Angular Momentum

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I know this sounds weird, but I studied QM and GR before classical physics, and I'm just lost when it comes to angular momentum problems.

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.
 

Answers and Replies

  • #2
Astronuc
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The friction is a product of [itex]\mu_k[/itex] and the weight (mg) or normal force to the horizontal surface.

The friction causes the ball to decelerate in terms of linear or translational motion while all causing the wall to increase in rotational velocity, i.e. the friction induces angular acceleration.

For moments of inertia, see - http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html, and
http://hyperphysics.phy-astr.gsu.edu/hbase/isph.html#sph

The ball stops sliding when Vcm = [itex]\omega[/itex]r, i.e. the tangential speed at the radius = translational speed.
 

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