Answer to Question #92557 in Classical Mechanics for Sho

Question

A spherical billiard ball of uniform density has mass m and radius R , and moment of inertia about the center of mass Icm = (2 / 5)mR^2. The ball, initially at rest on a table, is given a sharp horizontal impulse by a cue stick that is held an unknown distance h above the centerline. The force applied by the cue to the ball is sufficiently large that you may ignore the friction between the ball and the table during the impulse (as any pool player knows). The ball leaves the cue with a given speed v0 and an angular velocity w0. Because of its initial rotation, the ball eventually acquires a maximum speed of (9/7)v0.

a) Briefly explain why angular momentum is conserved about any point along the line of contact between the ball and the table after the impulse.
b) Use conservation of angular momentum about any point along the line of contact between the ball and the table, and your results from part a), to find the ratio h / R.

Answer 1

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