Solution

The shaft ( radius R) spins with angular velocity $\omega$ , but the sleeve (bushing) is prevented from rotating by the counterweight. So at the contact surface between shaft and sleeve there is relative sliding made of two perpendicular components:

1. a circumferential component, from the shaft's rotation: $u = \omega R$
2. an axial component, from the sleeve's motion along the shaft: $v$ ( the steady-state velocity we want)

Since these