Question 667: Centre of Mass and Rotational Motion

Question

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $$\omega $$. Two objects each of msass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

Accepted Answer

As no external torque is acting about the
axis, angular momentum of system remains
conserved.
I
1
$${\omega _1}$$ = I
2
$${\omega _2}$$
$$ \Rightarrow {\omega _2} = {{{I_1}{\omega _1}} \over {\left( {M + 2m} \right){r^2}}} = {{M\omega } \over {\left( {M + 2m} \right)}}$$

Answer

$${{\left( {M + 2m} \right)\omega } \over {2m}}$$

Answer

$${{2M\omega } \over {M + 2m}}$$

Answer

$${{\left( {M + 2m} \right)\omega } \over M}$$

Answer

$${{M\omega } \over {M + 2m}}$$

Centre of Mass and Rotational Motion

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $\omega $. Two objects each of msass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

Choose the correct answer: