Question 674: Centre of Mass and Rotational Motion

Question

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

Accepted Answer

As the masses are added to
the ring gently, there is no torque and
angular momentum is conserved.
$$I\omega  = I'\omega '$$
$$ \Rightarrow M{R^2}\omega  = \left( {M{R^2} + 2m{R^2}} \right)\omega '$$
$$ \Rightarrow \omega ' = {{M{R^2}\omega } \over {\left( {M + 2m} \right){R^2}}}$$
$$ \Rightarrow \omega ' = {{M\omega } \over {M + 2m}}$$

Answer

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

Answer

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

Answer

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

Answer

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

Centre of Mass and Rotational Motion

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