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A particle of mass m = 2 kg is attached to the end of a uniform rod of mass M = 5 kg and length L = 3 m. The rod is free to rotate in a vertical plane about a horizontal axis through the other end. The system is released from rest in a horizontal position. Find the angular acceleration of the system just after release (in rad/s²).
- 2.0 rad/s²
- 2.5 rad/s²
- 3.0 rad/s²
- 3.5 rad/s²
Correct answer: 2.5 rad/s²
Solution
When released from horizontal position, the net gravitational torque about the pivot causes angular acceleration. Both the rod's weight (at L/2) and particle's weight (at L) create clockwise torques. The moment of inertia is I = ML²/3 + mL².
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