# Angular acceleration from change in angular velocity and angle

1. Aug 4, 2013

### 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?

2. Aug 4, 2013

### 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.

3. Aug 4, 2013

### natasha13100

Does this work even if angular acceleration is not constant?

4. Aug 4, 2013

### WannabeNewton

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

5. Aug 4, 2013

### natasha13100

So α=ω(θ)*Δω/Δθ?

6. Aug 4, 2013

### D H

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

7. Aug 4, 2013

### 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.

8. Aug 4, 2013

### natasha13100

Okay so this only works with 2-D objects.

9. Aug 4, 2013