The ends of thin threads tightly wound on the axle of radius r of the Maxwell disc are attached to a horizontal bar. When the disc unwinds, the bar is raised to keep the disc at the same height. The mass of the disc with the axle is equal to m, the moment of inertia of the arrangement relative to its axis is I. Find the tension of each thread and the acceleration of the bar.

Explanation

For equilibrium of the disc and axle
`2T-mg` or `T=mg//2`
As the disc unwinds, it has an angular acceleration `beta` given by
`Ibeta=2Tr` or `beta=(2Tr)/(I)=(mgr)/(I)`
The corresponding linear acceleration is `rbeta=w=(mgr^2)/(I)`
Since the disc remains stationary under the combined action of this acceleration and the acceleration `(-w)` of the bar which is transmitted to the axle, we must have
`w=(mgr^2)/(I)`