# Rotational motion- potential and kinetic energy

1. Nov 14, 2014

### oxymoron man

http://i.imgur.com/0RtN9Ui.png?1

I am trying to find the linear velocity of the sphere as it leaves the cliff.

2. Relevant equations:
Moment of inertia of a sphere: I= 2/5 mr2

3. My attempt at a solution:

I know that I am supposed to solve this through the conservation of energy, but would I not have to account for friction somehow since it is rolling without slipping? I know how to find the kinetic and potential energies at both points but the solutions manual (i know, i know, i cheated) says nothing about accounting for the non-conservative force of friction that is necessary for rolling without slipping.
Either way, without friction I have

U-initial: 0
K-initial= 1/2 mv^2+(1/2)*(2/5*m*r^2)*v^2/r^2
k-initial= 1/2 mv^2+1/5 mv^2
k-initial: 7/10 mv^2

and for
U-final: mgh
K-final: 7/10 mvfinal^2

Could i just set these equal to each other and get the answer? No friction needed?

2. Nov 14, 2014

### Staff: Mentor

You're doing fine. Since the sphere is rolling without slipping, only static friction is involved. Static friction does no work because there's no relative motion. You start with some initial KE and lose some to gravitational PE as you've stated. No energy is lost due to friction.