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Suppose we have a friction less table, with an arm, fixed at one end, and sufficiently long at the other end. we place a ball at any point along the arm. We place it not on the arm, but beside it. Then we rotate the arm at a constant angular velocity 'w'. If we observe from an inertial frame, do we see the ball accelerate? What is the equation of motion of the ball? Please refer to the polar expression of acceleration. Also note that the arm only provides a tangential contact force on the ball, and the ball is not constrained to move radially.
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