A hemispherical bowl of radius R is set rotating about its axis of symmetry which is kept vertical. A small block kept in the bowl rotates with the bowl without slipping on its surface. If the surfaces of the bowl is smooth, and the angle made by the radius through the block with the vertical is `theta`, find the angular speed at which the bowl is rotating.

Explanation

To solve the problem of finding the angular speed at which a hemispherical bowl of radius \( R \) is rotating, with a small block inside it making an angle \( \theta \) with the vertical, we can follow these steps:

### Step 1: Understand the Forces Acting on the Block
The block experiences two main forces:
1. The gravitational force \( mg \) acting downwards.
2. The normal force \( N \) exerted by the surface of the bowl, acting perpendicular to the surface.

### Step 2: Analyze the Geometry
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