Rotational kinetic energy of a given body abo | vedclass

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(D) The rotational kinetic energy $(K_r)$ of a body is given by the formula $K_r = \frac{1}{2} I \omega^2$,where $I$ is the moment of inertia and $\om

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$(Time\ period)^{-2}$

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(D) The rotational kinetic energy $(K_r)$ of a body is given by the formula $K_r = \frac{1}{2} I \omega^2$,where $I$ is the moment of inertia and $\omega$ is the angular velocity.We know that the angular velocity $\omega$ is related to the time period $(T)$ by the relation $\omega = \frac{2\pi}{T}$.Substituting this into the expression for rotational kinetic energy,we get $K_r = \frac{1}{2} I \left( \frac{2\pi}{T} \right)^2$.Simplifying this,we get $K_r = \frac{1}{2} I \frac{4\pi^2}{T^2} = \frac{2\pi^2 I}{T^2}$.Since $I$ and $\pi$ are constants for a given body rotating about a fixed axis,we have $K_r \propto \frac{1}{T^2}$.Therefore,$K_r \propto (Time\ period)^{-2}$.

Rotational kinetic energy of a given body about an axis is proportional to

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