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When do vcm=rw and a=gsintheta/(1+I/(MR)^2) apply?

  1. Feb 8, 2015 #1
    1. The problem statement, all variables and given/known data
    Do the equations below only apply for rolling without slipping?

    2. Relevant equations
    vcm=rw, a=(gsintheta)/(1+I/(MR)^2)
    cm=center of mass

    3. The attempt at a solution

    I know that they both apply for rolling without slipping, but do they apply when there is slipping? Thank you.
     
  2. jcsd
  3. Feb 8, 2015 #2

    haruspex

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    Consider some simple examples of slipping - like a sphere sliding and not rotating at all. Does the first equation give the right answer?
    I don't recognise the second equation. You'll need to describe the set up it applies to.
     
  4. Feb 8, 2015 #3
    I see now. The equation vcm=rw would not apply if the ball was moving but not having rotational motion.

    This is how I set up the equation:

    Consider an object rolling down a inclined plane.

    Torque=RFs
    R=radius, Fs=static friction
    Also,
    Torque=I*alpha
    I=moment of inertia
    alpha=angular acceleration
    This leads to Torque = I*alpha=I*(a/R)
    where a=acceleration centripetal

    Setting RFs=I*(a/R) gives us Fs=(I*a)/R^2

    So we have Fnet=ma=gravitational force down the incline plane-force of friction
    which is=(mgsintheta)-(Ia)/R^2

    Solving for a and manipulating the equation gives that a=(gsintheta)/(1+(I*alpha)/MR^2)
     
    Last edited: Feb 8, 2015
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