Angular acceleration from change in angular velocity and angle

[natasha13100]

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?

 

[WannabeNewton]

$\alpha = \frac{\mathrm{d} \omega}{\mathrm{d} t} = \omega\frac{\mathrm{d} \omega}{\mathrm{d} \theta}$ so if you know $\omega(\theta)$ you don't need to consider time.

 

[natasha13100]

Does this work even if angular acceleration is not constant?

 

[WannabeNewton]

Yes certainly; the above is true for any angular acceleration whatsoever. All you need to know is $\omega$ as a function of $\theta$.

 

[natasha13100]

So α=ω(θ)*Δω/Δθ?

 

[D H]

Does this work even if angular acceleration is not constant?

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

 

[WannabeNewton]

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.

 

[natasha13100]

Okay so this only works with 2-D objects.

 

[WannabeNewton]

Yes because for 3d rigid body dynamics/kinematics the angular acceleration is much more complicated. See: http://ocw.mit.edu/courses/aeronaut...fall-2009/lecture-notes/MIT16_07F09_Lec25.pdf