Two particles move on a circular track in opposite directions with angular speeds 3 rad/s and 5 rad/s. Initially they are diametrically opposite. If they meet for the first time after π/N seconds, find N.
Physics · Circular Motion · relative angular velocity and radius of curvature
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Question

Two particles move on a circular track in opposite directions with angular speeds 3 rad/s and 5 rad/s. Initially they are diametrically opposite. If they meet for the first time after π/N seconds, find N.

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

G1 Physics · Accepted Answer

Initial angular separation is π rad. Since they move in opposite directions, relative angular speed is 3+5 = 8 rad/s. For the first meeting, relative angular displacement must reduce the initial separation π: 8t = π. Thus t = π/8 s and N = 8.