# Angular Acceleration without Angular Speed.

1. Apr 26, 2010

### Awkwardness

1. The problem statement, all variables and given/known data
A wheel rotating about a fixed axis has an angular position given by theta= 3.0 - 2.0t^3, where theta is measured in radians and t in seconds. What is the angular acceleration of the wheel at t = 2.0s?

2. Relevant equations
wf = w + at

3. The attempt at a solution
I realize I most likely should use that kinematic equation to find the angular acceleration, but how would I find the angular speed? dtheta/dt? If so, is it like -6t^2/2?
Assuming w is just -6t^2, then I then got -6t^2=at. Which should be -12=a but I don't see that as an answer. Closest would be -24 rad/s^2.

Last edited: Apr 26, 2010
2. Apr 26, 2010

### zachzach

Just look up the definition of angular acceleration:

$$\alpha = \frac{d^2\theta}{dt^2}$$

3. Apr 26, 2010

### Awkwardness

Hmm so it would be -24 rad/s2 wouldn't it?

4. Apr 26, 2010

### zachzach

That's what I got.

5. Apr 26, 2010

### Awkwardness

Alright thankyou. I was set on using the kinematic equation and completely overlooked the simpler method.

6. Apr 26, 2010

### zachzach

Also, the kinematic equations only work when there is constant acceleration (that is how they are derived). As you can see in this case the acceleration is NOT constant.

7. Apr 26, 2010

### Awkwardness

Thankyou, I'll keep that in mind. I appreciate it.