Mouse Jumps Onto An Exercise Wheel

[burnst14]

Homework Statement

The vertical exercise wheel in a mouse cage is initially at rest, but can turn without friction around a horizontal axis through the center of the wheel. The wheel has a moment of inertia I=0.0004kg m² and radius R = 0.06m An extremely smart pet mouse of mass m = 0.03 kg runs across her cage with initial speed v = 2 m/s, jumps onto the edge of her exercise wheel, holds on tightly, and rotates together with the wheel.

1. Determine the angular velocity of the "wheel plus mouse turning together" immediately after she jumps on.
2. Determine the maximum height of the mouse as she rides the wheel.

Homework Equations

The Attempt at a Solution

I solved the first one and got 7.09 rad/s by:
L = Rmv = Iω
0.06*0.03*2 = (0.0004+0.03*0.06²)ω
ω = 7.09 rad/s

However part 2, I can't wrap my head around. I have an answer packet, but it has already had a couple incorrect solutions in it so I'm not quick to trust it.
I tried 1/2Iω² = mgh

KE = 1/2(5.08E-4)(7.09)² = 0.03*9.81*h

where h is the maximum height and 0.03 kg is the mass of only the mouse because the wheel is a homogenous cylinder and has equal mass on all "sides".

I feel like I'm missing torque though.
Any ideas?

Thanks guys

 

[mfb]

The approach via energy conservation is good. Torque will vary along the ride, but you don't have to worry about that as energy is conserved and you can calculate it both before and after.

 

[burnst14]

So my answer is correct then? Or is my formula missing a piece?

Thanks!

 

[mfb]

I don't see a final answer, but ω and the approach look good. You should add units, however.