PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Four identical cars—P, Q, R, and S—move around four different circular test tracks. All four cars complete exactly one revolution every 18 s, but each track has a different radius:
• P: 30 m • Q: 45 m • R: 60 m • S: 75 m
(a) Derive an algebraic relationship between the magnitude of centripetal acceleration and track radius for any car that completes one revolution in a fixed time interval T=18s.
(b) Using your expression from part (a), calculate the centripetal acceleration of each car. Provide answers in m s⁻² with an appropriate number of significant figures.
(c) Rank the cars from greatest to least centripetal acceleration and justify the ranking without re-calculating numerical values.
(d) Suppose car P’s driver wants to double the magnitude of the centripetal acceleration without shortening the period. Determine the new radius required and explain your reasoning.