Work needed to stop a rolling hoop

[IAmPat]

Homework Statement

A thin hoop of mass 7.8kg rolls on a horizontal floor with a speed (at its center of mass) of 0.23 m/s. How much work must be done on the hoop to bring it to a stop.

Homework Equations

m = 7.8kg
Vcm = 0.23m/s

KE = 1/2*m*Vcm + 1/2Iw²

I = m*r²

The Attempt at a Solution

So the work done on the hoop to increase its KE is positive, so the work needed to stop it would be the same, but negative.

KE = 1/2*m*Vcm + 1/2*I*w²
KE = 1/2*(7.8)*(0.23) + 1/2*(m*r²) * w²

This is all I have, I don't know how to find all the necessary variables when I'm only given the mass and velocity.

 

[ashishsinghal]

r is required, you can't do without that unless one of these is mentioned:
1. There is no or negligible angular velocity
2. The radius is negligibly small

 

[lewando]

First, you should use the correct equation:

KE = KE_{translational} + KE_rotational = (1/2)mv_cm² + (1/2)Iw²


You should know (and use) the relationship between the tangetial velocity of a rotating wheel and w. It is this: v = wr


From this, you can see that w and r can be free to be anything as long as their product is V. This is also why neither were mentioned in the problem.