# Homework Help: Angular speed of a toy train

1. Nov 13, 2005

### ViewtifulBeau

A toy train track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis as shown in the figure above. The mass of the wheel plus track is 3.59 kg and the radius is 1.79 m. Ignore the mass of the spokes and hub. A toy train of mass 0.203 kg is placed on the track and, with the system initially at rest, the electric power is turned on. The train reaches a steady speed of 0.551 m/s with respect to the track. What is the angular speed of the wheel?

I found the momentum of the train and used conservation of momentum and applied it to the track. I have a question though. What two momentums should I be conserving? should it be the ( masses of the entire train-track system) * w =(mass of the train only) *(given velocity (converted to w))?

2. Nov 13, 2005

### ViewtifulBeau

w(t) = .30782 = (velocity/circumference) * 2*pi
I(t) = .65043 = m(t) * radius^2
I(system) = 12.15315 = (m(w)+m(t)) * (radius)^2
w(system) = w(t)*I(t) / I(system)
= .0165