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Ball rolling down an incline angular and linear acceleration

  1. Dec 6, 2017 #1
    1. The problem statement, all variables and given/known data

    A ball with moment of intertia bmr^2 rolls without slipping down a plane inclined at angle O. What is it’s linear acceleration?

    2. Relevant equations

    Fnet= ma

    T = F x r

    T = IO’’

    a = rO’’

    3. The attempt at a solution

    Fnet = mgcos(O) - Ff


    T = Ffr


    T = IO’’

    Ffr = bmr^2O’’

    Ff = bmrO’’


    Fnet = mgcos(O) - BmrO’’


    a = O’’r

    a/r = O’’


    Fnet = mgcos(O) - bma

    ma = mg cos(O) - bma
    a = gcos(O) - ba

    a + ba = gcos(O)

    a(1+b) = gcos(O)

    a = gcos(O)/(1+b)
     
  2. jcsd
  3. Dec 6, 2017 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Check this: What is the component of the weight parallel to the plane?
     
  4. Dec 6, 2017 #3
    Oops, would it be mgsin(O)?

    I believe that would give an answer of gsin(O)/(1+b) following the rest of my steps.
     
  5. Dec 6, 2017 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Yep.

    Looks good to me.
     
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