Question 595: Centre of Mass and Rotational Motion

Question

Two bodies rotate with kinetic energies 'E$$_1$$' and 'E$$_2$$'. Moments of inertia about their axis of rotation are 'I$$_1$$' and 'I$$_2$$'. If $$\mathrm{I_1=\frac{I_2}{3}}$$ and E$$_1$$ = 27 E$$_2$$, then the ratio of angular momenta 'L$$_1$$' to 'L$$_2$$' is

Accepted Answer

$$\begin{aligned} & \mathrm{E}_1=\frac{1}{2} \mathrm{I}_1 \omega_1^2 \ & \mathrm{E}_2=\frac{1}{2} \mathrm{I}_2 \omega_2^2=\frac{1}{2} \cdot 3 \mathrm{I}_1 \cdot \omega_1^2 \quad\left[\because \mathrm{I}_2=3 \mathrm{I}_1ight] \ & =\frac{3}{2} \mathrm{I}_1 \omega_2^2 \ & \mathrm{E}_1=27 \mathrm{E}_2=27 	imes \frac{3}{2} 	imes \mathrm{I}_1 \omega_2^2 \ \end{aligned}$$
$$\begin{aligned} & 	herefore \frac{1}{2} \mathrm{I}_1 \omega_2^2=\frac{81}{2} \mathrm{I}_1 \omega_2^2 \ & 	herefore \quad \omega_1=9 \omega_2 \ & \frac{L_1}{L_2}=\frac{\mathrm{I}_1 \omega_1}{\mathrm{I}_2 \omega_2}=\frac{\mathrm{I}_1 	imes 9 \omega_2}{3 \mathrm{I}_1 	imes \omega_2}=3 \ & \end{aligned}$$

Answer

1 : 3

Answer

3 : 1

Answer

1 : 1

Answer

2 : 1

Centre of Mass and Rotational Motion

Two bodies rotate with kinetic energies 'E$_1' and 'E_2'. Moments of inertia about their axis of rotation are 'I_1' and 'I_2'. If \mathrm{I_1=\frac{I_2}{3}} and E_1 = 27 E_2, then the ratio of angular momenta 'L_1' to 'L_2$' is

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