# Rotation qns which i am stuck for 2 hours

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.

mukundpa
Homework Helper
if the torque is taken about contect point(bottum) then torque due to all three forces is zero and we can conserve angular momentum.

so 1/2 I w^2= 1/2 MV^2 ?

yes, the kinetic energy of a rolling object is, as you have stated:
$$KE_{rolling} = \frac{1}{2}mv^2 + \frac{1}{2}I{\omega}^2$$

if the object is on the veeeeeeerge of rolling backwards, or back to the thrower, the inequality you have stated works.

Regards,