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Rotational Dynamics

  1. Nov 16, 2013 #1
    When I am browsing through my rotational dynamics chapter, I raise myself a question on the direction of frictional force under all kinds of possible circumstances:

    1. Pure rolling


    For pure rolling, the frictional force will always be 0;

    2. Non-pure rolling
    For this situation, I will analyse with a model: A rolling ball lying on a level ground. And to simplify my listing, I will ignore some situations if they are similar to each other.

    2.1 ω anti-clockwise v left

    (1) ωR<v

    Frictional force will tend to slow V down and increase ω, hence it is to the right;

    (2) ωR>v

    Frictional force will tend to increase V up and slow ω down. Hence it is to the left;

    2.2 ω anti-clockwise v right

    At first, the frictional force will be to the left(Slow down both ω and v)

    But later, I think two situations may occur:

    ω is not sufficiently large but v is sufficiently large, ω will be decreased to 0. And continuously, frictional force will be to the left to increase ω clockwisely until pure rolling occurs.

    v is not sufficiently large but ω is sufficiently large, v will be decreased to 0. And after that, frictional force will be to the left to increase v leftwards until pure rolling occurs.

    If ω and v just happen to be such nice that it will be decreased to 0 at the same time, the object will just stop then.


    My idea in analyzing the frictional force is that: Non-pure rolling will always tend to transit itself into pure-rolling condition.

    Thank you for spending time on reading this but could you please tell me whether my analysis is correct?
     
  2. jcsd
  3. Nov 16, 2013 #2

    CWatters

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    That seems consistent with what happens when you drive a car.
     
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