Laws of Motion

Syllabus Unit: Mechanics

Why it matters

Chapter overview

Newton's three laws are the engine of classical mechanics — this topic covers how the first law defines inertia and force, how the second law quantifies force as the rate of change of momentum, how the third law's action-reaction pairs lead directly to conservation of momentum, and how friction and circular dynamics apply all three laws to real surfaces and curved paths.

Physics Syllabus Mechanics 30%–35% weightage

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1Inertia (1st Law)Body resists change in state of motion

2Net Force AppliedAn unbalanced force acts on the body

3F = dp/dt (2nd Law)Momentum changes at a rate proportional to F

4Impulse J = ΔpForce × time equals the momentum change produced

1Newton's First & Second Laws

The first law defines force as whatever changes a state of rest or uniform motion; the second law quantifies exactly how much change a given force produces.

Learning Objectives

State Newton's first law and explain how it defines inertia and force qualitatively.
State Newton's second law in both forms: F = ma and F = dp/dt.
Explain why F = dp/dt is the more general form, applicable even when mass changes (e.g. rocket propulsion).
Define impulse and relate it to the change in momentum, J = FΔt = Δp.

Key Terms

InertiaThe natural tendency of a body to resist any change in its state of rest or uniform motion; mass is the quantitative measure of inertia.

Newton's First LawA body continues in its state of rest or uniform motion in a straight line unless acted upon by a net external force.

Newton's Second LawThe rate of change of momentum of a body is directly proportional to the applied net force and occurs in the direction of that force, F = dp/dt.

ImpulseThe product of force and the (short) time for which it acts, J = FΔt, numerically equal to the change in momentum it produces.

Newton's first two laws together set up the whole of dynamics: the first law says a net force is needed to change motion at all, and the second law says exactly how much motion changes for a given force.

The first law: force defined through inertia

Newton's first law says a body maintains its state (rest or uniform straight-line motion) unless a net external force acts — this is also called the law of inertia, and it is what actually defines 'force' as the cause of any change in that state.

The second law: quantifying force

F = ma (constant mass) ; F = dp/dt (general form, p = mv)

The second law is the working equation of dynamics — the net force on a body equals the rate of change of its momentum. For constant mass this reduces to the familiar F=ma, but the momentum form is essential for variable-mass systems.

Impulse — force acting briefly

J = F·Δt = Δp = m(v − u)

Key PointImpulse explains why cricketers 'give with the ball' while catching — increasing the contact time Δt for the same Δp reduces the average force F on the hands.

Common MistakeF=ma only applies when mass is constant — for a rocket losing mass as it burns fuel, you must use F = dp/dt = m(dv/dt) + v(dm/dt), not plain F=ma.