A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity . Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be
Solution:
If We take Ring and 4 small blocks as one system net Torque will be zero, Using Principal of conservation of angular momentum.
\[ I_{1}\omega= \left( I_{1}+ I_{2} \right)\omega_{1} \]
\[ MR^{2}\omega= \left( MR^{2}+ 4mR^{2} \right)\omega_{1} \]
\[ \omega_{1}= \left( \frac{M}{M+4m} \right)\omega \]
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