A kid of mass M stands at the edge of a platform of radius R , which is free to rotate about its axis. The moment of inertia of the platform is I . The system is initially at rest when a friend tosses a ball of mass m , and the kid catches it. If the ball's velocity is v horizontally along the tangent to the platform's edge at the moment it is caught, determine the angular speed of the platform following the event.

Step-by-step solution

By the principle of conservation of angular momentum about the axis of rotation of the platform, the initial angular momentum of the system is equal to the final angular momentum. The initial angular momentum of the system is entirely due to the ball, as the platform and the kid are initially at rest. Since the ball is moving horizontally along the tangent to the edge of the platform of radius R , its angular momentum is: L_i = mvR After the kid catches the ball, the platform, the kid, and the ball rotate together