Question 535: Centre of Mass and Rotational Motion

Question

A rotating body has angular momentum ' $L$ '. If its frequency is doubled and kinetic energy is halved, its angular momentum will be

Accepted Answer

Angular momentum of a particle performing UCM
$$\mathrm{L}=\mathrm{I} \omega\quad	ext{.... (i)}$$
Kinetic energy, $\mathrm{k}=\frac{1}{2} \mathrm{I} \omega^2\quad	ext{... (ii)}$
$$	herefore\quad\mathrm{L}=\frac{2 \mathrm{k}}{\omega}\quad	ext{...[From (i) and (ii)]}$$
$$\begin{aligned}
	herefore\quad& \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{\mathrm{k}_1}{\mathrm{k}_2} 	imes \frac{\omega_2}{\omega_1} \
& \frac{\mathrm{~L}}{\mathrm{~L}_2}=\frac{1}{\frac{1}{2}} 	imes \frac{2}{1} \quad	ext{... (given)}\
	herefore\quad & \mathrm{~L}_2=\frac{\mathrm{L}}{4}
\end{aligned}$$

Answer

$\mathrm{\frac{L}{4}}$

Answer

$\mathrm{\frac{L}{2}}$

Answer

$\mathrm{2L}$

Answer

$\mathrm{4L}$

Centre of Mass and Rotational Motion

A rotating body has angular momentum ' L '. If its frequency is doubled and kinetic energy is halved, its angular momentum will be

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