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Two particles A and B move anticlockwise in a horizontal plane on two concentric circles of equal radius r, with constant angular velocities 2*omega and omega respectively. Both start from the same point on the positive x-axis. Take omega = 3 rad/s and r = 2 m. Find the magnitude of the velocity of B relative to A at time t = pi/omega.

1. 18 m/s
2. 6 m/s
3. 8 m/s
4. 12 m/s

Correct answer: 18 m/s

Solution

At t = pi/omega, A is back on the +x axis with velocity (0, +12) and B is on the -x axis with velocity (0, -6); the relative velocity vB - vA = (0, -18), of magnitude 18 m/s.

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