Force on disc: angular velocity after 3 rotations

[iamtrojan3]

Homework Statement

Hi, this is my first time on this forum, so don't flame me for not doing things right. I'm a junior in high school and currently taking AP physics, this problem in my hwk has been bothering me for a while. I've never received the answer to this question and i just need to know if i did this right, since this is really the first moment of inertia problem i encountered...
the problem is:
A force of 15N is applied tangentially to the edge of a 0.88kg solid disc initially at rest. The radius of the disc is 0.55m. How fast will the disc be spinning after it has gone 3.0 complete rotations? (disregard all the friction/air resistance etc.)

Homework Equations

Torque = I (alpha) from F=ma
W^2= Wo^2 + 2 (alpha)(theta)
Torque= Lever arm x Force applied

The Attempt at a Solution

The moment of Inertia of a solid disc is I=1/2mr^2 >> I=1/2(0.88)(0.55^2) >> I=0.1331
Torque= Lever arm x Force applied Torque= 15N x 0.55m = 8.25Nm
Torque = alpha x I >>> 8.25= alpha x 0.1331 >>> alpha = 62 (this doesn't look right )
Then just use Kenematic Equations
since 3 rotations is 6pi
W^2=Wo^2x2(alpha)(Theta)
W^2=0(62)(6pi)>>> W= 48.35radians/sec (this doesn't look right either )

Feel free to correct me on watever...i admitt, i suck/hate these problems.
Thanks

 

[Mindscrape]

Looks okay to me, but it is always easy to follow someone's work and make the same simple mistake they did.