I would like to know what is "mechanical dynamic equation" in mechanics and engineering to convert from torque to rpm? I know the relation T = J*alpha. But how to include motor characteristics for example slip (induction motor), friction, number of poles, mutual inductance?
In the physics of linear motion you have:
(power) = (force) x (speed)
There is a direct equivalent for rotational motion:
(power) = (torque) x (rotational speed)
In each case you have to use consistent units of measure. So for linear motion you may have:
power [W] = force [N] x speed [m/s]
For rotational motion:
power [W] = torque [N m] x rotational speed [rad/s]
These are the mechanical equations.
For electrical equations you will need to consult an electrical engineering text.