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Speed Pertaining to Circular Motion

  1. Sep 20, 2013 #1
    Units for Speed Pertaining to Circular Motion


    So v=ω*r

    Where v = velocity in m/s
    ω = angular velocity in rad/s
    r = radius in m

    But I am confused...the units don't match! What happens to the rad?

    m/s = (rad/s)*s

    My textbook doesn't explain it, it simply does calculations like (56.5 rad/s)(0.030 m) = 1.7 m/s and the rad disappears. I have a feeling I am missing something obvious o_O. Any help?

    Last edited: Sep 20, 2013
  2. jcsd
  3. Sep 20, 2013 #2

    D H

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    Staff Emeritus
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    The measure of an angle θ, in radians, is defined as the ratio of a circular arc subtending that angle θ to the radius of the circle. Angles thus have units of length per length. In other words, angle is a unitless quantity. Using radians makes the constant of proportionality one when computing arc length, or when computing speed along a circular path.
  4. Sep 21, 2013 #3
    In other words, rads is not a unit. It's just a label.
  5. Sep 21, 2013 #4
    Cool, thanks a lot guys, I wish my book explained that :p
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