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Centrifugal acceleration - radians^2?

  1. Nov 5, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm working a problem concerning centrifugal acceleration and I've stumbled on something I don't quite understand:





    2. Relevant equations

    F=mrω2 where ω=rad/s

    So the resulting units: kg * m*rad2/s2


    3. The attempt at a solution

    I would expect acceleration to be in unit ms-2


    What's up with these radians? What do they mean?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 5, 2011 #2
    Note that there is 'linear acceleration' (i.e. rate of change of linear volocity) in m/s^2
    and 'angular acceleration' (i.e. rate of change of angular velocity) in mrad/s^2 but of course radian is not an S.I. unit.
     
    Last edited: Nov 5, 2011
  4. Nov 5, 2011 #3

    Doc Al

    User Avatar

    Staff: Mentor

    The radian is a dimensionless quantity. It's a unit of angle (really a ratio) that has no dimension, so the final units of acceleration will be m/s2 as expected. (See: http://en.wikipedia.org/wiki/Radian#Dimensional_analysis)
     
  5. Nov 5, 2011 #4
    'radian' is a measure for an angle.
    For example pi radians is equivalent to 180 degrees.
     
  6. Nov 5, 2011 #5
    I've never consider that a radian is a ratio of a circle. Thanks! that makes a lot more sense.
     
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