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I don't understand the concept of rotational potential energy.

During linear motion, when a force is applied, the work it does gets converted to kinetic energy and there is no change in the potential energy. Similarly, during rotational motion when a torque is applied to angularly accelerate a body, the work done by the torque leads to an increase in kinetic energy. Hence the total energy of the body also increases. This video says that the total energy of the body remains constant, hence there is a need for rotational potential energy in order to balance out the increase in the kinetic energy.

Shouldn't the total energy of the "system" including the person applying torque be conserved and the increase in kinetic energy be justified on the basis of the person's energy being decreased? Where does potential energy come into the picture?

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If you accept that no external work was done, then if there is a change in the state of a system through which the kinetic energy changed, there must be a corresponding change in potential energy.

The key to understanding the (rather poorly narrated) video is that the lecturer implies (at T=2:30) that $\Delta E=0$ from which it follows that $\Delta KE= - \Delta PE$

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  • $\begingroup$ But won't there always be some external work...? $\endgroup$ – oshhh Jun 25 '16 at 12:24
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    $\begingroup$ Imagine a spinning disk with a radial rail with a mass on it. If you release the mass it will move - and total angular momentum of system is unchanged but KE of system will change. $\endgroup$ – Floris Jun 25 '16 at 12:51

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