1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Instantaneous angular speed question

  1. Jul 21, 2016 #1
    1. The problem statement, all variables and given/known data
    How do you calculate instantaneous angular speed?

    2. Relevant equations
    I have been told that it is when delta t approaches 0, so its just the derivative of delta theta over delta t.

    3. The attempt at a solution
    does it involve tangent line like normal instantaneous velocity ?
  2. jcsd
  3. Jul 21, 2016 #2


    User Avatar
    Homework Helper
    Gold Member

    You are on the right track involving derivatives. See below.
    Yes, this is true.

    (I'm making a few assumptions about [itex] \theta (t) [/itex] not having a discontinuity at the point of t in question. But for simplicity sake, I'll just say, "yes, that's true," which it is for most cases.)
    Be careful here. It is not the derivative of [itex] \frac{\Delta \theta}{\Delta t} [/itex]. Be careful of your wording there.

    Rather, the instantaneous angular velocity [itex] \omega (t) [/itex] is the derivative of [itex] \theta (t) [/itex] with respect to t (not "over [itex] \Delta t [/itex]").

    Making the stipulations about smooth functions (not having discontinuities and so forth),

    [tex] \lim_{\Delta t \rightarrow 0} \frac{\Delta \theta}{\Delta t} = \frac{d}{dt} \{ \theta (t) \} = \omega (t) [/tex]

    That question has a simple answer, but I'll let you ponder that. If you objectively know the behavior a variable or function, say [itex] \theta(t) [/itex] which changes as a function of time, what is the instantaneous rate of change of that function? What is the derivative of a function?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted