Question

In the figure here, a 31 kg child stands on the edge of a stationary merry-go-round of radius 2.4 m. The rotational inertia of the merry-go-round about its rotation axis is 120 kg·m². The child catches a ball of mass 1.4 kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity of magnitude 9 m/s, at angle φ = 49 ˚ with a line tangent to the outer edge of the merry-go-round, as shown. What is the angular speed of the merry-go-round just after the ball is caught?

Answer 1

The sum of the initial angular momenta will be equal to the final angular momenta.

The initial angular moment is only due to the ball.

To calculate the final angular momentum, and hence the final angular velocity, we need to find the moment of inertia of the combined masses.

Now, the initial and final angular momentum will be equal, as per the principle of conservation of angular momentum.