Newton's three laws of motion describe how forces change the state of an object — whether it stays still, speeds up, slows down or turns. For CDS Science, this is the single most rewarding chapter: a handful of clear ideas (inertia, F = ma, action−reaction) and the rules of equilibrium generate a large slice of the physics paper, year after year.
Why this topic matters in CDS
Mechanics is the backbone of the CDS Science section, and Newton's laws sit right at its centre. Almost every motion-based question — a block on a table, a lift accelerating, a gun recoiling, a satellite in orbit — is solved by applying one of these three laws.
The questions are usually conceptual one-liners or single-step numericals. That makes the chapter high-yield: a little clarity earns marks quickly and reliably. Unlike rotational dynamics or thermodynamics, the maths here rarely goes beyond multiplication and division, so even candidates who fear physics can score full marks with steady practice.
The NCERT treatment introduces these laws gradually — force and pressure in the middle classes, then a formal statement of the three laws and momentum in Class 9 and Class 11. The CDS paper draws from this entire range, mixing simple recall ("state the law") with applied reasoning ("why does a fielder pull back his hands?"). Building a firm conceptual base here also pays off later in gravitation, work-energy and circular motion, which all rest on these same ideas.
Examiners love everyday examples — seatbelts, recoil of a gun, walking, rowing a boat. Learn the real-life illustration behind each law; the option is often phrased as a situation, not a formula.
Force, mass and inertia
A force is a push or pull that can change the speed, direction or shape of a body. Its SI unit is the newton (N), where 1 N is the force that gives a 1 kg mass an acceleration of 1 m/s2.
Inertia is the natural tendency of a body to resist any change in its state of rest or uniform motion. The more massive a body, the greater its inertia — that is why mass is called the measure of inertia.
- Inertia of rest — dust falls off a carpet when it is beaten.
- Inertia of motion — a passenger lurches forward when a bus brakes suddenly.
- Inertia of direction — mud flies off tangentially from a spinning wheel.
Inertia depends only on mass, never on speed. A heavy truck and a light scooter at the same velocity do not have the same inertia.
Newton's First Law (Law of Inertia)
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 defines force as the agent that changes a body's state of motion, and it tells us that no force is needed to keep a body moving at constant velocity — only to change that velocity.
If the net (resultant) force on a body is zero, its acceleration is zero. It may be at rest or moving with constant velocity — both are valid states of equilibrium.
Everyday proof: when a moving car stops suddenly, your upper body keeps moving forward (inertia of motion). The seatbelt supplies the external force that brings you to rest safely.
Historically this law overturned the old Aristotelian belief that a constant force is needed to keep a body moving. Galileo's experiments with smooth inclined planes showed that, in the absence of friction, a ball would roll on forever. Newton formalised this insight as the first law. In daily life friction and air resistance are the hidden external forces that eventually stop everything — remove them and motion continues unchanged, exactly as a satellite coasts through space without an engine running.
Newton's Second Law and F = ma
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.
Momentum is p = m×v. If mass is constant, the law reduces to the famous form below.
F = ma and F = Δp ÷ Δt
Impulse: J = F×t = Δp = m(v − u)
Units: force in N, momentum in kg·m/s, impulse in N·s.
The second law is the quantitative law — it lets you calculate the exact force or acceleration. It also explains why a cricketer draws their hands back while catching a ball: increasing the time of contact reduces the force for the same change in momentum.
Notice that the first law is really a special case of the second: when F = 0, then a = 0, so the body keeps its existing velocity. The second law also shows clearly why force is a vector — the acceleration always points in the direction of the net force. When several forces act, you must add them as vectors first and then apply F = ma to the resultant. This is why a heavy loaded truck accelerates sluggishly while an empty one of the same engine power picks up speed quickly: the same driving force divided by a larger mass yields a smaller acceleration.
For a constant force, acceleration is inversely proportional to mass. Double the mass for the same force and the acceleration halves — a frequent single-step MCQ.
Newton's Third Law (action and reaction)
To every action there is an equal and opposite reaction. The two forces are equal in magnitude, opposite in direction, and act along the same line — but on two different bodies.
This last point is crucial: because action and reaction act on different bodies, they never cancel each other out. Cancellation needs two forces on the same body.
- A swimmer pushes water backward; the water pushes the swimmer forward.
- A gun pushes the bullet forward; the bullet pushes the gun back (recoil).
- A rocket throws gases down; the gases push the rocket up.
Walking itself depends on this law: you push the ground backward with your foot, and the ground pushes you forward with an equal force (friction provides the grip). On a frictionless icy surface this push is lost, which is why walking becomes nearly impossible. Similarly, a jet engine and a rocket both work by throwing mass in one direction to gain thrust in the opposite direction.
Saying action and reaction cancel so motion is impossible. They act on different bodies, so each produces its own acceleration. Never add an action−reaction pair on a single free-body diagram.
Applications you must recognise
CDS often disguises a law inside a familiar scene and asks you to identify the principle. Keep this quick map ready.
- Seatbelt / headrest — first law (inertia of motion).
- Dusting a carpet by beating it — first law (inertia of rest).
- Catching a ball with hands drawn back — second law (longer time, smaller force).
- Karate chop breaking a tile — second law (very short time, very large force).
- Recoil of a gun, rocket and jet propulsion — third law and momentum conservation.
- Walking, swimming, rowing a boat — third law.
A second family of questions tests the difference between balanced and unbalanced forces. Balanced forces produce no change in motion (the body is in equilibrium); only an unbalanced, net force produces acceleration. When a book lies on a table, its weight is balanced by the upward normal reaction, so it stays at rest — a direct application of both the first law and the equilibrium condition.
The presence of motion does not mean a net force acts. A body moving at constant velocity has zero net force, exactly like a body at rest.
Conservation of momentum
The third law leads directly to one of physics' most powerful results. For an isolated system (no external force), the total momentum stays constant.
m1u1 + m2u2 = m1v1 + m2v2
Total momentum before collision = total momentum after collision.
This explains gun recoil: before firing, total momentum is zero, so afterwards the forward momentum of the bullet must equal the backward momentum of the gun. Because the gun is far heavier, its recoil velocity is small.
Momentum is conserved in every collision (elastic or inelastic). Kinetic energy is conserved only in a perfectly elastic collision.
Conditions for equilibrium
A body is in equilibrium when it has no acceleration — neither linear nor rotational. Two conditions must hold together.
- Translational equilibrium: the vector sum of all forces is zero → ΣF = 0 (so ΣFx = 0 and ΣFy = 0).
- Rotational equilibrium: the sum of all moments (torques) about any point is zero → Στ = 0.
The moment of a force (torque) about a point is τ = force × perpendicular distance from the point. Clockwise and anticlockwise moments must balance — this is the principle of moments, the basis of levers and beam balances.
Equilibrium has three flavours: stable (returns to position, like a cone on its base), unstable (moves further away, cone on its tip) and neutral (stays put, a ball on a flat table). Match the example to the type.
Free-body diagrams and weight vs mass
To solve any force problem, draw a free-body diagram (FBD): isolate one body and mark every force acting on it — weight (downward), normal reaction (perpendicular to surface), tension, friction and applied force.
Do not confuse two terms that CDS examiners love to test:
- Mass (m) — quantity of matter, measured in kg, the same everywhere.
- Weight (W = mg) — the gravitational force on the body, measured in newtons, varies with g.
Treating weight as constant on the Moon. Mass is unchanged, but the Moon's g is about one-sixth of Earth's, so your weight there is roughly one-sixth.
Worked example: force and acceleration
A 5 kg object moving at 2 m/s is brought to rest in 0.5 s by a constant braking force. Find (a) the acceleration and (b) the force.
Both routes — F = ma and the impulse−momentum method — give the same answer. Knowing both lets you pick whichever the data suits.
Previous-year style question
Q. A bullet of mass 20 g is fired from a gun of mass 4 kg with a muzzle velocity of 200 m/s. The recoil velocity of the gun is:
Answer: By conservation of momentum, mbvb = mgvg. So vg = (0.02 × 200) ÷ 4 = 4 ÷ 4 = 1 m/s, directed opposite to the bullet. The gun recoils slowly because it is far heavier than the bullet.
Always convert grams to kilograms before applying momentum conservation. Here 20 g = 0.02 kg — forgetting this is the commonest slip.
Quick revision
- First law — defines inertia; no net force → no change in motion.
- Second law — F = ma = Δp÷Δt; impulse = change in momentum.
- Third law — equal and opposite forces on two different bodies.
- Momentum is conserved for an isolated system; this explains recoil.
- Equilibrium needs ΣF = 0 and Στ = 0 — stable, unstable or neutral.
- Weight (mg) varies with g; mass does not.
Frequently asked questions
What is the difference between Newton's first and second laws?
The first law is qualitative: it tells us that a force is needed to change motion and defines inertia. The second law is quantitative: it gives the exact relation F = ma, letting you calculate the force or acceleration involved.
Why do action and reaction forces not cancel each other?
Because they act on two different bodies, not on the same one. Cancellation of forces only happens when two forces act on the same object. Action and reaction each cause their own effect on their own body.
What are the two conditions for a body to be in equilibrium?
The net force on the body must be zero (translational equilibrium, ΣF = 0) and the net torque about any point must be zero (rotational equilibrium, Στ = 0). Both must hold simultaneously.
Is momentum always conserved in a collision?
Yes, total momentum is conserved in every collision of an isolated system, whether elastic or inelastic. Kinetic energy, however, is conserved only in a perfectly elastic collision.
How is impulse useful in real life and in the exam?
Impulse equals the change in momentum (J = F×t). Increasing the contact time lowers the force for the same momentum change, which is why a cricketer pulls their hands back while catching and why airbags reduce injury.
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