Finding angular acceleration for this prob

[ballahboy]

A rotating wheel requires 3.00s to rotate 37.0 revolutions. Its angular velocity at the end of the 3.00-s interval is 98.0rad/s. What is the constant angular acceleration of the wheel?

What i did was i used average w=delta(theta)/delta time. Then i used average w=radical(w^2+wo^2) to find wo. Then i plugged it all into w=wo+alpha(t) and i got alpha=12.67. The answer is suppose to be 13.7rad/s^2. Can someone help me on this problem?
thanks

 

[Parth Dave]

There is a single formula, incorporating all the elements you are given: wf, t, theta, alpha. Find that, and just sub in values.

 

[ballahboy]

What is the formula? The ones I have all have "wi" in it and I'm not sure I calculated that correctly.

 

[Sirus]

Here's how you calculate the initial angular velocity.

Since angular acceleration is constant:
$$\frac{\Delta\theta}{\Delta t}=\omega_{av}=\frac{\omega+\omega_{0}}{2}$$
Since one revolution is $2\pi$ radians,
$$2\times\frac{37\times 2\pi}{3 s}-98.0\frac{rad}{s}=\omega_{0}$$

Now use $$\omega=\omega_{0}+\alpha\Delta t$$

 

[Parth Dave]

That method works, as does using: theta = (wf)t - .5*alpha*t^2.