Two particles start together and move in the same direction around a circle with periods 4 s and 6 s. During the first 24 s, excluding t = 0 but including t = 24 s, if they meet N times, find N.
Physics · Circular Motion · relative angular velocity and radius of curvature
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Question

Two particles start together and move in the same direction around a circle with periods 4 s and 6 s. During the first 24 s, excluding t = 0 but including t = 24 s, if they meet N times, find N.

G1 Physics · Accepted Answer

Angular speeds are π/2 and π/3 rad/s, so relative angular speed is π/6 rad/s. The reunion period is T_rel = 2π/(π/6) = 12 s. Therefore they meet again at t = 12 s and t = 24 s. Excluding t=0, the number of meetings is N = 2.