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A cylinder rolls without slipping- find the angle

  1. Nov 7, 2009 #1
    1. The problem statement, all variables and given/known data

    A cylinder with radius R and mass M rolls without slipping down an incline plane with angle[tex]\theta[/tex]. The coeff. of friction is [tex]\mu[/tex]. Find the maximum value for the angle for the cylinder to roll without slipping.

    2. Relevant equations

    The moment of inertia for a cylinder is I=(MR^2)/2.
    w=v/r

    3. The attempt at a solution

    If the cylinder rolls without slipping, energy must be conserved. So Mgh=1/2Mv^2+1/2Iw^2. If you plug in the equations from above and divide all terms by M, gh=3/4v^2.
    So we need to find v.
    The equation for the x-component of force (where x is along the plane of the incline), F=mg(cos[tex]\theta[/tex]-[tex]\mu[/tex])=ma
    and the y-component
    F=0=N-mgsin[tex]\theta[/tex] or N=mgsin[tex]\theta[/tex]

    I have no idea where to go from here and I'm not quite sure I did all of this right. Thank you so much for any help!!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 7, 2009 #2
    You should think when you will have the minimum value of angle.When you have the maximum of static friction.Also i think you have a mistake.In the direction of the slope the forces are Wy=mgsinθ and T<=μN
     
  4. Nov 7, 2009 #3
    Also N=mgcosθ not mgsinθ
     
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