Question 690: Centre of Mass and Rotational Motion

Question

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $$\omega $$. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be :

Accepted Answer

Applying conservation law of angular momentum, $${I_1}{\omega _1} = {I_2}{\omega _2}$$
$${I_2} = \left( {M{r^2}} \right) + 4\left( m \right)\left( {{r^2}} \right) = \left( {M + 4m} \right){r^2}$$
(Taking $${\omega _1} = \omega $$ and $${\omega _1} = \omega _1$$)
$$ \Rightarrow M{r^2}\omega  = \left( {M + 4m} \right){r^2}{\omega _1}$$
$$ \Rightarrow {\omega _1} = {{M\omega } \over {M + 4m}}$$

Answer

$${{M\omega } \over {4m}}$$

Answer

$${{M\omega } \over {M + 4m}}$$

Answer

$${{\left( {M + 4m} \right)\omega } \over M}$$

Answer

$${{\left( {M - 4m} \right)\omega } \over {M + 4m}}$$

Centre of Mass and Rotational Motion

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $\omega $. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be :

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