Angular Velocity of u Shape - Solving for Angular Velocity

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The discussion revolves around calculating the angular velocity of a "u" shaped rod that transitions from a straight configuration while rotating. Initially, the rod rotates at 9.37 rad/s about its center, and upon changing shape, it becomes a composite system with different mass distributions. Participants emphasize using the conservation of angular momentum to relate the initial and final states, specifically the equations I_1ω_1 = I_2ω_2. Key concepts include moment of inertia and net torque, which are crucial for solving the problem. The focus is on applying these principles to determine the new angular velocity after the transformation.
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Angular Velocity?

A thin uniform rod is rotating at an angular velocity of 9.37 rad/s about an axis that is perpendicular to the rod at its center. As the figure indicates, the rod is hinged at two places, one-quarter of the length from each end. Without the aid of external torques, the rod suddenly assumes a "u" shape, with the arms of the "u" parallel to the rotation axis. What is the angular velocity of the rotating "u"?

Before: The system is a single rod of mass M and length L rotating about an axis through its center.
After: The system consists of three parts; a rod of mass M/2 and length L/2 rotating about an axis through its center and two masses M/4 rotating at a distance L/4 from the axis. (Treat these masses as particles.)



I know I should use the conservation of momentum, moment of inerta for the rod, Net torque= Inertia x angular acceleration but I have no idea where to start!

Help me exam tomorrow!
 
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Indeed, conservation of momentum is the way to go.
The momentum before is I_1\omega_1 and after it's I_2\omega_2.
So ask yourself what's given, what can you calculate and what is the unknown?
 

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