Question 52: Centre of Mass and Rotational Motion

Question

A disc of moment of inertia 4 kg - m$$^2$$ revolving with 16 rad/s is placed on another disc of moment of inertia 8 kg - m$$^2$$ revolving 4 rad/s. The angular frequency of composite disc

Accepted Answer

Given that, moment of inertia of disc,
$$I_1=4$$ kg - m$$^2$$
$$I_2=8$$ kg - m$$^2$$
Angular velocities of discs,
$$\omega_1=16$$ rad/s
$$\omega_2=4$$ rad/s
From angular momentum conservation principle,
$$I_1\omega_1+I_2\omega_2=(I_1+I_2)\omega$$
$$\Rightarrow 4	imes16+8	imes4=(4+8)\omega$$
$$\Rightarrow 64+32=12\omega$$
$$\Rightarrow \omega=\frac{96}{12}=8$$ rad/s

Answer

4 rad/s

Answer

$$\frac{3}{16}$$ rad/s

Answer

8 rad/s

Answer

$$\frac{16}{3}$$ rad/s

Centre of Mass and Rotational Motion

A disc of moment of inertia 4 kg - m$^2 revolving with 16 rad/s is placed on another disc of moment of inertia 8 kg - m^2$ revolving 4 rad/s. The angular frequency of composite disc

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