A-Level Physics: Circular Motion and SHM

Circular motion and simple harmonic motion open the second year of A-Level Physics, and they share a mathematical spine — angular frequency — that this quiz keeps deliberately visible across both halves.

The circular-motion questions apply the core relations with concrete values: centripetal acceleration as v²/r for a particle on a half-metre circle, the centripetal force keeping a 1200 kg car on a 50-metre bend (5400 N, worked in full), and linear speed from angular speed and radius. These are the calculations that reappear inside gravitation and magnetic-field problems later, which is why the explanations spell out every substitution.

The SHM questions cover the defining conditions first — restoring force proportional to displacement and directed toward equilibrium, tested as a statement selection — then the standard quantitative repertoire: maximum velocity as ωA for a given amplitude and frequency, the period of a 1.6-metre pendulum, and the mass-spring system examined twice: once for period and total energy (period 0.31 s and total energy ½kA² = 0.10 J, against a maximum-acceleration distractor set at half the true value), and once for the frequency scaling when the mass doubles — the inverse-root-two proportionality reasoning exams reward over recalculation.

The energy-interchange question locates where kinetic equals potential energy (at A/√2, derived rather than memorised), and a resonance scenario-selection closes the set with the driving-frequency-matches-natural-frequency criterion.

All values are given in the questions, matching the data-booklet exam format, and every explanation privileges the proportionality argument where one exists — the faster, safer route under time pressure.

• Calculate centripetal acceleration and force with given values
• State the defining conditions of simple harmonic motion precisely
• Apply ωA and period formulae for pendulum and mass-spring systems
• Use proportionality reasoning when masses or lengths are scaled
• Locate energy interchange points in SHM and identify resonance conditions

Topic scope follows the A-level physics content — as organised, for example, in section 3.6.1 (Periodic motion) of the AQA A-level Physics (7408) specification: uniform circular motion, simple harmonic motion, pendulum and mass-spring systems, energy in SHM, damping and resonance.