1. Physics
  2. Laws of Motion
  3. Newton's First Law – Law of Inertia

Laws of Motion · JEE & NEET Physics

Newton's First Law – Law of Inertia: notes and previous year questions

Why a moving body needs no force to keep moving, what inertia is, and where the first law holds.

Newton's First Law – Law of Inertia in short

  • A body keeps its state of rest or uniform straight-line motion unless an external force acts on it.
  • A force is needed to change motion (start, stop, turn), not to keep it.
  • Things stop in daily life because friction and air resistance are real external forces.
  • Inertia is the property of matter that resists changes in motion; it is not a force.

1The first law

Stand in a bus and let the driver brake hard: you lurch forward. The brakes act on the bus, not on you. Your body was moving at the bus's speed, nothing slowed your upper body, so it simply kept going while the floor held your feet back.

Give three pucks the same push: on rough carpet friction stops one quickly, on smooth ice it slides much farther, and in space, with no friction at all, it never stops. Things around us stop because friction and air resistance are real external forces acting on them.

So a force is not needed to keep a body moving. A force is needed only to start it, stop it or turn it: a force changes motion.

2Inertia

Inertia is the property of matter that resists any change in its state of rest or of uniform motion. It is not a force; it is how matter behaves, and it is the reason the first law is true.

Inertia∝mass\text{Inertia} \propto \text{mass}Mass is the measure of inertia.

Give a 2 kg and a 5 kg crate on ice the same push, 10 N for 1 s: the 2 kg crate reaches 5 m/s, the 5 kg crate only 2 m/s. More mass means harder to start, stop or turn, which is why a loaded truck needs far longer to stop than a small car.

Example: block A is 2 kg and block B is 5 kg. B has more mass, so B has more inertia, whatever their speeds.

3Three kinds of inertia

KindThe body tends toExamples
Inertia of reststay at resta bus starts and you fall back; shake a tree and fruits fall; pull a tablecloth quickly and dishes stay; beat a carpet and dust falls out
Inertia of motionkeep movinga bus brakes and you lurch forward; a long jumper runs up first; a puck glides on ice; seat belts stop you in a crash
Inertia of directionkeep a straight linea car turns and you slide outward; a released hammer flies off along the tangent

Example: a passenger falls backward when a bus suddenly starts. The feet move with the bus, but the upper body tends to stay at rest: inertia of rest.

Example: an athlete runs before a long jump. The speed gained stays with the body in the air: inertia of motion carries the jump further.

In a sharp turn you feel pushed outward. No real force pushes you out: your body tends to keep going straight (inertia of direction), and the seat has to push you inward.

4No net force

The net force is the vector sum of all the forces on a body. If it is zero, the velocity stays constant: the body is at rest, or moves at a steady speed in a straight line. This is called equilibrium.

∑F⃗=0  ⇒  v⃗=constant\sum \vec F = 0 \;\Rightarrow\; \vec v = \text{constant}

A car moving along a straight road at a constant 60 km/h has zero net force on it: the engine's forward push just balances friction and air drag.

5Inertial frames

Drop a ball inside a train moving at a steady speed: it lands exactly below the release point. Drop it while the train speeds up: it lands behind that point, although nothing pushed it back. The ball keeps the speed the train had at release, while the train speeds up beneath it. Seen from inside, the first law fails.

FrameAccelerationFirst lawExamples
Inertialzeroholdsthe ground (very nearly), a train at constant velocity, a car at constant speed on a straight road
Non-inertialnot zerofails without pseudo forcesa braking car, a turning vehicle, a merry-go-round

6Pseudo forces

A bob hangs from the roof of a car accelerating at aa; the string tilts back by θ\theta. From the ground (inertial), the string's pull has a forward part that accelerates the bob:

Tsin⁡θ=ma,Tcos⁡θ=mgT\sin\theta = ma,\quad T\cos\theta = mg
tan⁡θ=ag\tan\theta = \frac{a}{g}Divide the two equations. With a = 7.5 m/s²: tan θ = 0.75, θ ≈ 37°. With a = g: θ = 45°.

From inside the car (non-inertial), the bob is at rest though the string is tilted. To use Newton's laws there, add a pseudo force −ma⃗-m\vec a to every body: it points opposite to the frame's acceleration. No body exerts it, so it has no reaction. The bob is then in equilibrium under mgmg, TT and mama backward, and the answer is the same: tan⁡θ=a/g\tan\theta = a/g.

In a car accelerating forward, the pseudo force on a passenger points backward: that is why you feel pressed into the seat.

7Inertia all around

  • Seat belts supply the force that stops you along with the car in a crash.
  • Hammer throw: released, the hammer flies off along the tangent, in a straight line.
  • Beating a carpet: the carpet moves, the dust stays and falls out.
  • Long jump: the run-up speed carries the body forward through the air.

Summary

Key ideas

  • A body keeps its state of rest or uniform straight-line motion unless an external force acts on it.
  • A force is needed to change motion (start, stop, turn), not to keep it.
  • Things stop in daily life because friction and air resistance are real external forces.
  • Inertia is the property of matter that resists changes in motion; it is not a force.
  • Mass is the measure of inertia: more mass, more inertia.
  • Inertia shows up as inertia of rest, of motion and of direction.
  • Zero net force means constant velocity: equilibrium.
  • Friction on a body at rest with no applied force is zero.
  • Inertial frames have zero acceleration and need not be at rest; the first law holds in them.
  • In an accelerating frame, add a pseudo force −ma, opposite to the frame's acceleration.
  • A bob hanging in a car with acceleration a tilts back by θ with tan θ = a/g.

Every equation

First law
∑F⃗=0⇒v⃗=constant\sum \vec F = 0 \Rightarrow \vec v = \text{constant}
Measure of inertia
inertia∝m\text{inertia} \propto m
While a force acts
a=F/ma = F/m
Speed after pushing
v=u+atv = u + at
Pseudo force
F⃗pseudo=−ma⃗frame\vec F_{\text{pseudo}} = -m\vec a_{\text{frame}}
Bob in a car
Tsin⁡θ=ma, Tcos⁡θ=mgT\sin\theta = ma,\ T\cos\theta = mg
String angle
tan⁡θ=a/g\tan\theta = a/g
Drop in an accelerating train
Δx=12at2\Delta x = \tfrac{1}{2} a t^2
Ring on a smooth rod
a=Mgcos⁡θMcos⁡2θ+ma = \frac{Mg\cos\theta}{M\cos^2\theta + m}

Previous year questions with solutions

Real JEE and NEET questions on newton's first law – law of inertia. Try each one before you open the solution.

Q1JEE Main 2025One correct option

A body of mass mm is suspended by two strings making angles θ1{\theta}_{1} and θ2{\theta}_{2} with the horizontal ceiling with tensions T1T_{1} and T2T_{2} simultaneously. T1T_{1} and T2T_{2} are related by T1=3T2T_{1}=\sqrt{3}T_{2}, the angles θ1{\theta}_{1} and θ2{\theta}_{2} are

  1. Aθ1=30∘θ2=60∘{\theta}_{1}={30}^{\circ }{\theta}_{2}={60}^{\circ } with T2=3mg4T_{2}=\frac{3\mathrm{mg}}{4}
  2. Bθ1=45∘θ2=45∘{\theta}_{1}={45}^{\circ }{\theta}_{2}={45}^{\circ } with T2=3mg4T_{2}=\frac{3mg}{4}
  3. Cθ1=30∘θ2=60∘{\theta}_{1}={30}^{\circ }{\theta}_{2}={60}^{\circ } with T2=4mg5T_{2}=\frac{4mg}{5}
  4. Dθ1=60∘θ2=30∘{\theta}_{1}={60}^{\circ }{\theta}_{2}={30}^{\circ } with T2=mg2T_{2}=\frac{mg}{2}
Show answer and solution

Answer: Option D

Resolve both ways. Horizontally T1cos⁡θ1=T2cos⁡θ2T_{1}\cos{\theta}_{1} = T_{2}\cos{\theta}_{2}, and substituting T1=3T2T_{1}=\sqrt{3}T_{2} leaves 3cos⁡θ1=cos⁡θ2\sqrt{3}\cos{\theta}_{1} = \cos{\theta}_{2}, which θ1=60∘{\theta}_{1} = 60^{\circ} and θ2=30∘{\theta}_{2} = 30^{\circ} satisfy, since 3×12=32\sqrt{3}\times\tfrac{1}{2} = \tfrac{\sqrt{3}}{2}. Then vertically, T1sin⁡θ1+T2sin⁡θ2=mgT_{1}\sin{\theta}_{1} + T_{2}\sin{\theta}_{2} = mg becomes 3T2×32+T2×12=2T2=mg\sqrt{3}T_{2}\times\tfrac{\sqrt{3}}{2} + T_{2}\times\tfrac{1}{2} = 2T_{2} = mg, so T2=mg2T_{2} = \dfrac{mg}{2}. The geometry is worth carrying away on its own: the steeper string takes the greater tension, so the 3\sqrt{3} had to belong to the 60∘60^{\circ} side before any algebra started.

Q2NEET 2024One correct option

A particle moving with uniform speed in a circular path maintains:

  1. AConstant velocity
  2. BConstant acceleration
  3. CConstant velocity but varying acceleration
  4. DVarying velocity and varying acceleration
Show answer and solution

Answer: Option D

Uniform speed is not uniform velocity. The speed is a number and it holds; the velocity is a vector along the tangent, and the tangent swings round as the particle goes, so the velocity is changing throughout. The acceleration is not constant either. Its size is v2r\dfrac{v^{2}}{r}, which never changes, but it points at the centre, and that direction turns with the particle — and a vector is constant only when its size and its direction are both fixed. So both vary. The two options offering "constant velocity" are there for anyone who reads velocity as speed, which is the only thing this question is really asking.

Q3JEE Advanced 2007One correct option

STATEMENT 1

A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.

STATEMENT 2

For every action there is an equal and opposite reaction.

  1. AStatement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
  2. BStatement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1s.
  3. CStatement-1 is True, Statement-2 is False.
  4. DStatement-1 is False, Statement-2 is True.
Show answer and solution

Answer: Option B

Take the two statements apart before comparing them. The first is true, and inertia is the reason: each dish is at rest, the cloth's friction acts on it only for the instant the cloth is sliding underneath, and a push that brief leaves the dish essentially where it stood. The second is true as well — it is the action and reaction rule, a law in its own right that this chapter reaches later. But it has nothing to say about the dishes. It is about the paired forces that two bodies exert on each other, not about what a body does when the force on it lasts almost no time. Two true statements with no link between them, which is exactly what this format is built to test.

Practice questions, easy to hard

Three questions from the newton's first law – law of inertia practice ladder: one easy, one medium, one hard.

Q4One correct option

The other word doing work is external. Forces between the parts of a system act inside it and cancel within it, so they can shift the system as a whole not at all. Only a force from outside can.

You sit in a stationary car with the doors closed and push as hard as you can on the dashboard. What happens to the car?

  1. AIt moves forward, since a force has been applied to it
  2. BIt moves backward, since the dashboard pushes back on you
  3. CIt moves whichever way you push, but far too slowly to notice
  4. DIt does not move, because your push is internal to the system of you and the car
Show answer and solution

Answer: Option D

You and the car together are the system, and your push on the dashboard is matched by the dashboard's push on you — both of them inside it. The only place an external force could come from is the road. This is why nobody has ever lifted themselves by pulling on their own belt, and why the law takes the trouble to say external.

Q5Numerical answer

The normal reaction is whatever it has to be — it is not a fixed property of the table. Put a heavier book down and the table pushes harder, up to the point where it gives way. For a book resting on a level table with nothing else touching it, NN must match the Earth's pull, and the Earth pulls a mass mm with a force mgmg. That pull is a force, measured in newtons; the mass is not a force, and stays a plain kg\mathrm{kg}.

A book of mass 2 kg2\ \mathrm{kg} rests on a level table. What is the normal reaction on it, in N\mathrm{N}? (Take g=10 m/s2g = 10\ \mathrm{m/s^{2}})

Show answer and solution

Answer: 20 N

The book is at rest, so the net force on it is zero and N=mg=2×10=20 NN = mg = 2 \times 10 = 20\ \mathrm{N}. Keep the two quantities apart: the mass is 2 kg2\ \mathrm{kg} and travels with the book wherever it goes, while the weight is the 20 N20\ \mathrm{N} force the Earth exerts on it. And N=mgN = mg is not a law — it is what this one arrangement happens to force. Tilt the table, or press down with a hand, and NN comes out as something else.

Q6One or more correct options

A lamp of weight 100 N100\ \mathrm{N} hangs from two chains fixed to the ceiling, one making 30∘30^{\circ} with the ceiling and the other 60∘60^{\circ}, so the two chains happen to be at right angles to each other. Call the tensions T30T_{30} and T60T_{60}.

Which of the following are correct?

  1. AT30=50 NT_{30} = 50\ \mathrm{N}
  2. BThe angle Lami's theorem pairs with the weight is 90∘90^{\circ}
  3. CT30+T60=100 NT_{30} + T_{60} = 100\ \mathrm{N}, since between them the chains carry the lamp
  4. DResolving into components and applying Lami's theorem give the same two tensions
Show answer and solution

Answer: Options A, B, D

The angle between the two tensions is 90∘90^{\circ}, so that is the one paired with the weight. The angle between T60T_{60} and the weight is 90∘+60∘=150∘90^{\circ}+60^{\circ} = 150^{\circ} and the one between T30T_{30} and the weight is 120∘120^{\circ}, which checks out because the three have to total 360∘360^{\circ}. Lami then gives T30sin⁡150∘=Wsin⁡90∘\dfrac{T_{30}}{\sin 150^{\circ}} = \dfrac{W}{\sin 90^{\circ}}, so T30=100sin⁡150∘=50 NT_{30} = 100\sin 150^{\circ} = 50\ \mathrm{N}, and the same line with sin⁡120∘\sin 120^{\circ} gives T60=503≈86.6 NT_{60} = 50\sqrt{3} \approx 86.6\ \mathrm{N}. Resolving horizontally and vertically returns those same two numbers, because Lami is that pair of equations wearing a triangle. C is the trap: tensions are vectors pointing different ways, so it is their vertical components that add to 100 N100\ \mathrm{N}, not their magnitudes, which come to about 136.6 N136.6\ \mathrm{N}.