Question

The rotational kinetic energy of a body is ${{K}_{rot}}$ and its moment of inertia is $I$ . The angular momentum of body is:

• A. $I{{K}_{rot}}$
• B. $2\sqrt{I{{K}_{rot}}}$
• C. $\sqrt{2I{{K}_{rot}}}$
• D. $2I{{K}_{rot}}$

Answer 1

Answer: (C)

$\sqrt{2I{{K}_{rot}}}$

Answer 2

The rotational kinetic energy of a body is given by $K_{\text {rot }}=\frac{1}{2} I \omega^{2}$ $\Rightarrow I \omega^{2}=2 K_{\text {rot }}$ $\Rightarrow \omega=\sqrt{\frac{2 K_{\text {rot }}}{I}}$ Angular momentum of body is given by $J =I \omega \equiv I \times \sqrt{\frac{2 K_{ rot }}{I}}$ $=\sqrt{2 K_{\text {rot }} I}$