I have a small brushless motor running at 3 V and a cardboard disc (about 5.5 cm radius, 3 mm thick) which can be attached and detached from the shaft of the motor. When the disc is not attached the current drawn is 0.015 A and 0.11 A when the disc is attached.
I agree that the angular velocity of the system is lower with the disc attached because of the conservation of angular momentum. However, I am unsure what the torques values I have calculated actually represent. By using
$$ \tau=\frac{P}{\omega}$$
after measuring the angular velocity with and without the disk to be \$ \omega_{disc}=105 \ rad/s\$ and \$ \omega=418 \ rad/s\$ I calculated the torque with the disk to be \$\tau_{disc}=0.003 \ Nm\$ and without the disc to be \$\tau=0.0001 \ {Nm}\$ . But what do these torque values represent?
I prefer to think about these rotational system as if they were linear systems as I find them easier to think about conceptually. Let's say I have a box on the ground and I push on it to accelerate it. My force must be larger than the frictional force. Once I have accelerated it to a desired speed my force decreases to the point where my force equals the frictional force and the box is travelling at this desired speed. Let's say the system uses 100 W of power when travelling at constant velocity. Using
$$ F=\frac{P}{v}$$
will only tell you the force I am exerting to counteract friction. It does not tell you the force I exerted to accelerate the box in the first place.
Is this the same principle as the torque of the motor? Is it telling you the torque required to maintain a certain angular velocity? If so, how can we calculate the max torque output of the motor?