Wheel with constant external torque and friction stopping

[spirited]

Homework Statement

A wheel mounted on an axis that is not frictionless is initially at rest. A constant external torque of +49 N•m is applied to the wheel for 18 s, giving the wheel an angular velocity of +500 rev/min. The external torque is then removed, and the wheel comes to rest 120 s later.

(a) the moment of intertia of the wheel
(b) the frictional torque, which is assumed to be constant.

Homework Equations

angular acceleration *a* = angular velocity/ t = *w*/t
*a* = *t*/I (torque / Moment of Inertia)
I = (*t*t)/w
*t* fric = *t*t2/t1

The Attempt at a Solution

(a) For part a, I used the I = equation and got 16.844 kgm^2
(b) For part b, I used the equation *t* fric = and got 2.53 Nm

Please help me with this problem. I believe that the answers are wrong...
Thanks

 

[ak1948]

I think you solve this as 2 equations with 2 unknowns. Let T be frictional torque and I be moment of inertia.

1) wheel speeds up: (49 - T) * 18 / I = 500

2) wheel slows down: 500 / 120 = T/I