Solving Angular Rotation w/ Constant Acceleration - Emilie

[~angel~]

I've been trying to do this question in the textbook, but I can't seem to get the answer.

Emilie's potter's whel rotates with a constant 2.25 rad/s^2 angular acceleration. After 4 seconds the wheel has rotated through an angle of 60.0 rad. What was hte angular velocty of the wheel at the beginning of the 4.00 second interval.

I thought I could use a = (w2-w1)/ (t2-t1), but I end up with 6 as my answer, which is incorrect.

Thank you in advance.

 

[SpaceTiger]

Perhaps this thread will help.

 

[~angel~]

Ok, I've got it. But why is my method incorrect?

 

[SpaceTiger]

Ok, I've got it. But why is my method incorrect?

Because:

$$\omega_2\ne\frac{\Delta \theta}{\Delta t}=15\ rad/s$$

Actually,

$$\bar{\omega}=\frac{\omega_2+\omega_1}{2}=\frac{\Delta \theta}{\Delta t}$$