Question 162: Centre of Mass and Rotational Motion

Question

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads
$$-$$1
in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two
objects each of mass m be attached gently to the
opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads
$$-$$1
).

Accepted Answer

$${I_1}{\omega _1} = {I_2}{\omega _2}$$
$$M{R^2}{\omega _1} = (M{R^2} + 2m{R^2}){\omega _2}$$
$${\omega _2} = \left( {{M \over {M + 2m}}} \right){\omega _1}$$
$${\omega _2} = 2\left( {{M \over {M + 2m}}} \right)$$

Answer

$${M \over {(M + m)}}$$

Answer

$${{(M + 2m)} \over {2M}}$$

Answer

$${{2M} \over {(M + 2m)}}$$

Answer

$${{2(M + 2m)} \over M}$$

Centre of Mass and Rotational Motion

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