Dynamics: Newton's Laws and Momentum

This guide covers Topic 3, Dynamics, in full — subtopics 3.1 Momentum and Newton’s laws of motion, 3.2 Non-uniform motion and 3.3 Linear momentum and its conservation — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is AS Level content, and an understanding of forces from Cambridge IGCSE/O Level Physics or equivalent is assumed.

Before studying this

This resource assumes the equations of motion from Kinematics: Equations of Motion and a basic IGCSE/O Level understanding of what a force is. It does not re-teach the idea of force from scratch.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — AS Level, Topic 3

3.1 Momentum and Newton’s laws of motion — mass as the property resisting change in motion; F = ma and the fact that acceleration and resultant force share a direction; linear momentum as mass × velocity; force as rate of change of momentum; Newton’s three laws of motion; weight as the effect of a gravitational field on mass, with weight = mass × g.

3.2 Non-uniform motion — a qualitative understanding of frictional and viscous/drag forces including air resistance; describing and explaining motion in a uniform gravitational field with air resistance present; terminal (constant) velocity.

3.3 Linear momentum and its conservation — the principle of conservation of momentum; applying it to elastic and inelastic collisions in one and two dimensions; recalling that total kinetic energy is conserved in an elastic collision and that relative speed of approach equals relative speed of separation; understanding that momentum is always conserved in an interaction even where kinetic energy is not.

Newton’s three laws

1. First law: an object continues at constant velocity (including rest) unless acted on by a resultant force.
2. Second law: the resultant force on an object equals its rate of change of momentum, giving F = ma for constant mass, where acceleration and resultant force always act in the same direction.
3. Third law: if object A exerts a force on object B, object B exerts an equal and opposite force on A — the two forces act on different objects and are of the same type.

Weight is the gravitational force on a mass: weight = mg, where g is the acceleration of free fall. Weight is not the same thing as mass — mass is constant, weight depends on the local gravitational field.

Linear momentum

Momentum p is defined as p = mv (mass × velocity), and is a vector, taking its direction from velocity. Newton’s second law can be expressed more generally as force = rate of change of momentum, which reduces to F = ma when mass is constant.

Non-uniform motion and terminal velocity

Without air resistance, a falling object accelerates uniformly at g. With air resistance present, drag increases as speed increases (a simple qualitative model is sufficient — no coefficients of friction or viscosity are required), so the resultant force — and therefore the acceleration — decreases as the object speeds up. Eventually drag equals weight, resultant force is zero, and the object falls at a constant terminal velocity.

Conservation of momentum

The principle of conservation of momentum states that the total momentum of a system is unchanged, provided no external resultant force acts on it. This applies to collisions and explosions in one or two dimensions, and holds whether or not kinetic energy is conserved.

• Elastic collision: total kinetic energy is conserved, and the relative speed of approach equals the relative speed of separation.
• Inelastic collision: momentum is still conserved, but total kinetic energy is not — some is transformed into other forms (heat, sound, deformation).

Worked example. A 2.0 kg trolley moving at 3.0 m s⁻¹ collides with a stationary 1.0 kg trolley, and they stick together (a perfectly inelastic collision). By conservation of momentum:

m₁u₁ + m₂u₂ = (m₁ + m₂)v
(2.0 × 3.0) + (1.0 × 0) = (2.0 + 1.0)v
6.0 = 3.0v
v = 2.0 m s⁻¹

Kinetic energy before: ½ × 2.0 × 3.0² = 9.0 J. Kinetic energy after: ½ × 3.0 × 2.0² = 6.0 J. The 3.0 J difference is lost to heat and sound — momentum is conserved, kinetic energy is not, confirming this is an inelastic collision.

Common mistakes

• Applying “force = rate of change of momentum” to a rocket’s own momentum alone and treating that as the fix for its changing mass — this omits the momentum carried away by the ejected fuel. F = ma still applies to the rocket itself provided the thrust produced by the escaping exhaust is included as an external force; the rate-of-change-of-momentum form only avoids this issue when it is applied to the total momentum of the closed rocket-plus-exhaust system.
• Assuming kinetic energy is always conserved in a collision — only true for elastic collisions; always check by comparing kinetic energy before and after if the collision type isn’t stated.
• Forgetting that momentum is a vector — in two-dimensional collision problems, momentum must be conserved separately in each perpendicular direction, not just as a total magnitude.
• Describing terminal velocity as “constant speed with constant forces still increasing” — at terminal velocity, resultant force is zero; drag and weight are equal and opposite, not still changing.

Quick revision checklist

• F = ma and the direction relationship between force and acceleration
• Newton’s three laws, stated precisely (not just “equal and opposite reactions”)
• Momentum p = mv, and force as rate of change of momentum
• Weight = mg, distinguished from mass
• Terminal velocity as the point where drag equals weight
• Conservation of momentum, and the elastic vs. inelastic distinction using kinetic energy

Related resources

• Kinematics: Equations of Motion — the motion equations this topic applies force to
• Forces, Density and Pressure — the next AS topic
• Work, Energy and Power — kinetic energy defined and used in depth
• Cambridge AS & A Level Physics hub

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.