Confused by radial vs. centripetal acceleration

  1. Hi

    I've been working through some examples from the course material we use in physics class, but one thing keeps confusing me: What is the difference between centripetal and radial acceleration?

    For instance, when we have a particle traveling in a circular path, the acceleration towards the center of the circle may be written as Ar (a sub r)=-Ac= - v^2/r, while other times it is written simply as Ac=v^2/r. The text book (JS Physics for Scientists and Engineers) seems to use both.

    Where is the negative sign coming from? I made a quick sketch. Am I right if i think that the radial acceleration is negative in the first circle (to the left) and it is positive in the circle to the right? Is it just due to how I pick the axis and how I define positive direction?


    Thanks in advance.
     

    Attached Files:

    • ac.jpg
      ac.jpg
      File size:
      27.6 KB
      Views:
      89
  2. jcsd
  3. Doc Al

    Staff: Mentor

    Same thing.
    v^2/r is the magnitude of the radial acceleration; the direction is toward the center. Whether that's positive or negative just depends on how you define your sign convention.

    Yes.
     
  4. Thank you very much. :)
     
  5. K^2

    K^2 2,470
    Science Advisor

    Radial acceleration is equal to centripetal acceleration when the radius remains constant (with a +/- sign depending on definition). If radius changes as a function of time, you have to add the explicit second derivative of radius with respect to time.

    [tex]a_r = a_c + \ddot{r} = -\omega^2 r + \frac{d^2r}{dt^2}[/tex]

    Similarly, tangential acceleration will pick up a term that depends on the second derivative of angle with respect to time and a Coriolis Effect term.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?