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Angular acceleration and linear acceleration

  1. Nov 21, 2004 #1
    For a disk in the x-y plane that is rotating about the z-axis which travels through its center of mass, how does the angular acceleration relate to the linear acceleration of a particle on the body? Is the direction and the magnitude both affected? How do we calculate these in vector form? I would greatly appreciate it if someone would enlighten me about this.
     
  2. jcsd
  3. Nov 22, 2004 #2

    Galileo

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    The angular velocity is related to the linear velocity by:
    [tex]\omega = \dot \theta = \frac{v}{r}[/tex]

    Taking the time derivative of both sides and using that r is independent of time:

    [tex]\alpha = \ddot \theta = \frac{a}{r}[/tex]

    The direction is always pointing towards the axis of rotation.
     
  4. Nov 22, 2004 #3
    Thanks for replying, but would there be a tangential component? And if alpha=a/r, how is it that the linear acceleration is maintained constant?
     
  5. Nov 22, 2004 #4

    Doc Al

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    For a rotating object undergoing an angular acceleration, a point on that object will have both a radial and tangential component of linear acceleration:
    [tex]a_r = \omega^2 r[/tex]
    [tex]a_t = \alpha r[/tex]
     
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