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Relationship between radial and angular acceleration

  1. Sep 16, 2007 #1
    1. The problem statement, all variables and given/known data

    State the Relatrionship between radial and angular acceleration.

    2. Relevant equations

    Well I presume the equations would be "radial acceleration = v(squared)/radius"

    3. The attempt at a solution

    I cannot find the equation for radial AND angular acceleration??

    I know this may seem trivial but I'm a novice in this part of the course

  2. jcsd
  3. Sep 16, 2007 #2


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    there is no relation that I can see. The angular acceleration alpha is related to the *tangential* acceleration a_T by
    [tex] \alpha = \frac{a_T}{R} [/tex]. But this does not involve the radial acceleration (which is related to the derivative of the speed). If you move at constant speed in a circle, for example, a_T and alpha are zero but a_r is not zero.
  4. Sep 16, 2007 #3


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    Could they just be looking for something like 'they are perpendicular to one another'? As you say, there certainly isn't an automatic algebraic relation to one another.
  5. Sep 18, 2007 #4
    hi thanks for all your help

    turns out that they were looking for a_T=r * "alpha"

    maybe there was a misprint?

    Thanks for all your help neway.

  6. Sep 18, 2007 #5


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    And that's exactly the relation I posted :-)

    Yes, there must have been a misprint in the question. They meant to ask : what is the relationship between the angular acceleration and the tangential acceleration !

    You are welcome
  7. Nov 28, 2008 #6
    What I want to know is, for example, if you have a ball in a string and let it rotate in a circle, what happens with the spin rate if you pull the string? Will it spin faster? I mean, f=m*v*v/r. If you increase f, will v increase too? (A side effect is that the center of rotation will move). In other words, how do you combine rotation with linear acceleration like this? If you hold the string in your hand, it is obvious that you can make it spin faster by moving the hand up and down. But what are the equations?
  8. Oct 20, 2010 #7
    According to my knowledge.
    Radial acceleration (a_r) (or centripetal) is the acceleration that points to center of circular motion and causes it to turn. Then Tangential acceleration (a_t) in tangent to the circle and causes the particle to change speed.

    a_r and a_t are components of an overall acceleration a, which, according to definition, is the change rate of velocity with time.
    If a_t = 0, then a = a_r and the motion is circular uniform; if a_r = 0, then a = a_t and the motion is linear (no curvature).
    If neither a_t nor a_r is zero, the motion will follow a generic curved trajectory.

    Angular acceleration is the rate of change of angular velocity w with time. Its symbol is usually alpha (don't confound it with the angular displacement), and its unit is rad/s².
    Since w = V/r, then alpha = a_t / r.
    Last edited: Oct 20, 2010
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