Angular acceleration of a motor

[Dangousity]

Homework Statement

I have a motor, with an armature that has a mass of 250kg , and a diameter of 30 cm. Assuming the mass of the armature is evenly distributed, the rotational inertia of the armature is 22.5 kg-m^2.
Now the motor accelerating unloaded, with armature current regulated so that the armature develops a constant torque of 120 N-m, would be coming up to speed at 35.8 rad/sec^2? (Did I get this wrong?)
Assume the torque stays the same, How long will it take for the unloaded armature to accelerate from 0 to 3000 rpm.

Homework Equations

T=Ia 22.5 kg-m^2(3000(pie)-15cm(pie))/(T)
22.5(3000(pie)-.15m(pie))/(T)

I think I am doing something wrong here cause I get stuck here.

The Attempt at a Solution

 

[JaWiB]

Mmm. Pie...

It looks like you're trying to convert RPM to rad/s? I don't quite follow your equations.

3000 revolution/min * 2pi rad/revolution * 1 min/60 s

Should give you your angular speed.

To figure out how long it takes, you can probably use the fact that net torque = dL/dt (the time rate of change of angular momentum) or you could use rotational kinematic equations to solve for the time.

 

[Dangousity]

Mmm. Pie...

It looks like you're trying to convert RPM to rad/s?

Correct, I am attempting to do that