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I have a uniform rod of length 0.5m and mass 0.1kg, and on this rod are two balls of mass 0.03kg both at a distance of 9.997cm away from the center of the rod. There is a pin about the center of the rod upon which it rotates. The angular velocity I have worked out to be 20rad/s and the tangential velocity of the beads are 1.679m/s. The balls are released and move to the end of the rod and I want to find the work done by the pin dur to friction. I know the final kinetic energy is 0.1566J so I thought about using the work kinetic energy theorem but the result is not correct. Maybe I have been calculating the initial energies incorrectly. I took 1/2Iw^2 + 2(1/2)(Mass of ball)(Tangetial Velocity)^2 and used that. Is this the correct method?

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I know the final kinetic energy is 0.1566J

How did you find the final kinetic energy?

To find the final state of the system you have to assume that there are no external torques acting on the system and that angular momentum is conserved.

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