object.”

What is Newton’s Third Law of Motion?

Newton’s Third Law of Motion also called the Law of Action and Reaction as it states that, “Every action has its equal and opposite reaction.”