- #1

PrettyLights

- 7

- 0

## Homework Statement

A bowling ball is released with speed V and no rotational kinetic energy. After a period of sliding and rotating, the ball enters pure rotational motion. The coefficient of friction between the ball and the ground while sliding is Uk.

a. Show that the rotational acceleration of the ball during the initial period of diluting is alpha=5gUk/2R, where g is the acceleration due to gravity and r is the radius of the ball (a solid sphere).

b. Show that when sliding finishes and rolling begins, the speed of the center of mass is Vc=5V/7

## Homework Equations

Rotational Kinetic Energy= 1/2IW^2

Force due to friction= Ukmg

Kinetic Energy= 1/2mv^2

## The Attempt at a Solution

I tried this problem from the angle of energy conservation but it quickly gets complicated. I tried to work from:

Potential energy of the ball + energy lost due to friction + Rotational energy = Total Kinetic, and then subbing in I and solving for V, plugging V into w=v/R and then l x V = alpha. Any help is appreciated.