Understanding Motor speed, torque, voltage

[AriMindell]

I am working on programming a motor simulator for FRC motors, which allows a user to input a set of motors, a gear reduction, and an attachment in the form of a moment of inertia.
The simulator should calculate the angle, angular velocity, and angular acceleration of the attachment at any time.
Currently, I calculate the angular acceleration (alpha) of the attachment, then add alpha(*dt) to the angular velocity (omega), and omega to the position (theta).
I had determined the following formula for torque of the motor, given voltage and current speed: stallTorque * (percentVoltage - (omega / freeSpeed)
and I know from physics that: alpha=torque/moment.
This does not work as expected, and I think it's because my formula for torque is wrong, and I don't fully understand DC motors.
How are speed and torque related? by most explanations, speed should have an inverse relationship with torque, but this system would indicate that it does not. Am I making a false assumption?