kinetic rotational energy?

Question

if i sit on a stool with my arms outstretched and then i bring my arms together to increase my angular speed...did i increase my kinetic rotational energy? i recognize that while one factor ("I" the moment of inertia) goes down but i'm not sure if this is equivalent to the square of my angular speed

Answer 1

since no external force gives it a torque the angular momentum remain conserved and hence the angular velocity goes up .by the fact that rotational energy is proportional to product of moment of inertia and square of angular velocity the net rotational kinetic energy increases

Answer 2

The kinetic rotational energy it is the same,neglecting the friction.Be sure that the product between the moment of inertia with the square of angular speed it is constant.

Answer 3

Your arm muscles have to *work* to maintain the centripetal acceleration while you bring them in. That work goes into the energy increase required to conserve angular momentum.

Answer 4

You use energy to bring your arms together so kinetic rotational energy increased. (qualitative)

Momentum = IW (constant)
KE = 1/2 Iw^2 = 1/2.M.w so as w increases so does KE