Question about rotation w/ an additioanl object.

[hakujin]

First, while this is "homework" related I'm not seeking any direct answers. I'm stuck on a concept that I'm not sure even exists.

In short I've got a rotating disk with a weight at the edge with "an initial" ω. If that object was to decrease the distance towards the center, would the ω change and if so why?

The phrase "an initial" led me to believe that there was a starting force or torque which would remain constant which was required to not only rotate the mass of the disk but compensate for the mass at the edge of the disk. If that's true, given the mass at the edge has any factor at all on the needed initial energy/force/torque, I couldn't figure out how to calculate it. I check over my book and am completely missing it.

I assumed the mass at the edge would have be a factor since it's basically a m*g*d Newton force down (since the disk is horizontal in this situation), but I don't know how to calculate the needed force to create the initial ω.

I figured it would be something to the effect of... g[(mass of the disk)+(mass of the object*distance)] but that's the best I've got since mainly what we've done is bridge based problems an rotation around a fixed point.

If anything, a jumping off point on terminology to look up would be a big help.

 

[Simon Bridge]

If a rigid mass distribution is rotated about anywhere other than the center of mass, then it will wobble unless there is a balancing force applied. In 3D the disk+mass will also try to precess. This is how wheel-balancing machines (you know: when you get a new tire fitted?) work.

It would be an easier problem if there were two small masses on the rim, diametrically opposite each other, and they were both drawn closer to the center at the same time... so I suspect that you are overthinking things.

I suppose you need to decide if energy is being supplied to the configuration.

 

[mfb]

If that object was to decrease the distance towards the center, would the ω change and if so why?

Assuming your disk is fixed to rotate in the horizontal plane around its geometric center, without external torques, ω would increase as the moment of inertia reduces and the product of both is conserved.

 

[Simon Bridge]

That was my take - it's the ice-skater demo all over again.
When I was a kid there was this huge round-a-bout that we'd push up to speed then jump on. We'd start close to the edge and walk all over it ... I'm picturing something like that with a kid as the small mass.