The angular momentum of a rotating body is 'L'. When the frequency of rotating body is tripled and its kinetic energy is made one-third, the new angular momentum becomes

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The kinetic energy of a rotating body is given by $K = \frac{1}{2} L ω$

Since $ω = 2 π f$ , we can write $K = π L f$

Therefore, the angular momentum is $L = \frac{K}{π f}$

Given that the new frequency is $f^{'} = 3 f$ and the new kinetic energy is $K^{'} = \frac{K}{3}$

The new angular momentum is $L^{'} = \frac{K ^{'}}{π f ^{'}} = \frac{\frac{K}{3}}{π ( 3 f )} = \frac{1}{9} \frac{K}{π f} = \frac{L}{9}$

Answer: $\frac{L}{9}$

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