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Rotation qns which i am stuck for 2 hours

  1. Aug 21, 2005 #1

    Wen

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    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.
     
  2. jcsd
  3. Aug 21, 2005 #2

    mukundpa

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    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.
     
  4. Aug 22, 2005 #3

    Wen

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    so 1/2 I w^2= 1/2 MV^2 ?
     
  5. Aug 22, 2005 #4
    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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