A large ball (radius=0.75m) with an initial rotation speed of 36rad/s is rolling up an incline without slipping . If 54m up the incline it has slowed to a rotation rate of 12rad/s, what is its angular and linear deceleration? How far up the ramp will it go before starting to roll back down? How long will it take the ball to roll back down to its initial starting position?

Physics for Scientists and Engineers: Foundations and Connections
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ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter12: Rotation I: Kinematics And Dynamics
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Problem 35PQ: In testing an automobile tire for proper alignment, a technicianmarks a spot on the tire 0.200 m...
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A large ball (radius=0.75m) with an initial rotation
speed of 36rad/s is rolling up an incline without slipping .
If 54m up the incline it has slowed to a rotation rate of
12rad/s, what is its angular and linear deceleration? How
far up the ramp will it go before starting to roll back
down? How long will it take the ball to roll back down to
its initial starting position? 

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