Let a particle of mass m be rotating in a circle, radius be r, axis of rotation through the center and perpendicular to the plane of motion. Now if the radius is made decrease somehow at some rate until it get's zero, how do I find the rate of change in angular velocity? Also, the angular momentum being conserved, dL/dt=0, ie, no torque acts on it. Yet since the angular velocity is changing, there has to be an angular acceleration. So how can there not be a torque? Is it because w*dI/dt exactly cancels I*dw/dt?