Newton's Laws of Motions (1st, 2nd & 3rd)

Newton's Laws of Motion

Physics Notes • Definitions • Important Points • Equations & Formulas

1. Newton's First Law of Motion

Definition

“An object remains at rest or continues to move with uniform velocity in a straight line unless an external unbalanced force acts on it.”

Easy Meaning

👉 No unbalanced force → No change in motion.

• Object at rest → remains at rest.
• Moving object → keeps moving with the same speed and direction.
• A force is required to change the state of motion.

Important Concept: Inertia

The tendency of an object to resist any change in its state of motion is called inertia.

Important:
Inertia is directly related to mass.

More mass → More inertia

Types of Inertia

1. Inertia of Rest

A passenger falls backward when a bus suddenly starts.

2. Inertia of Motion

A passenger falls forward when a moving bus suddenly stops.

3. Inertia of Direction

A passenger is pushed sideways when a bus takes a sharp turn.

Formula / Equation

For a body moving with constant velocity:

Net Force

\( F_{\text{net}} = 0 \)

Acceleration

\( a = 0 \)

Velocity

\( v = \text{constant} \)

Examples

• A book lying on a table remains at rest.
• A hockey puck keeps moving on a smooth surface until friction or another force changes its motion.
• Dust comes out when a carpet is beaten.

2. Newton's Second Law of Motion

Definition

“The rate of change of momentum of an object is directly proportional to the applied unbalanced force and takes place in the direction of the force.”

Easy Meaning

👉 More force → More acceleration.
👉 More mass → Less acceleration for the same force.

Momentum

Momentum is the product of mass and velocity.

\( p = mv \)

Symbol	Meaning
p	Momentum
m	Mass
v	Velocity

Mathematical Form

According to Newton's Second Law:

\( F \propto \frac{\Delta p}{\Delta t} \)

In SI units:

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

Since:

\( p = mv \)

For constant mass:

\( \boxed{F = ma} \)

This is the most important formula of Newton's Laws of Motion.

Derivation of \(F = ma\)

Initial Momentum:

\( p_1 = mu \)

Final Momentum:

\( p_2 = mv \)

Change in Momentum:

\( \Delta p = mv - mu \)

According to Newton's Second Law:

\( F = \frac{mv-mu}{t} \)

Taking \(m\) common:

\( F = m\frac{v-u}{t} \)

But,

\( a = \frac{v-u}{t} \)

\( \boxed{F = ma} \)

SI Unit of Force

\( 1\,N = 1\,kg \times 1\,m/s^2 \)

Therefore:

\( \boxed{1N = 1kg\,m/s^2} \)

Important Rearranged Formulas

From:

\( F = ma \)

Therefore:

\( \boxed{a = \frac{F}{m}} \)

\( \boxed{m = \frac{F}{a}} \)

Example

Given:

\( m = 5\,kg \)
\( a = 2\,m/s^2 \)

Formula:

\( F = ma \)

Solution:

\( F = 5 \times 2 \)

\( \boxed{F = 10N} \)

3. Newton's Third Law of Motion

Definition

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

More precisely, when one object exerts a force on another object, the second object simultaneously exerts an equal-magnitude force in the opposite direction on the first object.

Easy Meaning

👉 Action and reaction always occur in pairs.

Mathematical Form

If object A applies force on object B:

\( F_{AB} = -F_{BA} \)

Therefore:

\( \boxed{|F_{\text{action}}| = |F_{\text{reaction}}|} \)

Their directions are opposite.

Important Points

1. Action and reaction are equal in magnitude.
2. They are opposite in direction.
3. They act simultaneously.
4. They act on different objects.
5. Therefore, they do not cancel each other.

Examples of Newton's Third Law

🚶 Walking

Your foot pushes the ground backward → the ground pushes your foot forward.

🏊 Swimming

A swimmer pushes water backward → water pushes the swimmer forward.

🚀 Rocket

Rocket gases are pushed downward → the rocket moves upward.

🔫 Gun Recoil

The bullet moves forward → the gun experiences a backward force.

⭐ Newton's Three Laws — Quick Revision

Law	Main Idea	Important Formula
1st Law	No unbalanced force → no change in motion	\( F_{\text{net}} = 0,\quad a = 0 \)
2nd Law	Force produces acceleration	\( \boxed{F = ma} \)
3rd Law	Action and reaction	\( \boxed{F_{AB}=-F_{BA}} \)