I have problem to see clearly the case of rotation of a body about a point with decreasing radius.this can be viewed as a body being rotated about a point with the help of a thread which passes through a hole in a disc and the thread is being pulled to apply a tension and gradually to decrease the length of the thread.I have attached a word doc. to have a clear pic. about it.It can seen that here that the instantaneous velocity has two components ,one perpendicular to the radius & other along radius. The tension is along the thread or radial. there are some points to be noted. 1 .the tension being perpendicular cannot do any work on the perpendicular comp. of velocity & cannot change its magnitude. 2.there is no torque about the center as tension is radial. So, angular momentum should be conserved. But the problem is angl. momen. is rXp . or " r*mvperpendicular". as angu. momen. is constant so r*mvperpendicular should be constant. Then if r decreases so then vperpendicular must change. And it means that the perpendicular comp. of velocity changes ,which violate the 1st point.