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GeneralOJB

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I read that for a rotating body the kinetic energy ##E_k = \sum \frac{1}{2}mv^2 = \frac{1}{2}{\omega}^2∑mr^2 = \frac{1}{2}I{\omega}^2## where ##I## is the moment of inertia.

If we did the same thing for momentum then ##P = ∑mv = \omega\sum mr##

So why is angular momentum ##I\omega=\omega\sum mr^2##? Shouldn't the momentum just be the sum of the momentum of all the particles, like we did with kinetic energy?

Also why should I believe that this quantity ##I\omega## is conserved?

If we did the same thing for momentum then ##P = ∑mv = \omega\sum mr##

So why is angular momentum ##I\omega=\omega\sum mr^2##? Shouldn't the momentum just be the sum of the momentum of all the particles, like we did with kinetic energy?

Also why should I believe that this quantity ##I\omega## is conserved?

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