I have been stuck at this qns for 2 hours. A gymnast often toss a hoop forward while giving it a backward spin. the hoop has a radius R and mass M, and is thrown forward with speed V. Find the minimum backward angular velocity w the gymnast must give in order to make sure it spin back eventually . Take both its static and kinectic coefficent of friction to be #. Since friction is acting , its nett torque is not 0. Hence conserv. of angular momentum cannot be applied. if its nett torque is Mg#R, how should i relate this to the translational and rotational K.E.? Please teach me how to solve this.