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Question

Two small balls A and B, each of mass m, are joined rigidly by a light horizontal rod of length L. The rod is clamped at the centre in such a way that it can rotate freely about a vertical axis through its centre. The system is rotated with an angular speed ω about the axis. A particle P of mass m kept at rest sticks to the ball A as the ball collides with it. Find the new angular speed of the rod.

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Solution

Here, Net torque = 0

Since the angular momentum is conserved.

So, I1w1=I2w2

2mL2.w=3mL2w

w=23w


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