Theme A · Space, Time and Motion · SL + HL · 10 hours

A.2 Forces and Momentum

How can knowledge of forces and momentum predict the behaviour of interacting bodies?

Forces are interactions between bodies, and Newton's three laws tell us precisely how those interactions determine motion. The first law defines what inertia means; the second connects force to the rate of change of momentum; the third tells us that forces always come in pairs of equal magnitude acting on different bodies. Mastering free-body diagrams — drawing every force correctly, then finding the resultant — is the practical skill that runs through the rest of the course.

Momentum is conserved whenever the net external force on a system is zero. This is one of the most powerful principles in all of physics: it applies from billiard balls to rocket engines to particle accelerators. Impulse — the product of force and time — connects force to the change in momentum, and understanding this connection explains why a longer contact time reduces the peak force in a collision (the engineering principle behind crumple zones, airbags, and sports padding).

A 0.15 kg cricket ball travelling at 25 m s⁻¹ is caught by a fielder who brings it to rest in 0.25 s. Calculate the average force exerted on the ball, and explain why the fielder "gives" with the catch.

Key equations

F = ma (constant mass); F = Δp/Δt (general form, allows for changing mass)

Impulse: J = FΔt = Δp

Centripetal acceleration: a = v²/r = ω²r = 4π²r/T²

Hooke's law: F_H = −kx | Stokes drag: F_d = 6πηrv | Buoyancy: F_b = ρVg

What students must understand

Newton's three laws of motion — applied to both translational equilibrium and accelerating systems
Forces as interactions between bodies; free-body diagrams for 1D and 2D situations
Contact forces: normal force, static and dynamic friction (with coefficients μ_s and μ_d), tension, elastic restoring force, viscous drag, buoyancy
Field forces: gravitational (F_g = mg), electric, and magnetic
Linear momentum p = mv is conserved unless an external resultant force acts
Impulse J = FΔt equals the change in momentum
Elastic collisions (KE conserved) vs inelastic collisions (KE not conserved); explosions
Centripetal acceleration directed towards the centre; centripetal force causes direction change, not speed change
Angular velocity ω and linear speed v = ωr; period and frequency of circular motion

Linking questions

How do collisions between charge carriers and atomic cores produce thermal energy? → B.1, B.5
How do electrical and magnetic forces change the motion of charged particles? → D.2, D.3
How does a restoring force acting on a particle produce simple harmonic motion? → C.1
Why is no work done on a body moving along a circular trajectory? → A.3
How is conservation of momentum relevant to a nuclear power station? → E.4

Practice worksheets

Forces worksheets — 9 worksheets · 5 with answers
Momentum worksheets — 5 worksheets · 5 with answers

Labs

Forces & Circular Motion labs — instruction sheets from the Physics Lab Library

Video Support

Khan Academy

Systems and Objects | Dynamics

Contact Forces | Dynamics