Introduction

Newton's laws of motion are three foundational rules that describe how objects move — or stay still — under the influence of forces. They're the starting point for almost every mechanics problem in JEE, NEET, KCET and Board exams, and they underlie topics you'll meet later, like friction, circular motion, and momentum conservation.

The First Law — Law of Inertia

An object at rest stays at rest, and an object in motion continues moving at constant velocity in a straight line, unless acted on by a net external force. This property of "resisting a change in motion" is called inertia, and it's the reason you feel pushed back into your seat when a car accelerates forward.

The first law is really a special case of the second law (when net force is zero), but it's stated separately because it defines what a force actually is: something that changes a state of rest or uniform motion.

The Second Law — F = ma

The net force acting on an object equals the rate of change of its momentum. For objects with constant mass, this simplifies to the most-used equation in mechanics:

Formula F = m·a
where F is the net force (newtons, N), m is mass (kg), and a is acceleration (m/s²).

More generally: F = dp/dt, where p = m·v is momentum.

This law tells you two things at once: force causes acceleration (not velocity directly), and heavier objects need more force to achieve the same acceleration.

The Third Law — Action and Reaction

For every action, there is an equal and opposite reaction. If object A exerts a force on object B, object B exerts an equal and opposite force back on object A — and crucially, these two forces act on different objects, so they never cancel each other out.

Worked example A 2 kg block on a frictionless surface is pushed with a force of 6 N. Find its acceleration.

Using F = m·a → a = F / m = 6 / 2 = 3 m/s².
Worked example A rocket expels gas backward to move forward. Which law explains this? The third law — the rocket pushes gas backward (action), and the gas pushes the rocket forward (reaction) with equal force.

Common mistakes

Watch out for
  • Confusing "no motion" with "no force" — an object can have balanced forces (net force = 0) and still be in motion at constant velocity.
  • Applying action-reaction pairs to the same object — they always act on two different bodies, so they can't cancel in a free-body diagram of one object.
  • Forgetting that F = ma uses net force, not a single applied force — you must add up all forces (including friction, gravity, normal force) first.
  • Mixing up mass and weight — mass (kg) is constant; weight (N) = mass × g and changes with gravity.

Exam preparation tips

Tip
  • Always draw a free-body diagram before applying F = ma — list every force acting on the object.
  • For JEE/KCET numericals, keep units consistent (SI units) before substituting into formulas.
  • For NEET/Boards conceptual questions, be ready to identify which law explains a given real-world scenario (seatbelts, rocket propulsion, walking).
  • Practice problems involving connected bodies (blocks connected by strings, pulleys) — these test all three laws together.

Summary

Newton's first law defines inertia and says no force means no change in motion. The second law, F = ma, quantifies how force produces acceleration. The third law says forces always come in equal, opposite pairs acting on different objects. Together, they form the basis for solving almost any classical mechanics problem you'll face in exams.

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