Newton's First Law - Law of Inertia

Master the concept of inertia and Newton's First Law with real-world examples, tricks, and JEE problems for Physics

Prerequisites

Before studying this topic, make sure you understand:


The Hook: Why Don’t We Fly Off When Trains Brake?

Connect: Jawan's Train Chase Scene

Remember the iconic train scenes in Jawan (2023)? When Shah Rukh Khan’s character stands on top of a moving train and it suddenly brakes, he lurches forward. But why? The train stopped — so why does he keep moving forward?

This isn’t just movie physics — it’s Newton’s First Law in action! Your body “wants” to keep moving at the train’s original speed even when the train stops.

The Big Question: What makes objects resist changes in their state of motion?


The Core Concept: Inertia

Newton’s First Law Statement

$$\boxed{\text{A body at rest stays at rest, and a body in motion continues in uniform motion}}$$ $$\boxed{\text{in a straight line, unless acted upon by an external force}}$$

In simple terms: Objects are “lazy” — they don’t like to change what they’re doing!

What is Inertia?

Inertia is the inherent property of matter to resist any change in its state of rest or uniform motion.

Three Types of Inertia
  1. Inertia of Rest: A book on a table stays at rest until you pick it up
  2. Inertia of Motion: A moving car continues moving until brakes are applied
  3. Inertia of Direction: A turning car tries to keep going straight (you feel pushed outward)

Interactive Demo: Visualize Free Body Diagrams

Learn how to identify and draw forces acting on objects.

Measure of Inertia

$$\boxed{\text{Inertia} \propto \text{Mass}}$$

The mass of an object is the quantitative measure of its inertia.

  • Heavier objects have more inertia (harder to start/stop)
  • Lighter objects have less inertia (easier to start/stop)
Fast X Connection
In Fast X (2023), why do those massive trucks take so long to stop compared to sports cars? More mass = more inertia = harder to stop!

Why Do We Need an External Force?

Without any external force:

  • A body at rest will never start moving on its own
  • A moving body will never stop or change direction

Real-world twist: Then why does a rolling ball eventually stop on the ground?

Because there ARE external forces acting:

  • Friction between ball and ground
  • Air resistance

In the absence of friction (like in space), objects truly continue moving forever!


Inertial and Non-Inertial Frames

Inertial Frame of Reference

A frame of reference in which Newton’s First Law holds true.

Examples:

  • A train moving with constant velocity
  • A car moving on a straight road at constant speed
  • The Earth (approximately, ignoring rotation)

Non-Inertial Frame of Reference

A frame that is accelerating. Newton’s First Law does NOT hold in such frames without introducing pseudo forces.

Examples:

  • A braking car
  • A turning vehicle
  • A rotating merry-go-round
Common Mistake

Don’t confuse: “An inertial frame must be at rest”

Wrong! An inertial frame can be moving — but with constant velocity (zero acceleration).


Memory Tricks & Patterns

Mnemonic for First Law

“REST is BEST, MOTION is LOTION”

  • Bodies prefer to maintain their current state
  • Rest stays rest
  • Motion stays motion

Pattern Recognition for JEE

ScenarioWhat HappensWhy
Shake a treeFruits fallFruits have inertia of rest; tree moves, fruits stay
Pull a tablecloth quicklyDishes stay in placeInertia of rest keeps dishes from moving
Car suddenly acceleratesYou feel pushed backYour body has inertia of rest
Car suddenly brakesYou lurch forwardYour body has inertia of motion
Turn a car sharplyYou feel pushed outwardYour body has inertia of direction

Real-World Applications

1. Seat Belts

Safety Physics
During a collision, the car stops suddenly but your body continues forward due to inertia of motion. Seat belts provide the external force needed to stop you with the car.

2. Athletic Hammer Throw

The athlete spins with the hammer and then releases it. The hammer flies off tangentially due to inertia of direction — it “wants” to continue in a straight line!

3. Beating Dust from Carpet

When you beat a carpet, the carpet moves but dust particles maintain their inertia of rest and separate from the carpet.


Common Mistakes to Avoid

Trap #1: Force Needed to Maintain Motion

Wrong thinking: “A moving object needs a force to keep moving”

Correct thinking: A moving object needs NO force to maintain constant velocity. Forces are needed only to:

  • Start motion (overcome inertia of rest)
  • Stop motion (overcome inertia of motion)
  • Change direction (overcome inertia of direction)
Trap #2: Inertia is a Force

Wrong: Inertia is a force acting on the body

Correct: Inertia is a property of matter, NOT a force. It’s the tendency to resist change.

Trap #3: Heavier Objects Always Win

Scenario: Two objects collide — does the heavier one always “push” the lighter one?

Truth: During collision, forces are equal and opposite (Newton’s Third Law). But the lighter object accelerates more because it has less inertia!


Practice Problems

Level 1: Foundation (NCERT)

Problem 1.1: Identify Inertia Type

A passenger in a bus falls backward when the bus suddenly starts. Which type of inertia is demonstrated?

Solution: The passenger was at rest. When the bus accelerates, the passenger’s body tends to remain at rest due to inertia of rest. The feet (in contact with the bus) move forward, but the upper body lags behind — causing the backward fall.

Answer: Inertia of rest

Problem 1.2: Mass and Inertia

Two blocks A (2 kg) and B (5 kg) are at rest. Which has greater inertia?

Solution: Inertia is directly proportional to mass.

  • Block A: 2 kg
  • Block B: 5 kg

Since B has greater mass, B has greater inertia.

Answer: Block B (5 kg)

Problem 1.3: Real-World Application

Why do athletes run before taking a long jump?

Solution: By running, the athlete gains velocity. Due to inertia of motion, when the athlete jumps, they continue moving forward in the air, achieving greater horizontal distance.

Answer: To utilize inertia of motion for greater jump distance


Level 2: JEE Main

Problem 2.1: Conceptual Understanding

A block of mass 5 kg is placed on a smooth horizontal surface (frictionless). A force of 10 N is applied for 2 seconds and then removed. What happens to the block after the force is removed?

Solution: While force is applied (0 to 2s):

  • $a = F/m = 10/5 = 2 \text{ m/s}^2$
  • After 2s: $v = u + at = 0 + 2(2) = 4 \text{ m/s}$

After force is removed: Since the surface is frictionless (no external force), by Newton’s First Law, the block continues moving with constant velocity of 4 m/s.

Answer: The block continues moving at 4 m/s indefinitely

Problem 2.2: Inertial Frames

A ball is dropped inside a train. In which case will the ball land exactly below the release point? (A) Train at rest (B) Train moving with constant velocity (C) Train accelerating (D) Both A and B

Solution: For the ball to land exactly below the release point, the horizontal velocity of ball and train must remain the same throughout the fall.

Case A: Train at rest → Both ball and train have zero horizontal velocity → Lands below ✓

Case B: Train moving with constant velocity → Both ball and train have same constant horizontal velocity → Lands below ✓

Case C: Train accelerating → Train’s velocity changes, but ball retains initial horizontal velocity → Does NOT land below ✗

Answer: (D) Both A and B (both are inertial frames)

Problem 2.3: Multi-Concept

A block is placed on a rough horizontal surface (coefficient of friction μ = 0.3). If no external force is applied, what is the acceleration of the block?

Solution: Key insight: The block is initially at rest.

By Newton’s First Law, a body at rest remains at rest unless acted upon by an external force.

Friction is NOT an applied force here! Friction only opposes motion or tendency of motion. Since there’s no applied force and the block is at rest, there’s no tendency to move.

Therefore: a = 0

Common mistake: Thinking friction causes deceleration even when block is at rest.

Answer: 0 m/s²


Level 3: JEE Advanced

Problem 3.1: Non-Inertial Frame

A bob hangs from the ceiling of a car by a string. When the car accelerates forward with acceleration $a$, at what angle does the string make with the vertical?

Solution: From ground frame (inertial):

  • Horizontal: $T\sin\theta = ma$
  • Vertical: $T\cos\theta = mg$

Dividing:

$$\tan\theta = \frac{a}{g}$$ $$\boxed{\theta = \tan^{-1}\left(\frac{a}{g}\right)}$$

From car frame (non-inertial): We must introduce a pseudo force $ma$ backward (opposite to car’s acceleration).

The bob is in equilibrium in this frame:

  • Real force: $mg$ downward, $T$ along string
  • Pseudo force: $ma$ backward

Same result: $\tan\theta = a/g$

Answer: $\theta = \tan^{-1}(a/g)$ backward from vertical

Problem 3.2: Conceptual Depth

A rocket in deep space (far from any gravitational field) has its engines off. A small mass inside the rocket is moving with velocity $v$ relative to the rocket. What happens to this mass?

Solution: In deep space with engines off, the rocket is an inertial frame (no acceleration, no external forces).

By Newton’s First Law, the small mass will continue moving with constant velocity $v$ relative to the rocket.

It will NOT:

  • Slow down (no friction in space)
  • Speed up (no force)
  • Change direction (no force)

Answer: Continues with constant velocity $v$ relative to rocket indefinitely

Problem 3.3: Advanced Application

A smooth ring of mass $m$ can slide on a fixed horizontal rod. A string attached to the ring passes over a frictionless pulley and carries a mass $M$ at its other end. The pulley is at a height $h$ above the rod and at a horizontal distance $d$ from the initial position of the ring. Find the acceleration of the ring just after the system is released from rest.

Given: The string makes angle $\theta$ with horizontal initially, where $\tan\theta = h/d$

Solution: This is a constraint motion problem.

Forces on ring (smooth rod, no friction):

  • Tension $T$ along string (at angle $\theta$)
  • Normal reaction $N$ from rod (vertical)
  • Weight $mg$ (vertical)

For ring (horizontal motion only):

$$ma_{\text{ring}} = T\cos\theta$$

For mass $M$:

$$Ma_M = Mg - T$$

Constraint: Since string is inextensible, the rate at which string length changes must be consistent.

Component of ring’s velocity along string = Velocity of mass $M$

$$a_{\text{ring}}\cos\theta = a_M$$

From equations:

$$a_{\text{ring}}\cos\theta = \frac{Mg - T}{M}$$ $$T = ma_{\text{ring}}/\cos\theta$$

Substituting:

$$a_{\text{ring}}\cos\theta = \frac{Mg - ma_{\text{ring}}/\cos\theta}{M}$$ $$a_{\text{ring}}\cos\theta + \frac{ma_{\text{ring}}}{M\cos\theta} = g$$ $$a_{\text{ring}}\left(\cos\theta + \frac{m}{M\cos\theta}\right) = g$$ $$\boxed{a_{\text{ring}} = \frac{Mg\cos\theta}{M\cos^2\theta + m}}$$

Or in terms of $h$ and $d$:

$$a_{\text{ring}} = \frac{Mgd^2}{M d^2 + m(h^2 + d^2)}$$

Answer: $a = \frac{Mg\cos\theta}{M\cos^2\theta + m}$


Quick Revision Box

ConceptKey PointFormula/Fact
First LawBody resists change in motionNo net force → constant velocity
InertiaProperty to resist changeInertia ∝ Mass
TypesRest, Motion, DirectionAll resist change
Inertial FrameFirst Law holds trueZero acceleration frame
Non-InertialFirst Law needs pseudo forceAccelerating frame
ApplicationSeat belts, dust removalSafety devices

When to Use This Concept

Decision Tree for Problem-Solving

Use Newton’s First Law when:

  1. System is in equilibrium (net force = 0)
  2. Object is moving with constant velocity
  3. Identifying inertial vs non-inertial frames
  4. Conceptual questions about inertia

Move to Newton’s Second Law when:

  • Acceleration is present
  • Need to calculate forces/mass/acceleration
  • Quantitative problems involving F = ma

JEE Exam Strategy

Weightage

  • JEE Main: 1-2 conceptual questions per year
  • JEE Advanced: Often combined with other laws in multi-concept problems

Common Question Types

  1. Identify type of inertia (easy, 1 marker)
  2. Inertial frame identification (moderate, 2-3 marks)
  3. Pseudo force problems (advanced, 4 marks)
  4. Application-based conceptual (easy-moderate, 2 marks)

Time-Saving Tricks

  • If net force = 0, immediately think: “equilibrium or constant velocity”
  • For non-inertial frames, always draw pseudo force opposite to frame’s acceleration
  • Mass ratio problems: Inertia ratio = Mass ratio (direct proportion)

Teacher’s Summary

Key Takeaways
  1. Inertia is resistance to change — it’s not a force, it’s a property
  2. Mass measures inertia — more mass, more resistance to change
  3. Three types: Rest (staying still), Motion (keeping moving), Direction (going straight)
  4. First Law defines inertial frames — frames where the law holds without pseudo forces
  5. Real world: Friction and air resistance are why moving objects stop (external forces!)

“Objects don’t need force to keep moving — they need force to CHANGE their motion!”


Within Laws of Motion

Connected Chapters

Math Connections