A solid sphere is in purely rotational motion | vedclass

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(C) The angular momentum of a rotating body is given by $L = I\omega$,where $I$ is the moment of inertia and $\omega$ is the angular velocity.The rota

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$14$

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(C) The angular momentum of a rotating body is given by $L = I\omega$,where $I$ is the moment of inertia and $\omega$ is the angular velocity.The rotational kinetic energy is given by $K = \frac{1}{2} I \omega^2$.The ratio of angular momentum to kinetic energy is $\frac{L}{K} = \frac{I\omega}{\frac{1}{2} I \omega^2} = \frac{2}{\omega}$.Given the ratio $\frac{L}{K} = \frac{\pi}{22}$,we equate the two expressions:$\frac{2}{\omega} = \frac{\pi}{22}$.Substituting $\pi = \frac{22}{7}$ into the equation:$\frac{2}{\omega} = \frac{22/7}{22} = \frac{1}{7}$.Solving for $\omega$:$\omega = 2 	imes 7 = 14 \ rad/s$.Thus,the angular velocity of the sphere is $14 \ rad/s$.

$A$ solid sphere is in purely rotational motion about its diameter. The ratio of its angular momentum $(L)$ and kinetic energy $(K)$ is $\frac{\pi}{22}$. Find the angular velocity $(\omega)$ of the sphere. (Take $\pi = \frac{22}{7}$) (in $rad/s$)

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