A billiards player strikes a cue ball at a height h above thecenter. The cue is
ID: 1751709 • Letter: A
Question
A billiards player strikes a cue ball at a height h above thecenter. The cue is level, moves with speed v0, and hasmass m. The cue ball has mass M.
a.) What is the physical principle used for calculating therotational speed?
b.) What is the final rotational speed of the cue ball? (Hint,what is the center of rotation?)
c.) Compute the torque that the cue applies to the billiard ballfor the three cases, h=R/2, h=0, h=-R/2. What is most advantageousvalue of h? Why? Which value corresponds to “backspin”?
Explanation / Answer
Giventhat the mass of cue ball is M Radiusof cue ball is R Initialspeed of stick ball is vo mass ofstick is m ----------------------------------------------------------------------------------- (a) Conservation of angular momentum is used to find theangular speed of the cue ball (b) Fromthe conservation of angularmomentum Total intial angular momentum = Total final angularmomentum (ball+ stick) (ball+ stick ) 0 + m*vo*h = I* m*vo*h= (2/5)M*R2* where the moment of inertia of the ball is I =(2/5)M*R2 about center then = m*vo*h / (2/5)M*R2 This is the rotational speed of the cue ball. (c) The torque depends on thedistace between the center of the ball and applied force bystick so themost advantageous value of h is R/2 h=-R/2. value corresponds to “backspin”Related Questions
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