## Question about units for angular velocity, time constant

Here is a link to page in a book which contains an example problem:

http://imgur.com/OPrlw.jpg

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.
 PhysOrg.com science news on PhysOrg.com >> New language discovery reveals linguistic insights>> US official: Solar plane to help ground energy use (Update)>> Four microphones, computer algorithm enough to produce 3-D model of simple, convex room
 Blog Entries: 2 Recognitions: Gold Member Science Advisor 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/Time_constant http://en.wikipedia.org/wiki/Period_(physics)
 If you know the question, cross post it here also please.

 Tags units

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