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What is the notation for angular distance travelled?

  1. Feb 12, 2015 #1
    What is the notation for the angular distance travelled by an object moving in circular motion?

    s is for regular distance (m,ft,inches, etc.).

    What I want is some x to be the distance in either degrees or radians.

    How should I call that x?
     
  2. jcsd
  3. Feb 12, 2015 #2
    I would just use ##\theta(t)## and defined it as the total amount of radians that the object has traveled. In your case of circular motion, I would have it be that angle away from its original starting point, ##\theta_0## if ##\theta(t) \in [-2\pi+\theta_0\leq\theta(t)\leq 2\pi-\theta_0 ]##. Only include the ##\theta_0## if you are measuring the angle from the origin. If you aren't, and you're measuring the angle from ##\theta_0##,it's just ##[-2\pi\leq\theta(t)\leq2\pi]##

    BUT
    If ##\theta(t)\notin [-2\pi+\theta_0\leq\theta(t)\leq 2\pi-\theta_0]##which means your not restricting it to one full revolution, than I would say it is the ##\textbf{TOTAL}## angle traveled by the object in time t. The comment about ##\theta_0## being included or not from above applies here as well. (The part about measuring from the origin or ##\theta_0##)
     
    Last edited: Feb 12, 2015
  4. Feb 12, 2015 #3
    Does that answer your question adequately?
     
  5. Feb 12, 2015 #4
    It'll suffice. We'll see if anyone has seen different notation though.
     
  6. Feb 12, 2015 #5
    You can really use any notation you want, as long as you define what you're doing. For example I could use any of the following ( or anything else, really) for what we are describing, as long as It's stated somewhere.
    ##
    \phi(t)\\
    \pi(t)\\
    \epsilon(t)\\
    \zeta(t)\\
    A(t)\\
    Q(t)\\
    \eta(t)\\
    \text{etc.,}
    ##

    But I don't think that's what you mean. Typically for angles you usually see either ##\phi\\ \text{or}\\ \theta##, which are known as phi and theta, as you may know.
     
    Last edited: Feb 12, 2015
  7. Feb 13, 2015 #6
    This may help:
     

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