Conservation of angular momentum and energy

[StatusX]

if you have a spinning body, and then its shape changes so that the moment of inertia changes, what happens? If angular velocity is conserved, since there's no net torque, then it spins a different speed, but the same direction. But then has the rotational kinetic energy changed? And if so, does this mean the excess kinetic energy must take the form of translational motion? Does it matter if the change in shape was symmetrical?

 

[pervect]

Consider a very simple example - two weights connected by a cord spinning around their common center.

If you pull the weights in, it will require work to do so. (The easiest way to see this is to go to a non-inertial frame that's corotating with the weights, and consider the centrifugal force). Similarly, if you let the weights go out, work will be generated and must be dissipated (perhaps by friction).

Energy and angular momentum will both be conserved.

 

[arildno]

The (instantaneous) angular velocity may well change its direction, since (for one) we cannot assume that the shapechange does not affect the inertial tensor (with respect to the C.M).
The angular momentum, remains, however, constant.