How Does Friction Affect the Angular Momentum of a Bowling Ball?

[Kaln0s]

Homework Statement

This has 4 parts, I'm confident about 2.

1. The remaining problems involve a bowling ball with a uniformly distibuted mass of 6 kg and a radius of 0.20 m. The ball is initially thrown at a speed of 10 m/s, with a backspin of 6 rad/s (this means it has an angular velocity in the opposite direction of what it would have if it were rolling without slipping). The coefficient of static friction between the ball and bowling alley is 0.15, and the coefficient of kinetic friction is 0.10. What is the moment of inertia of the ball about its center, in kg m^2?

For this.. uniform distribution, MI = 2/5 MR² = 2/5 (6)(.2)² = 0.096 kg m².

2. For the bowling ball in problem 5, what is the magnitude of the frictional force (in N) acting on it as it is initially released?

0.1*6*10 = 6 N

It's the next 2 that I'm confused on..

Homework Equations

t = rFsin0

The Attempt at a Solution

3. What is the magnitude of the torque on the bowling ball, about its center, produced by the frictional force? Your answer should be in Nm.

For this I want to use T = rFSin(theta), but I don't know the angle and am confused.

4. So, as the ball slides down the alley, the torque due to friction slows down its backspin and makes it start spinning the other way until it is rolling without slipping. At the same time, the friction slows down the ball's translational motion as well. What time elapses between the ball's initial release and when it begins rolling without slipping? Your answer should be in seconds.

I have no idea how to do this part.

 

[Delphi51]

For #3, the angle between the force of friction (horizontal) and the moment arm which is a radius to the point of contact (vertical) is 90 degrees.

If it was a linear problem you would use F = ma to find the deceleration and then
V = Vi + at to find the time. For rotational motion, use the rotational analogs to these formulas.