Question
A small block of mass m is placed in a hemispherical bowl of radius r and bowl is set rotating about its axis of symmetry with angular velocity 
. Find the radius of circle in which block revolves and the angular position of block with vertical at equilibrium position while bowl is rotating.
Solution
Let, at equilibrium, the block be at A when the bowl rotates with angular velocity ω.
Let x = AN be the radius of circle in which block revolves.
The forces acting on the block are:
(i) Weight mg, in vertically downward direction.
(ii) Normal reaction N, along AO.
Resolve the components of N as shown in the figure above.
The component N cosθ balances the weight mg of the mass and component.
The component T sinθ provides the necessary centripetal force to revolve the block.
Thus,
Hence, the result.
Let x = AN be the radius of circle in which block revolves.
The forces acting on the block are:
(i) Weight mg, in vertically downward direction.
(ii) Normal reaction N, along AO.
Resolve the components of N as shown in the figure above.
The component N cosθ balances the weight mg of the mass and component.
The component T sinθ provides the necessary centripetal force to revolve the block.
Thus,
Hence, the result.
