A thin circular ring of mass 0.2 kg is rotating about its axis with an angular speed of 51 rad/s. Two particles having mass 2 g each are now attached at diametrically opposite points on the ring. Then the angular speed of the system is:
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In a system with rotating bodies, angular momentum is conserved unless acted upon by external forces.
- The angular momentum of the system is conserved. The initial angular momentum is given by the angular momentum of the ring, and the final angular momentum is the sum of the angular momentum of the ring and the angular momentum of the two added particles.
- The moment of inertia of the ring is \( I_{\text{ring}} = m_{\text{ring}} r^2 \), and the moment of inertia of the particles is \( I_{\text{particles}} = 2 \times m_{\text{particle}} r^2 \) because two particles are added.
- By conservation of angular momentum:
\[
I_{\text{initial}} \omega_{\text{initial}} = I_{\text{final}} \omega_{\text{final}}
\]
After solving, the new angular speed of the system is \( 50 \, \text{rad/s} \).
