First slide

Angular momentum

Question

The kinetic energy of an object rotating about a fixed axis with angular momentum L = I $ω$ can be written as

Easy

A

$K = \frac{L^{2}}{2 I}$
B

$K = \frac{2 L^{2}}{I}$
C

$K = \frac{L^{2}}{I}$
D

$K = \frac{\sqrt{2} L^{2}}{I}$

Solution

$\begin{array}{l} K = \frac{1}{2} I ω^{2}, L = I ω \Rightarrow ω = \frac{L}{I} \\ K = \frac{1}{2} I . {[\frac{L}{I}]}^{2} = \frac{L^{2}}{2 I} \end{array}$

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