# Object rolling down an incline

1. Jul 13, 2007

### Momentum09

1. The problem statement, all variables and given/known data

A solid sphere of radius 20cm is positioned at the top of an incline that makes 22 degrees angle with the horizontal. This initial position of the sphere is a vertical distance 1.8m above its position when at the bottom of the incline. Moment of inertia of a sphere with respect to an axis through its center is 2/3MR^2. Calculate the speed of the sphere when it reaches the bottom of the incline in the case where it slips frictionlessly without rolling.

2. Relevant equations

mgh = 1/2Iw^2 + 1/2mv^2

3. The attempt at a solution

I know how to calculate the speed when the object rolls down without slipping, but what do I do if it does? if there a formula? Thank you for your help!

2. Jul 13, 2007

### Staff: Mentor

If it slips without rolling then there is no rotational KE, just translational KE.

If it rolls without slipping then there is both rotational and translational KE. The are related by the condition for "rolling without slipping", which is: $v = \omega r$.

3. Jul 13, 2007

### Momentum09

Thank you so much!