Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about units for angular velocity, time constant

  1. Jul 25, 2011 #1
    Here is a link to page in a book which contains an example problem:


    In the book, they work out the natural frequency of a hydraulic cylinder and come out with an answer in rad/sec. This number is then inverted to get a time constant, and the resultant unit is seconds.

    I understand that a radian is dimensionless, and 1 rad/sec really equals 1/sec. So, it makes sense that you invert it and get seconds. However, you would also get seconds if you first convert the frequency from rad/sec to cycle/sec, and then invert.

    My question is: how do you know which to use? When do you want to use sec/cycle, vs. sec/rad? It seems ambiguous, and the numbers would come out very differently.

    I know the result of this equation is in radians. What if you experimentally measured the natural frequency in cycles/sec, and then inverted to get the time constant in seconds? You would get a different answer, but I don't think anything was done wrong.

    Can anyone shed some light on this? I think I am missing something.
    Last edited by a moderator: Apr 26, 2017
  2. jcsd
  3. Jul 25, 2011 #2


    User Avatar
    Science Advisor
    Gold Member

    I think you may be confusing a "time constant" vs. a "period." One is a parameter which is indicitive of a system's response, the other is the length of time for one cycle.


    http://en.wikipedia.org/wiki/Period_(physics [Broken])
    Last edited by a moderator: May 5, 2017
  4. Oct 23, 2011 #3
    Last edited by a moderator: Apr 26, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook