How Does Wheel Radius Affect Rotational Kinetic Energy?

[truho]

Homework Statement

You attach a mass M to a string and wind the string around the circumference of a wheel. The wheel has two hubs with radii R1 and R2 with R2 > R1. You perform two experiments. First you wind the string around the smaller radius wheel and allow the mass to fall a distance h. In the second experiment you wind the string around the larger radius wheel and allow the mass to fall a distance h. Rank the rotational kinetic energy Krot of the wheel for each experiment.

Homework Equations

1/2I(ω^2)

The Attempt at a Solution

Basically I was thinking that ω is independent of the radius so they would be equal
but then if I=m(r^2) and ω = v/r then
I(ω^2)=1/2m(r^2)(v^2/r^2) and the r's cancel out giving us rotational kinetic energy = 1/2mv
So would the rotational kinetic energies be equal or would 1 be larger than the other?

 

[gneill]

Think about energy conservation. Where does the energy come from to turn the wheel?

 

[truho]

Wouldn't it have came from the potential energy mgh?

 

[gneill]

Wouldn't it have came from the potential energy mgh?

Is that a guess?

 

[truho]

haha alright, I think I got it, thanks