Almost every NDA Physics paper carries questions on Newton's Laws of Motion and momentum. The good news? The whole topic rests on just three short laws and one big idea — that force changes motion. Get the logic once, and the numerical and conceptual questions both become easy marks. This guide builds that logic step by step.
Why This Topic Matters for NDA
Laws of Motion is one of the highest-scoring chapters in the NDA General Science section. Year after year you will see 2−4 questions drawn from it — some pure theory (define inertia, which law explains recoil) and some quick numericals (find acceleration, find force).
The chapter is also the foundation for almost everything else in mechanics: gravitation, circular motion, work and energy all use force and momentum. So time spent here pays back many times over.
Another reason to master it is that the questions are short and direct. You will rarely face a long multi-step derivation here. Most items test whether you can recall a law correctly or plug numbers into one simple formula. With clear basics, this becomes a chapter where you should not lose a single mark.
The entire chapter is built on one sentence: a force is needed to change the state of motion of a body — not to keep it moving.
Force and Inertia
A force is a push or a pull. It can make a body start moving, stop, speed up, slow down, or change direction. Its SI unit is the newton (N).
Inertia is the natural tendency of a body to resist any change in its state of rest or motion. A body at rest wants to stay at rest; a moving body wants to keep moving in a straight line at the same speed.
Inertia depends on mass
The more mass a body has, the more inertia it has. A loaded truck is far harder to push or stop than a bicycle — that is greater inertia because of greater mass. Mass is the measure of inertia.
Three kinds of inertia
- Inertia of rest: dust flies off a carpet when you beat it — the carpet moves, the dust stays.
- Inertia of motion: a passenger lurches forward when a bus brakes suddenly.
- Inertia of direction: mud flies off tangentially from a spinning cycle wheel.
If a question describes a sudden start or stop and asks “why,” the answer is almost always inertia (the relevant kind), linked to Newton's first law.
Newton's First Law (Law of Inertia)
Newton's First Law: a body continues in its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force.
This law tells us two things at once:
- It defines what a force does — it changes the state of motion.
- It tells us that without a net force, velocity stays constant (which includes staying at rest).
Balanced vs unbalanced forces
When forces on a body cancel out, the net force is zero and the motion does not change — these are balanced forces. Only an unbalanced (net) force can accelerate a body.
Students think a moving body needs a continuous force to keep moving. It does not. In space, with no friction, a body keeps moving forever. On Earth, motion stops only because friction acts as the unbalanced force.
Linear Momentum
Before the second law, we need the idea of momentum. Momentum measures the “quantity of motion” in a body. It depends on both how heavy the body is and how fast it moves.
Momentum, p = m × v
where m = mass (kg), v = velocity (m/s).
SI unit of momentum: kg·m/s (or N·s). It is a vector — it has direction.
A heavy truck moving slowly can have the same momentum as a light bike moving fast. This is why momentum, not just speed, decides how hard a collision hits.
Quick feel for momentum
- A cricket ball at 30 m/s has small mass but high speed → moderate momentum.
- A loaded truck at 5 m/s has huge mass → very large momentum and is very hard to stop.
This is also why momentum and not speed alone decides the damage in a road accident. A heavy vehicle, even at a modest speed, carries large momentum and needs a large force over a long time to be brought to rest. Understanding this prepares you directly for the second law, which connects force with the rate of change of momentum.
Newton's Second Law — The Key Formula
Newton's Second Law: the rate of change of momentum of a body is directly proportional to the applied force, and takes place in the direction of the force.
F = rate of change of momentum = (mv − mu) ÷ t
For constant mass this simplifies to the famous form:
F = m × a
1 newton = the force that gives a 1 kg mass an acceleration of 1 m/s2.
This is the most-used formula in the chapter. From it you can find force, mass or acceleration if the other two are known.
Why heavier bodies are harder to accelerate
From a = F/m, for the same force a larger mass gives smaller acceleration. That is why a push that easily moves a chair barely moves a sofa.
The first law is actually a special case of the second: if F = 0, then a = 0, so velocity stays constant. NDA loves this link.
Impulse
Impulse is the effect of a force acting for a short time. It equals force multiplied by the time for which it acts, and it equals the change in momentum it produces.
Impulse = F × t = change in momentum = mΔv
SI unit: N·s (same as kg·m/s).
Why we extend the time of impact
Because impulse (the momentum change) is fixed, a longer contact time means a smaller force. This single idea explains many everyday and exam examples:
- A cricketer pulls his hands back while catching — longer time, smaller force, no injury.
- Cars have crumple zones and airbags — they increase impact time and cut the peak force.
- A high jumper lands on a soft mattress instead of hard ground.
Same momentum change, more time → less force. Same momentum change, less time → more force (a hard, sudden hit).
Newton's Third Law — Action and Reaction
Newton's Third Law: to every action there is an equal and opposite reaction.
Forces always occur in pairs. If body A pushes body B, then body B pushes A back with an equal force in the opposite direction.
Two crucial conditions
- Action and reaction are equal in magnitude and opposite in direction.
- They act on two different bodies — never on the same body.
Because they act on different bodies, action and reaction do not cancel each other. Cancellation needs two forces on the same body.
Everyday examples
- Walking: your foot pushes the ground back; the ground pushes you forward.
- Swimming: you push water back; water pushes you forward.
- Rocket and jet propulsion: hot gases are pushed down/back; the rocket is pushed up/forward.
- A gun recoils backward when a bullet is fired forward.
Conservation of Momentum
This is the most powerful result of the third law. In the absence of an external force, the total momentum of a system stays constant.
Total momentum before = Total momentum after
m1u1 + m2u2 = m1v1 + m2v2
Recoil of a gun
Before firing, both gun and bullet are at rest, so total momentum is zero. After firing, the bullet carries forward momentum, so the gun must carry an equal backward momentum to keep the total at zero. Since the gun is far heavier, its recoil velocity is small.
Rocket propulsion
A rocket ejects gas downward at high speed (large momentum down), so it gains equal momentum upward. This works even in the vacuum of space, where there is nothing to push against — it relies only on momentum conservation.
Whenever a question mentions firing, explosion, recoil, collision or rockets, reach for conservation of momentum first.
Worked Example
A gun of mass 4 kg fires a bullet of mass 20 g (0.02 kg) with a muzzle velocity of 400 m/s. Find the recoil velocity of the gun.
Answer: the gun recoils at 2 m/s backward.
A force of 10 N acts on a 2 kg body for 5 s. Find the acceleration and the change in momentum.
Answer: acceleration = 5 m/s2; change in momentum = 50 kg·m/s.
Common Mistakes to Avoid
NDA examiners repeat the same traps. Watch for these:
- Unit slips: convert grams to kilograms (20 g = 0.02 kg) and cm to metres before using F = ma or p = mv.
- Confusing mass and weight: mass (kg) is fixed; weight (N) is the force of gravity, W = mg, and changes with location.
- Thinking action and reaction cancel: they act on different bodies, so they never cancel.
- Forgetting momentum is a vector: opposite directions get opposite signs — this is why recoil works.
- Assuming motion needs force: uniform motion needs zero net force, not a constant force.
Mixing up the laws. First law → inertia; Second law → F = ma and impulse; Third law → action−reaction and recoil. Memorise this mapping.
Previous-Year Style Question
Q. A body of mass 5 kg is moving with a velocity of 10 m/s. A constant force brings it to rest in 2 seconds. The magnitude of the force is:
Answer: Change in momentum = m(v − u) = 5(0 − 10) = −50 kg·m/s. Force = change in momentum ÷ time = −50 ÷ 2 = −25 N. The magnitude of the retarding force is 25 N.
Q. Which one of Newton's laws explains the working of a rocket?
Answer: Newton's third law (action−reaction), supported by the principle of conservation of momentum. The rocket pushes gases backward and is pushed forward in return.
Quick Revision
- Inertia: resistance to change in motion; measured by mass.
- First law: no net force → no change in motion (law of inertia).
- Momentum: p = m × v; a vector; unit kg·m/s.
- Second law: F = ma; impulse = F × t = change in momentum.
- Third law: equal and opposite forces on two different bodies.
- Conservation: total momentum is constant with no external force — explains recoil, collisions and rockets.
- Practical idea: longer impact time → smaller force (airbags, catching a ball).
If you remember just one line for the whole chapter: force changes momentum, and momentum is always conserved when no outside force acts.
Frequently asked questions
What is the difference between mass and inertia?
Inertia is the property of a body to resist a change in its state of rest or motion. Mass is the quantitative measure of inertia — the greater the mass, the greater the inertia.
What is the SI unit of force and how is it defined?
The SI unit of force is the newton (N). One newton is the force that gives a mass of 1 kilogram an acceleration of 1 metre per second squared (1 N = 1 kg·m/s²).
Why don't action and reaction forces cancel each other?
Because they act on two different bodies, not on the same body. For forces to cancel and produce equilibrium, they must act on the same body. Action and reaction act on different bodies, so each produces its own effect.
How does conservation of momentum explain a gun's recoil?
Before firing, the total momentum of the gun-bullet system is zero. After firing, the bullet moves forward with momentum, so the gun must move backward with equal momentum to keep the total at zero. Because the gun is heavier, its recoil speed is small.
Which law of motion is most important for NDA numericals?
Newton's second law, F = ma, along with the impulse-momentum relation, is used in most numericals. For collision, explosion and recoil problems, conservation of momentum is the key tool.
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