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Standard XII

Physics

The 'e' Equation

Two small bal...

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, $I_{1} w_{1} = I_{2} w_{2}$

$2 m L^{2} . w = 3 m L^{2} w^{'}$

$\Rightarrow w^{'} = \frac{2}{3} w$

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Here, Net torque = 0 Since the angular momentum is conserved. So, I1w1=I2w2 2mL2.w=3mL2w′ ⇒w′=23w

Here, Net torque = 0

Since the angular momentum is conserved.

So, $I_{1} w_{1} = I_{2} w_{2}$

$2 m L^{2} . w = 3 m L^{2} w^{'}$

$\Rightarrow w^{'} = \frac{2}{3} w$