Question 558: Centre of Mass and Rotational Motion

Question

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio

Accepted Answer

The equation for angular momentum is
$$\mathrm{L}=\sqrt{2 \mathrm{~K}_{	ext {Rot }} 	imes \mathrm{I}}$$
So, $$\mathrm{L} \propto \sqrt{\mathrm{I}}$$
$$	herefore \quad$$ The ratio of angular momentum of the two bodies is
$$\frac{\mathrm{L}_1}{\mathrm{~L}_2}=\sqrt{\frac{\mathrm{I}_1}{\mathrm{I}_2}}$$
$$\frac{\mathrm{L}_1}{\mathrm{~L}_2} =\sqrt{\frac{\mathrm{I}}{2 \mathrm{I}}} \quad .... (	ext{given} ~\mathrm{I}_2=2 \mathrm{I})$$
$$	herefore \quad \frac{\mathrm{L}_1}{\mathrm{~L}_2}  =\frac{1}{\sqrt{2}}$$

Answer

$$1: 2$$

Answer

$$\sqrt{2}: 1$$

Answer

$$2: 1$$

Answer

$$1: \sqrt{2}$$

Centre of Mass and Rotational Motion

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio

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