A.2 Forces and momentum

Newton's laws

• First law: an object keeps its velocity unless a net force acts on it.
• Second law: F_net = ma, or more generally F_net = Δp / Δt.
• Third law: forces come in pairs. The two forces are of the same type, equal in magnitude, opposite in direction and act on different objects.

Common forces

• Weight W = mg, with g = 9.81 m s⁻² near the Earth's surface.
• Dynamic friction f = μd R and the limit of static friction f ≤ μs R, where R is the normal reaction.
• On a slope of angle θ the component of the weight along the slope is mg sin θ and perpendicular to it mg cos θ.
• Draw a free-body diagram before writing any equation.

Momentum and impulse

• Linear momentum p = mv (vector, N s).
• Impulse J = FΔt = Δp. On a force against time graph the impulse is the area under the graph.
• In an isolated system the total momentum is conserved.
• Elastic collision: kinetic energy is conserved. Inelastic: some kinetic energy is transferred to other forms. If the objects stick together the collision is perfectly inelastic.

Circular motion

• Centripetal acceleration a = v² / r = ω²r, directed towards the centre.
• The centripetal force F = mv² / r is the net force towards the centre, not an extra force on the free-body diagram.