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Uniform Circular Motion confusion.

  1. Nov 12, 2009 #1
    How can v = 2[tex]\pi[/tex]r[tex]\omega[/tex]?

    I've looked at this a hundred different ways... I've found that v = 2[tex]\pi[/tex]r2[tex]\omega[/tex] only.
     
  2. jcsd
  3. Nov 12, 2009 #2

    Doc Al

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    Staff: Mentor

    You'll have to give us at least a hint of what you are talking about. :tongue:

    Please explain the problem you are trying to solve and what your equations are describing.

    For uniform circular motion of radius r, the tangential speed v (measured in m/s) is related to the angular speed ω (measured in rad/s) by the formula: v = ωr.
     
  4. Nov 12, 2009 #3
    The issue arose in the following problem;

    A very small cube of mass m is placed on the inside of a funnel rotating around a vertical axis at a constant rate of v revolutions per second. The wall of the funnel makes an angle [tex]\theta[/tex] with the horizontal. The coefficient of static friction between cube and funnel is [tex]\mu[/tex]s and the center of the cube is at a distance r from the axis of rotation. Find (a) largest and (b) smallest values of v for which the cube will not move with respect to the funnel.

    I consulted my handy dandy solutions manual and it wanted to work with the assumption that speed in this case = 2 [tex]\pi[/tex] r [tex]\omega[/tex].

    I'm still scratching my head.

    The purposes of defining the speed in this way is to get that F = 4 [tex]\pi[/tex]2 m r [tex]\omega[/tex]2.

    Sorry for the ambiguity, I thought that someone would recognize the issue right away.

    BTW, I don't know what's up with the editing but pi and omega are not powers. They just look that way... :blushing:
     
  5. Nov 12, 2009 #4

    Doc Al

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    Makes no sense to me. What textbook is this?
    That's because you're mixing Latex and regular text. Try doing it all with Latex, like this: [tex]2 \pi r \omega[/tex]. Even better is to use 'inline' latex, using the 'itex' tag: [itex]2 \pi r \omega[/itex].
     
  6. Nov 12, 2009 #5
    It's from Resnick Haliday and Krane 4th edition volume 1.
     
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