Angular Acceleration without Angular Speed.

AI Thread Summary
The discussion centers on calculating the angular acceleration of a wheel with a given angular position equation, theta = 3.0 - 2.0t^3. The correct method involves using the definition of angular acceleration, α = d²θ/dt², rather than relying on kinematic equations, which apply only under constant acceleration. Upon differentiation, the angular acceleration is determined to be -24 rad/s² at t = 2.0 seconds. The conversation highlights the importance of recognizing when to apply different physics principles. Ultimately, the simpler method of differentiation provided the correct answer.
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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.
 
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Just look up the definition of angular acceleration:

\alpha = \frac{d^2\theta}{dt^2}
 
zachzach said:
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?
 
That's what I got.
 
zachzach said:
That's what I got.

Alright thankyou. I was set on using the kinematic equation and completely overlooked the simpler method.
 
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.
 
Thankyou, I'll keep that in mind. I appreciate it.
 
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