Find angular velocity of motor I'm quite bad at this, but I'm trying to change that and I need some assistance. Please bare with me while I attempt to explain what I'm trying to figure out and correct me where I'm wrong.
Basically I know that a moment is a force times length. That makes sense, however I cannot picture motors' moment. For example if an electromotor produces a moment of about 100 Nm, if I apply a force equal to 10 N to the end of a lever that's 10 m long connected to the motor's output shaft proportionally, would that mean that the motor's moment and the moment I create are the same and thus the motor will stop rotating?
The other thing I cannot figure out is what is the relation between the moment of an engine and it's angular velocity.
If I have a motor that has a constant torque (moment) of 400 Nm, apply a 200 Nm momentum, in a direction opposite of the direction of rotation of the motor, what is going to be the motor's angular velocity after 2 seconds, if the initial angular velocity was 188.5 rad/s?
 A: The actual formula for moment (Which I call Torque) is given as $$\tau = \overrightarrow F \times \overrightarrow r.$$ where r is the position vector to the point where the force is applied from the axis of rotation. If the force is applied perpendicular to the axis, torque becomes length times force. 
To your first question, the answer is yes. The motor will stop. This is because the torque generated is enough to keep the motor at a constant angular velocity, opposing dissipative forces like friction. You need apply only a fraction of the motors net torque to stop it's rotation.
Your second question is relatively straightforward, and can be found easily on the internet. Nonetheless, I will answer it. Torque can be written as: $$\tau = I \alpha$$ where $\alpha$ is the angular acceleration. Both $\alpha$ and $I$. Are measured about an axis passing through the centrer of mass. Also, if $\omega$ is the angular velocity, $$\omega_{final} = \omega_{initial} + \alpha t$$. With that said, I'll leave plugging in the values and obtaining an answer to you.
(All anglular value use radian measure)
