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Rotational motion begining with kinetic friction.

  1. Jul 27, 2009 #1
    1. The problem statement, all variables and given/known data

    A ball is suddenly kicked across a floor. It initial will have a linear velocity, but no initial angular velocity. The object will slide for a distance "d" until perfect rolling kicks in.

    all are in terms of variables and not specific numbers

    A.) derive an equation for linear acceleration of center of mass.
    B.) deriave an equation for angular acceleration.
    C.) Find final speed of the ball when pure rolling beings in terms of Vo
    D.) determine the time and distance that the ball slid.

    2. Relevant equations

    I=2/5mR^2
    Torque=(I)(alpha)
    alpha = a/R
    mgr?
    wf = 2(alpha)(theta) + wi
    3. The attempt at a solution

    A.) T=I(alpha)
    mgur = I(alpha)
    mgur = I(a/R)
    a= 5gu/2?

    B.) alpha = u5g/2r?

    very lost with the rest.
     
  2. jcsd
  3. Jul 27, 2009 #2

    alphysicist

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    Hi MarkChoo,

    This last step is not true; since the ball has not started pure rolling yet (it is sliding as it rolls), then alpha is not equal to a/R.

    Instead of using torque, draw a force diagram and use Newton's law.

    That looks right to me.
     
  4. Jul 27, 2009 #3
    im lost then how to get the linear acceleration, because that was the only way I saw how to get alpha(a rad/s^2 value) in terms of a m/s^2 value. If thats what they mean by linear.
     
  5. Jul 27, 2009 #4

    alphysicist

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    You get it the same way that you find the acceleration in simpler (non-rotational) problems. Draw a force diagram for the ball with all forces acting on it. Then use Newton's law (Fnet=ma) in the horizontal and vertical directions to get two equations; by putting them together you can find the acceleration.
     
  6. Jul 27, 2009 #5
    how about if i use Wf=alpha(t) + Wo and plug into my alpha to get...
    t= 2rWf/5gu

    then plug time t it into Vf= at + Vo
    then I solve for a?
     
  7. Jul 28, 2009 #6

    alphysicist

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    I don't believe that will give you what you want by itself; you'll end up with an expression that contains either the final angular velocity or final linear velocity, which is what the problem later wants you to find (in part c).

    Have you tried to use a force diagram to find the linear acceleration, as I mentioned in my last post? What does that give you?
     
  8. Jul 28, 2009 #7
    yea ive tried a force diagram.

    ive also tried F = ma and since Ff = n u

    nu=ma

    then

    a = nu/m
     
  9. Jul 28, 2009 #8

    alphysicist

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    Exactly; that's what the horizontal equation of the force diagram gives you.

    Now just write an expression for the vertical forces, and that will tell you what n is in your equation. There are two vertical forces here; how are they related to each other?
     
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