Question

A horizontal uniform disc can rotate freely on a rigid vertical axis passing through its centre $O$. A man stands at rest at the edge of the disc at a point $A$. The mass of the disc is $22$ times the mass of the man. The man starts walking along the edge of the disc anticlockwise. When he reaches $A$ after completing one rotation relative to the disc, find the angle the disc has rotated through.

Answer 1

A horizontal uniform disc can rotate freely on rigid vertical axis passing through in the centre

From the law of conservation of angular momentum,

$I_1{w}_1=I_2{w}_2\frac{1}{2}\left(22m\right)R^2\left(\frac{Q}{I}\right)=m{R}^2\frac{(2\pi -\theta )}{t}$

Solving,

$11m{R}^2\frac{\theta }{t}=m{R}^2\frac{(2\pi -\theta )}{t}11\theta =2\pi -theta12\theta =2\pi 6\theta =\pi \theta =\frac{\pi }{6}=30°$