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## Homework Statement

A sphere is moving along a lane. It slides initially then rolls. The initial speed is [tex]V_{cm}[/tex] and initial angular speed [tex]\omega[/tex]. The coefficient of kinetic friction between the ball and the lane is also known. The kinetic frictional force acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When [tex]V_{cm}[/tex] has decreased enough and [tex]\omega[/tex] has increased enough, the ball stops sliding and rolls smoothly.

Given: [tex]V_{cm}[/tex] initial, [tex]\omega[/tex] initial, [tex]\mu[/tex]k.

What is [tex]V_{cm}[/tex] in terms of [tex]\omega[/tex]?

While the ball is sliding, what is the ball's linear and angular acceleration?

How Long does the ball slide?

How Far does the ball slide?

What is the linear speed of the ball when smooth rolling begins?

## Homework Equations

We know since it is sliding initially that the initial angular speed is zero

R[tex]f_{s}[/tex] = [tex]I_{cm}[/tex][tex]\alpha[/tex]

Beyond this, I'm lost.