Laws of Motion

Concept overview

Newton's three laws of motion connect forces and motion. The first law defines inertia — objects continue at rest or in uniform motion unless a net force acts. The second law quantifies the connection: F = ma. The third law says every force has an equal and opposite reaction on a different body.

The workhorse skill of this chapter is the free-body diagram (FBD). For any object in a problem, draw only the forces acting on it — gravity, normal reaction, tension, friction, and any applied force — and apply Newton's second law in each coordinate direction. Master this and pulley/incline problems become mechanical.

Friction complicates the picture. Static friction adjusts up to a maximum value f_s ≤ μ_s N; once you exceed this, motion begins and kinetic friction f_k = μ_k N takes over (typically μ_k < μ_s). Rolling friction is smaller still. The direction of friction always opposes relative motion (or tendency of relative motion).

Constraints link the motion of connected objects. For an ideal string over a frictionless pulley, tension is uniform and the accelerations of the two connected masses are equal in magnitude. For a wedge sliding while a block on it slides too, constraint equations connect the two accelerations — this is where JEE Advanced problems get interesting.

Key formulas & concepts

• Newton's second law: F_net = ma (in each direction)
• Weight: W = mg (vertical, downward)
• Static friction limit: f_s ≤ μ_s N
• Kinetic friction: f_k = μ_k N (opposes motion)
• Atwood machine (ideal): a = (m₁ − m₂)g / (m₁ + m₂); T = 2m₁m₂g / (m₁ + m₂)
• Block on incline (μ = 0): a = g sinθ (down the slope)
• Impulse: J = ∫F dt = Δp (change in momentum)

Common mistakes to avoid

• Including the reaction force in an FBD for the wrong body — Newton's third-law pairs act on different bodies.
• Using μ_s N as the friction force when the surface is actually sliding — it's μ_k N once motion begins.
• Confusing constraint acceleration for a pulley system — the string is inextensible, so |a₁| = |a₂|; the signs may differ depending on the coordinate convention.
• Applying F = ma to a system as if it were a single body when internal forces differ — always split into FBDs of each object.

JEE Main relevance

JEE Main asks 2 questions every paper — usually one FBD/pulley/incline problem and one friction numerical. Both are pattern-driven once FBDs are second nature.

JEE Advanced relevance

Advanced problems combine constraints with variable-mass or non-inertial frames. Problems involving a block on a moving wedge, spring-mass systems with friction, or pseudo-forces in an accelerating frame are standard Advanced patterns.

Previous-year questions (PYQ)

Friction problems and pulley-constraint problems are the two most common PYQ archetypes. Practise 15 of each in a dedicated session.