# Homework Help: Bowling ball rotation

1. Mar 24, 2004

### Xamfy19

a bowling ball is given an initial speed vo on an alley such that it initially slides without rolling. The coefficient of friction between ball and alley is u.

find the speed of the ball's center of mass vCM at the time pure rolling motion occurs.

i used (1/2)mvo^2=(1/2)mVCM^2 + (1/2)Iw^2
I=(2/5)mr^2

i got vo^2=(7/5)v^2 which is wrong.

how do i solve this problem?

2. Mar 24, 2004

### Staff: Mentor

It looks like you are assuming that energy is conserved. Why?

3. Mar 25, 2004

### Xamfy19

Well, I think the friction must have consumed certain energy too. However, I have no idea how to incorporate it into the equation.

4. Mar 25, 2004

### Staff: Mentor

There are several ways to attack this problem. Here's one way:

Picture what's happening. The ball starts with pure translational motion. The friction slows the translational motion, and starts the ball rotating. So write equations for the translational motion and for the rotational motion, due to the friction. The ball will slow down (but increase rotational speed) until the speed is just right to stop slipping.