Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and there is no torque acting? E.g. if a planet is rotating about its axis and it shrinks to half of its radius then according to conservation of angular momentum velocity will doubled, i.e. its kinetic energy will increase. Does this mean that without any external force the kinetic energy of any thing can be increased? Please explain!
Does this mean that without any external force the kinetic energy of any thing can be increased?
No, of course not. Just because there is no torque that doesn't mean that there isn't a force. In this particular case, you have an inwards radial force that is performing work by countering and exceeding the centrifugal force. This work is what causes the increase in kinetic energy.