Express the kinetic energy of a rotating body in terms of its angular momentum.
Q 99
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The kinetic energy of a body of moment of inertia I and rotating with a constant angular velocity $\omega$ is
$
\mathrm{E}=\frac{1}{2} I \omega^2
$
The angular momentum of the body, $L=\mid \omega$.
$
\therefore \mathrm{E}=\frac{1}{2}(I \omega) \omega=\frac{1}{2} L \omega
$
This is the required relation.
$
\mathrm{E}=\frac{1}{2} I \omega^2
$
The angular momentum of the body, $L=\mid \omega$.
$
\therefore \mathrm{E}=\frac{1}{2}(I \omega) \omega=\frac{1}{2} L \omega
$
This is the required relation.
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