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Angular acceleration from change in angular velocity and angle

  1. Aug 4, 2013 #1
    Is there a way to calculate angular acceleration from the change in angular velocity and the change in the angle without considering time? How would you accomplish this?
     
  2. jcsd
  3. Aug 4, 2013 #2

    WannabeNewton

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    ##\alpha = \frac{\mathrm{d} \omega}{\mathrm{d} t} = \omega\frac{\mathrm{d} \omega}{\mathrm{d} \theta}## so if you know ##\omega(\theta)## you don't need to consider time.
     
  4. Aug 4, 2013 #3
    Does this work even if angular acceleration is not constant?
     
  5. Aug 4, 2013 #4

    WannabeNewton

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    Yes certainly; the above is true for any angular acceleration whatsoever. All you need to know is ##\omega## as a function of ##\theta##.
     
  6. Aug 4, 2013 #5
    So α=ω(θ)*Δω/Δθ?
     
  7. Aug 4, 2013 #6

    D H

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    It doesn't even work if angular acceleration is constant, at least not in three dimensional space (or higher).
     
  8. Aug 4, 2013 #7

    WannabeNewton

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    I think the OP is just talking about the angular acceleration ##\alpha = \frac{\Delta \omega}{\Delta t}## for "pancake objects" constrained to lie on a plane, in which case the above is just a consequence of the chain rule.
     
  9. Aug 4, 2013 #8
    Okay so this only works with 2-D objects.
     
  10. Aug 4, 2013 #9

    WannabeNewton

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