Circular Motion, Gravitation and Oscillations
What the exam tests
This domain covers angular motion, centripetal force, gravitational fields and orbits, simple harmonic motion (SHM), damping and resonance. Expect questions linking force diagrams to circular motion and energy or timing calculations to oscillations.
Core rules
- Angular velocity ω = 2π/T; linear speed v = rω; centripetal acceleration a = v²/r = rω².
- Centripetal force is the resultant force towards the centre, not an extra force in the diagram.
- Gravitational field strength g = GM/r²; orbital speed v = √(GM/r), where r is measured from the centre of the central body.
- SHM requires acceleration proportional to displacement and directed towards equilibrium: a = −ω²x.
- For a mass-spring system T = 2π√(m/k); for a simple pendulum T = 2π√(l/g).
- Damping removes energy; light damping decays amplitude gradually, critical damping returns quickest without oscillation, and forced resonance occurs near the natural frequency.
Worked example
A 0.50 kg mass on a spring of force constant 200 N m⁻¹ oscillates with amplitude 0.10 m. Find the period and maximum speed. ω = √(k/m) = √(200/0.50) = 20 rad s⁻¹. T = 2π/ω = 2π/20 = 0.31 s. Maximum speed vmax = ωA = 20 × 0.10 = 2.0 m s⁻¹. At maximum speed the mass passes through equilibrium, where the acceleration is zero and all energy is kinetic.
Traps
Adding centripetal force as well as tension or weight; using the Earth's surface radius instead of the orbital radius; treating SHM acceleration as constant; confusing amplitude with displacement; assuming resonance always increases amplitude without limit in a damped system.