Rotation Review problems 2006.2007

# Rotation Review problems 2006.2007 - 1. A billiard ball has...

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A billiard ball has mass M, radius R and a rotational inertia about the center of mass I cm = 2 / 5 MR 2 . The ball is struck by a cue stick along a horizontal line through the ball’s center of mass so that the ball initially slides with a velocity v o as shown above. As the ball moves across the rough billiard table (coefficient of sliding friction μ ), its motion gradually changes from pure translation through rolling with slipping to rolling without slipping. a) Develop an expression for the linear velocity v of the center of mass of the ball as a function of time while it is rolling with slipping. b) Develop an expression for the angular velocity ϖ of the ball as a function of time while it is rolling with slipping. c) Determine the time at which the ball begins to roll without slipping. d) When the ball is struck is acquires an angular momentum about the fixed point P on the surface of the table. During the subsequent motion the angular momentum about point P remains constant despite the frictional

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## This note was uploaded on 11/11/2008 for the course PH X taught by Professor Goodlore during the Spring '05 term at SouthArk.

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Rotation Review problems 2006.2007 - 1. A billiard ball has...

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