When a person standing on a rotating table stretches his hands which force causes the loss in K.E ? Explain via force not via angular momentum? Please explain which force(s) causes the loss in kinetic energy and also explain which force(s) changes the angular velocity of the system when a person extends his arm. You could use another example to explain this concept as well but the main thing should remain the same i.e. the angular momentum is constant and the energy decreases.
 A: I believe your reasoning is something like this:
When the man is spinning with his hands down, he has a certain angular velocity, and when his arms are extended, his angular velocity has decreased (so an angular [de]acceleration has occurred), and so therefore there must have been  some force because of the change in angular velocity.
So let's consider the man with his arms half stretched out and to simplify things, say that each of his hands/arms are small dumbbells (as opposed to considering the complicated mass distribution of his arms/hands). Now at this point, both of the dumbbells are experiencing a centripetal force since they are moving in circles. As he lifts his arms, it is logical to then think that work is done by the force, thus decreasing the angular velocity. So we have a case with angular acceleration, but without an external torque. All of this is happening internally to the system.
So indeed there is an acceleration brought about by the centripetal force doing work, resulting in a decrease in angular velocity, and hence a decrease in rotational kinetic energy. A correlation to the work-energy theorem exists, whereby work done equals the change in kinetic energy.
This is valid provided we are careful to note that there are no external torques$^1$. The change in angular velocity is not due to an external torque.

$^1$ Why a change in angular momentum requires an external torque.
The angular momentum of such as system can be defined by $$L=I\omega$$ where $\omega$ is the angular velocity, and the moment of inertia $$I =\sum_i m_i r_i^2$$ where $r_i$ is the distance from the rotation axis to a mass element $m_i$. Let's consider mass elements $m_h$ say his hands/arms. This means that there is an increase in $I$ as the arms are raised as $I$ is proportional to (the square of) the distance of masses $m_h$. The decrease in angular angular velocity happens as a direct result of this change. When $I$ increases, $\omega$ decreases, and overall $L$ remains constant.  Angular momentum is conserved unless external torques are operating.
But the rotating table (provided there is not a constant torque spinning the table) will not spin forever, and so even after the arms are outstretched the table slows down, and it will not spin forever.
This means some dissipative forces are slowing the table, like friction and air resistance.
