Suppose in the previous problem, the child stays at rest on the platform and one of his friend throws a ball of mas `m_(1)` towards him with a velocity of `v` from a direction tangential to the platform and the child on the platform catches the ball. Find the angular velocity of the platform after he catches the ball.

Explanation

To solve the problem, we need to apply the principle of conservation of angular momentum. Here are the steps to find the angular velocity of the platform after the child catches the ball:

### Step-by-Step Solution:

1. **Identify the Initial Conditions:**
- The system consists of a child of mass \( m \) standing on a circular platform with moment of inertia \( I \) and radius \( r \).
- A ball of mass \( m_1 \) is thrown towards the child with a velocity \( v \) tangentially.

...