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Angular speed units question

  1. Feb 20, 2005 #1

    tony873004

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    velocity = 0.5 m/s
    radius = 1 m

    [tex]\omega = \frac{v}{r}[/tex]

    [tex]\omega = \frac{0.5 m/s}{1 m}[/tex]

    the meters cancel and I'm left with

    [tex]\omega = 0.5 s[/tex]

    But [tex]\omega[/tex] is supposed to be expressed in radians/s

    How do I get those output units with the given input units?
     
  2. jcsd
  3. Feb 20, 2005 #2

    AKG

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    Why do you have "w = 0.5s" when your calculations suggest it should be "w = 0.5/s = 0.5 Hz"? Note that radians are dimensionless, so rad/s is equivalent to 1/s, or Hz.
     
  4. Feb 21, 2005 #3

    ehild

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    Hertz (Hz) is the unit of frequency, and the unit of angular velocity is rad/s. Both frequency and angular velocity have the dimension of 1/[time], so they can be written also as 1/s.

    See http://physics.nist.gov/cuu/Units/units.html

    ehild
     
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