A uniform circular disc can rotate freely about a rigid vertical axis through its centre `O.A` man stands at rest at `A` on the edge due east of `O`. The mass of the disc is `22` times the mass of the man. The man starts walking anticlockwise. When he reaches the point `A` after completing one rotation relative to the disc, what will be his position ?

Answer

`60^@` east of south, `30^@` south of east

Explanation

As no enternal torque is acting So its angular momentum will remain conserve. Since man is walking anticlockwise disc will rotate clockwise.
`I_(1) omega_(1) = I_(2) omega_(2)`
let `theta` is angle moved by disc, so in one rotation angle moved by man is `(2 pi - theta)`
`mR^(2)((2pi-theta))/(T) =(1)/(2)(22m) R^(2) (theta)/(T)`
`theta = (pi)/(6)` or `30^@`.
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