A-Level Kinematics of uniform circular motion and centripetal acceleration: worked solution

Question

(b) A university researcher plans to reproduce Fizeau's experiment at a reduced size, setting the gap between the mirror and the toothed wheel at 92.4 m. The wheel he intends to build will have 16 gaps between its teeth. Show that the wheel must be rotated at roughly three million revolutions per minute (rpm).

Light makes a round trip 2d = 2(92.4) = 184.8 m, taking t = 2d/c = 184.8/(3.0×10⁸) = 6.16×10⁻⁷ s. With 16 gaps there are 16 tooth+gap units per revolution; the first eclipse occurs when the wheel turns by half a unit = 1/(2×16) = 1/32 of a revolution during time t. So f = (1/32)/t = 1/(32 × 6.16×10⁻⁷) = 5.07×10⁴ rev s⁻¹. In rpm: 5.07×10⁴ × 60 = 3.0×10⁶ rpm.