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Explanation of Angular Speed Change

  1. Sep 15, 2009 #1
    You have a weight on one end of a piece of string and you run that piece of string through a tube, and then on the other end you attach a cork. You hold on to the tube and try and keep the cork spinning at a constant radius, such that the weight stays dangling at the same height. As you increase the radius of the circle, the time to complete a revolution takes longer. Why does the angular speed decrease when the radius is increased?

    I guess it's sort of the same question as, if Mercury were the same size as Earth, would it's speed during revolution still be faster than Earth's? And if so, why?
     
    Last edited: Sep 15, 2009
  2. jcsd
  3. Sep 15, 2009 #2
    Your question is incomplete as stated. If you keep the energy of the system constant then it makes more sense. The equation for rotational kinetic energy is KEr=Iw^2/2 Where I is the rotational inertia and w is the angular velocity. For a very simple problem like yours I=Mr^2. So substituting for I we get KEr=M(r*w)^2/2. Going through a lot of steps and simplifying we can see that r=k/w where k is a the constant the squareroot of 2KEr/M. So you can see in the case of constant KE there is a inverse relationship between radius and rotational velocity.
     
  4. Sep 16, 2009 #3
     
  5. Sep 16, 2009 #4

    A.T.

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    To keep the linear speed constant: linear_speed = radius * angular_speed
     
  6. Sep 16, 2009 #5
    The linear speed doesn't remain constant, it increases. The angular momentum, wich is
    linear speed * radius remains constant.
     
  7. Sep 17, 2009 #6

    rcgldr

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    Last edited: Sep 17, 2009
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