How to Calculate Revolutions of a Wheel with Applied Brakes?

[Digdug12]

Homework Statement

A wheel, with circumference 0.6 m and moment of inertial 43 kg m2 about its center, rotates about a frictionless axle with angular velocity 13 radians per second. A brake is applied which supplies a constant force to a point on the perimeter of the wheel of 9 N, tangent to the wheel and opposing the motion. How many revolutions will the wheel make before coming to rest?

Homework Equations

KE_rotational=I*Omega²
Torque=I*alpha
I=M*R²

The Attempt at a Solution

I'm lost at how to start this problem, I tried to get the deceleration caused by the 9N force applied on the wheel by Newton's Second Law but I couldn't get the mass, so i used the I=M*R² equation to get the mass and then used F=M*a to find the deceleration, took that answer and divided by 2pi to find the revolutions, but the answer was off. What am I missing?

 

[rock.freak667]

The angular deceleration is given by a= \alpha r. Find \alpha. Then use the equations of rotational motion to find the total angular displacement from the initial angular velocity to rest.

 

[Digdug12]

I used a=alpha*r and i got the alpha to be .003, using Omega_f²=Omega_i²+2*alpha*Theta i get 28166, but the answer should be 672.9

EDIT: nevermind, i got it, thanks!