Total energy supplied to a flyball governor

[Bugsy23]

Homework Statement

A flyball governor has an angular speed of 8.10 rad s^-1. Find the total energy supplied to the flyball governor in order for it to reach this angular speed

Homework Equations

Kinetic energy=rotational energy+translational energy

translational energy=(1/2)m*v^2, where v is the speed of the body's centre of mass

The Attempt at a Solution

I've already calculated the rotational energy, but I don't know if the centre of mass of the body refers to the centre of mass of the device itself, which would be the spindle, in which case the translational energy should be zero, as the device is not moving through space; or whether it refers to the centres of mass of the individual masses at the ends of the arms, which are moving through space. Can someone help clarify this? Thanks

 

[bobred]

I would say that there is no linear motion only rotational, I think gravitational potential energy should be included

$$E=\frac{1}{2}I\omega^2+mgh$$

James