Three particles A, B and C start simultaneously from the same point and move in the same direction with periods 2 s, 3 s and 4 s respectively. If all three first meet again at the starting point after N seconds, find N.
Physics · Circular Motion · relative angular velocity and radius of curvature
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Question

Three particles A, B and C start simultaneously from the same point and move in the same direction with periods 2 s, 3 s and 4 s respectively. If all three first meet again at the starting point after N seconds, find N.

Physics · Circular Motion · relative angular velocity and radius of curvature

G1 Physics · Accepted Answer

For all three to be simultaneously back at the starting point, the elapsed time must be a common multiple of all three periods. The least such time is LCM(2,3,4) = 12 s. Hence N = 12.