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Rotation qns which i am stuck for 2 hours

  • Thread starter Wen
  • Start date
  • #1
Wen
44
0
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.
 

Answers and Replies

  • #2
mukundpa
Homework Helper
524
3
if the torque is taken about contect point(bottum) then torque due to all three forces is zero and we can conserve angular momentum.
 
  • #3
Wen
44
0
so 1/2 I w^2= 1/2 MV^2 ?
 
  • #4
698
0
yes, the kinetic energy of a rolling object is, as you have stated:
[tex] KE_{rolling} = \frac{1}{2}mv^2 + \frac{1}{2}I{\omega}^2 [/tex]

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

Regards,

Nenad
 

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