A solid cylinder of mass 'M' and radius 'R' is rotating along its axis with angular velocity `omega` without friction. A particle of mass 'm' moving with velocity v collides aganist the cylinder and sticks to its rim. After the impact calculate angular velocity of cylinder .

Explanation

To solve the problem, we will use the principle of conservation of angular momentum. Here are the steps to find the angular velocity of the cylinder after the particle sticks to its rim.

### Step 1: Identify the initial angular momentum of the system
The initial angular momentum of the solid cylinder can be calculated using the formula:
\[ L_{initial} = I_{cylinder} \cdot \omega \]
where \( I_{cylinder} \) is the moment of inertia of the solid cylinder, given by:
\[ I_{cylinder} = \frac{1}{2} M R^2 \]
Thus, the initial angular momentum of the cylinder is:
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