Newton's Laws of Motion - Notes, Topics, Formulas, Books, FAQs

Laws of Motion Class 11th Topics (NCERT Syllabus)

1 Introduction

Motion of objects occurs due to forces acting on them. Forces can change the speed, direction, or shape of a body. Newton's laws provide a systematic way to understand and predict how forces affect motion in daily life and engineering.

2. Aristotle's Fallacy

Aristotle claimed that a body requires a continuous force to keep moving. Experiments later proved this wrong, showing that a body moves at constant velocity unless acted upon by an external force like friction.

3. The Law of Inertia

Inertia is the tendency of a body to resist change in its state of motion.

• A body at rest stays at rest; a body in motion continues in uniform motion unless acted upon by a net force.
• This principle is the foundation of Newton's first law.

Law of Inertia

4. Newton's First Law of Motion

Also called the law of inertia, it states:
"A body remains at rest or in uniform motion in a straight line unless acted upon by a net external force."
Explains why seat belts are necessary in vehicles and why objects continue moving when forces like friction are absent.

• Newton's First Law of Motion

5. Newton's Second Law of Motion

Newton's Second Law provides a quantitative description of how forces affect the motion of a body. It states:
"The rate of change of momentum of a body is directly proportional to the net external force applied on it and occurs in the direction of the force."

Mathematical Formulation
If a body of mass $m$ is acted upon by a net force $\vec{F}$ :

$
\vec{F}=\frac{d \vec{p}}{d t}
$

Where $\vec{p}=m \vec{v}$ is the momentum of the body.
For a constant mass, this simplifies to:

$
\vec{F}=m \vec{a}
$

Newton's Second Law of Motion

6. Newton's Third Law of Motion

Newton's Third Law states:
"For every action, there is an equal and opposite reaction."
This means that whenever a body $\mathbf{A}$ exerts a force on body $\mathbf{B}$, body $\mathbf{B}$ exerts an equal and opposite force on body A.
These forces are equal in magnitude, opposite in direction, and act on different bodies.

$
\vec{F}_{A B}=-\vec{F}_{B A}
$
Where:
$\vec{F}_{A B}=$ Force on body B due to A
$\vec{F}_{B A}=$ Force on body A due to B

Examples:

Walking: Feet push the ground backward (action), ground pushes forward (reaction).

Rocket propulsion: Gases expelled backward (action), rocket moves forward (reaction).

Swimming: Hands push water backward (action), body moves forward (reaction).

Recoil of a gun: Bullet moves forward (action), gun moves backward (reaction).

• Newton's Third Law of Motion

7. Conservation of Momentum

The principle of conservation of momentum states:
"If no external force acts on a system of particles, the total momentum of the system remains constant in both magnitude and direction."
Momentum $(\vec{p})$ of a body is the product of its mass and velocity:

$
\vec{p}=m \vec{v}
$

For a system of two bodies before and after interaction (e.g., collision):

$
\begin{aligned}
\vec{p}_{\text {initial }} & =\vec{p}_{\text {final }} \\
m_1 \vec{v}_1+m_2 \vec{v}_2 & =m_1 \vec{v}_1^{\prime}+m_2 \vec{v}_2^{\prime}
\end{aligned}
$

Examples:

Collisions: Two billiard balls hitting each other.

Recoil of a gun: Momentum of bullet and gun system is conserved.

Rocket propulsion: Momentum of expelled gases balances rocket motion.

• Conservation of Momentum

8. Equilibrium of a Particle

A particle is said to be in equilibrium when it remains at rest or moves with uniform velocity, i.e., there is no acceleration.

Condition for Equilibrium
A particle is in equilibrium if the net force acting on it is zero:

$
\sum \vec{F}=0
$

In two dimensions, this condition can be written as:

$
\sum F_x=0 \quad \text { and } \quad \sum F_y=0
$

In three dimensions:

$
\sum F_x=0, \quad \sum F_y=0, \quad \sum F_z=0
$

Types of Equilibrium
1. Stable Equilibrium: If displaced, the particle returns to its original position.
Example: A ball at the bottom of a bowl.
2. Unstable Equilibrium: If displaced, the particle moves further away.
Example: A ball on top of a hill.
3. Neutral Equilibrium: If displaced, the particle stays in the new position.
Example: A ball on a flat surface.

9. Common Forces in Mechanics

Gravitational force: Weight of a body, acts downwards.

Normal force: Perpendicular reaction from a surface.

Friction: Opposes relative motion.

Tension: Force in strings or ropes.

Centripetal force: Keeps bodies in circular motion.

• Force: Contact Force and Non-Contact Force
• Frictional Force

• Conservative Force

• Balanced Force

10. Circular Motion

When a body moves along a circular path of radius $r$ with a certain speed $v$, it is said to be in circular motion. Even if the speed is constant, the velocity is changing because its direction continuously changes.

Centripetal Acceleration

The acceleration directed towards the center of the circle is called centripetal acceleration:

$
a_c=\frac{v^2}{r}
$

This acceleration is responsible for continuously changing the direction of the velocity.

Centripetal Force

A net force directed towards the center is required to maintain circular motion:

$
F_c=m a_c=m \frac{v^2}{r}
$

It can be provided by tension, gravity, friction, or normal force depending on the situation.

Examples of Circular Motion
1. A car turning on a circular track (friction provides centripetal force).
2. Earth revolving around the Sun (gravitational force provides centripetal force).
3. Stone tied to a string and whirled in a circle (tension provides centripetal force).

• Uniform Circular Motion

11. Solving Problems in Mechanics

Steps to solve problems:

• Draw a diagram showing forces and motion.
• Identify knowns and unknowns.
• Apply Newton’s laws or momentum/energy principles.
• Use kinematic relations as needed.
• Check units and reasonableness of answers.

Newton's Laws of Motion Formulas

1. Equilibrium of a Particle (First Law)

For a particle in equilibrium:

$
\sum \vec{F}_{\text {net }}=0
$

or, in components:

$
\sum F_x=0, \quad \sum F_y=0, \quad \sum F_z=0
$

2. Lami's Theorem

For three coplanar, concurrent, non-collinear forces in equilibrium:

$
\frac{F_1}{\sin \alpha}=\frac{F_2}{\sin \beta}=\frac{F_3}{\sin \gamma}
$

3. Spring Force (Hooke's Law)

Restoring force exerted by a spring:

$
F=-k x
$

$k=$ spring constant, $x=$ displacement from equilibrium

4. Newton's Second Law of Motion

$
\vec{F}=m \vec{a}
$

5. Newton's Third Law of Motion

$
\vec{F}_{A B}=-\vec{F}_{B A}
$

Every action has an equal and opposite reaction

6. Linear Momentum

$
\vec{P}=m \vec{v}
$

Momentum $=$ mass $\times$ velocity

7. Impulse

$
\vec{I}=\int_{t_1}^{t_2} \vec{F} d t
$

Impulse = effect of a force over a short time interval

8. Impulse-Momentum Theorem

$
\int_{t_1}^{t_2} \vec{F} d t=\Delta \vec{P}=\vec{P}_2-\vec{P}_1
$

Impulse = change in momentum

9. Centripetal Force

$
F_c=m \omega^2 r
$

Force that keeps a body moving in a circular path towards the center

10. Kinetic Friction Force

$
f_k=\mu_k R
$

Opposes relative motion between surfaces

11. Limiting (Maximum) Static Friction

$
f_{\ell}=\mu_s R
$

Maximum static friction before motion begins

Laws of Motion – Exam Weightage

Real-Life Examples of Laws of Motion

1. Newton’s First Law (Law of Inertia)

Objects resist change in motion.

Examples:

• Passengers in a moving bus lurch forward when the bus suddenly stops.
• A tablecloth quickly pulled from under dishes without moving them.

2. Newton’s Second Law (F = ma)

Acceleration of a body is proportional to the net force applied.

Examples:

• Pushing a car: harder push → greater acceleration.
• Kicking a football: stronger kick → faster motion.

3. Newton’s Third Law (Action-Reaction)

Every action has an equal and opposite reaction.

Examples:

• Rocket propulsion: gases expelled backward push the rocket forward.
• Walking: feet push ground backward, ground pushes you forward.

Swimming: hands push water backward, body moves forward.

4. Conservation of Momentum

Momentum of a system remains constant if no external force acts.

Examples:

• Recoil of a gun when a bullet is fired.
• Collision of billiard balls on a pool table.

5. Circular Motion & Centripetal Force

A force acts toward the center to keep a body in circular motion.

Examples:

• Car turning on a curved road (friction provides centripetal force).
• Earth revolving around the Sun (gravitational force acts as centripetal force).

6. Friction & Impulse

Friction opposes motion; impulse changes momentum.

Examples:

• Brakes in vehicles slow them down (friction).
• Hitting a cricket ball changes its momentum over a short time (impulse).

How to prepare Newton's Laws of Motion

First, you should have a good command of the concepts of Newton's Laws of motion, and you should also know how to apply them well at the time of the entrance exam or while solving questions. Please try to understand each concept from this chapter, with the help of theory, solved questions and video lectures on each important concept. For each concept, practice enough problems so that you have a thorough understanding of the concept. Solve all the questions with proper concentration and try to do all calculations by yourself without checking the solution first.

How to Solve Newton's Laws of Motion Questions

1. Choose a convenient system.

2. Draw a diagram which schematically shows the various parts of a system.

3. Draw the free-body diagram of each part of the system.

4. In a free-body diagram, you must include information about forces (their magnitudes and directions).

5. The rest should be treated as unknowns or to be determined using the laws of motion.

6. Apply Newton's third law wherever necessary.

If a system is in equilibrium, or all the forces working on a body are Concurrent Forces, then the calculations of the question would be easy. Need a clear understanding of the concept of solving problems related to the Recoiling of Guns, Firing of Bullets, and Rocket Propulsion. The answer sheet should have neat and clean calculations to avoid negative markings. Question-related friction gets more and more complicated when we involve more blocks in contact, inclined planes, pulleys, etc, variable external force, etc. But you can solve these questions with ease with a proper study plan.

Newton's Laws of Motion Books

For Newton's Laws of Motion, the chapter concepts in the NCERT are enough, but you have to practice different types of questions, including previous years' questions and also attend online mock tests.

The standard books available for competitive exam preparation:

• ‘Concepts of Physics’ (Vol. 1 and Vol. 2) by H.C. Verma

• ‘Understanding Physics’ by D. C. Pandey (Arihant Publications).

• ‘Comprehensive Physics for Class 12’ by J.P. Sharma

NCERT Notes Subject Wise Link:

• NCERT notes Class 11 Maths

• NCERT notes Class 11 Physics

• NCERT notes Class 11 Chemistry

• NCERT notes Class 11 Biology

NCERT Solutions Subject-wise link:

• NCERT solutions for class 11 Physics.

• NCERT solutions for class 11 Chemistry.

• NCERT solutions for class 11 Mathematics.

• NCERT solutions for class 11 Biology.

NCERT Exemplar Solutions Subject-wise link:

• NCERT exemplar solutions for class 11 Physics.

• NCERT exemplar solutions for class 11 Chemistry.

• NCERT exemplar solutions for class 11 Mathematics.

• NCERT exemplar solutions for class 11 Biology.