# A problem on rotation

The method suggested by the hints in that PDF is equivalent to the solution that @haruspex and I propose.
The constant @harsuspex said is it mgμ?

The constant @harsuspex said is it mgμ?
You have been helped quite a lot already. You should be able to use your knowledge and the help given to you to construct the solution from the ground up.

haruspex
Homework Helper
Gold Member
The constant @harsuspex said is it mgμ?
Does it matter what it is?

kuruman
In the steady-state situation, perhaps a new approach would be to view mass element ##dm## on the disk being in a static force field ##\vec F=\kappa \frac{(\vec{\omega}' \times \vec{r}'-\vec{\omega} \times \vec{s})}{\left| (\vec{\omega}' \times \vec{r}'-\vec{\omega} \times \vec{s}) \right |}##. The goal then is to find under what condition(s) the curl of this field is zero. The rationale is that when this is the case, the work done by the force field on ##dm## over the closed loop of a complete revolution would be zero. With ##\vec s=\vec d+\vec r## and ##\vec d## along the x-axis,$$\vec F=\kappa \frac{-(\omega '-\omega)y ~\hat x+[(\omega '-\omega)x-\omega d]~\hat y}{\sqrt{ [(\omega '-\omega)x-\omega d]^2+[(\omega '-\omega)y]^2 }}$$ $$\vec{\nabla} \times \vec F=\kappa \frac{(\omega '-\omega)~\hat z}{\sqrt{ [(\omega '-\omega)x-\omega d]^2+[(\omega '-\omega)y]^2 }}$$