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