Angular Acceleration without Angular Speed.

[Awkwardness]

Homework Statement

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?

Homework Equations

wf = w + at

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.

 

[zachzach]

Just look up the definition of angular acceleration:

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

 

[Awkwardness]

Just look up the definition of angular acceleration:

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

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

 

[zachzach]

That's what I got.

 

[Awkwardness]

That's what I got.

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

 

[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.

 

[Awkwardness]

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