On a level billiards table a cue ball, initially at rest at point O on the table, is struck so that it leaves the cue stick with a center-of-mass speed v_0 and a "reverse" spin of angular speed w_0. A kinetic friction force acts on the ball as it initially skids across the table.
a) Using conservation of angular momentum, find the critical angular speed w_c such that, if w_0 = w_c, kinetic friction will bring the ball to a complete (as opposed to momentary) stop.
b)f w_0 is 20% smaller than w_c i.e., w_0 = 0.80w_c, determine the ball's center of mass velocity (v_CM) when it starts to roll without slipping.
A uniform ladder of mass M and length L leans at an angle theta against a frictionless wall. If the coefficient of static friction between the ladder and the ground is U, determine a formula for the minimum angle at which the ladder will not slip.
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1 answer