Question

- A wheel  is spinning with angular velocity ω=8rad/s. We drop a second identical ring exactly on top of the first. The two rings get stuck and start spinning together with a new angular velocity. How much is this angular velocity?

Answer 1

Let moment of inertia of each wheel = I

Therefore initial angular momentum of wheel = I×w

= 8I

Now , when another identical ring is dropped, total moment of inertia of system= I+I

= 2I

Using conservation of angular momentum

8I = 2I ×w_1

w_1 = 4 rad/sec

Therefore, new angular velocity of the system = 4 rad/sec

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