A hollow bowling ball of mass M = 3 kg and radius R = 20 cm is thrown across a f

Question

A hollow bowling ball of mass M = 3 kg and radius R = 20 cm is thrown across a frictionless surface with a translational speed of 6.0 m/s. Initially the ball is not rolling across the surface, i.e. its motion is only translational. Some time later, the ball encounters a rough surface which instantly causes it to rotate without slipping, a condition which allows us to relate the translational and rotational motions of the ball using ? = VCM / R, where VCM is the velocity of the center of mass. What is the translational velocity of the center of mass in m/s after the bowling ball encounters the rough surface?

Explanation / Answer

conservation of energy I =2/3 M R^2 1/2 m v^2 = 1/2 mv^2 + 1/2 I w^2 3*6^2 = 3*v^2 + (2/3*3*.2^2) * (v/.2)^2 solve for v v=4.65 m/s

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