Physics - Circular Motion Question with Solution | TestHub

Angular momentum$\mathit{\text{L}}=\mathit{\text{I}}\omega$

Rotational kinetic energy$\left(\mathit{\text{K}}\right)=\frac{1}{2}\mathit{\text{I}}{\omega }^2$

$\therefore$$\frac{\mathit{\text{L}}}{\mathit{\text{K}}}=\frac{\mathit{\text{I}}\omega \times 2}{\mathit{\text{I}}{\omega }^2}=\frac{2}{\omega }\Rightarrow \mathit{\text{L}}=\frac{2\mathit{\text{K}}}{\omega }$

or$\frac{{\mathit{\text{L}}}_1}{{\mathit{\text{L}}}_2}=\frac{{\mathit{\text{K}}}_1}{{\mathit{\text{K}}}_2}\times \frac{{\omega }_2}{{\omega }_1}=2\times 2=4$

$\therefore$${\mathit{\text{L}}}_2=\frac{{\mathit{\text{L}}}_1}{4}=\frac{\mathit{\text{L}}}{4}$.