Clear as mud! Can anyone do better?
Power, in watts, is the work done in unit time, ie, 1 second.
Torque, in N.m, is a force that tends to rotate a body about a chosen point.
For an electric motor power is torque times angular velocity in radians per second.
It may be helpful to do a dimensional analysis. In SI base units the Watt is equivalent to kg.m²/s³. Additionally the newton is kg.m/s².
For a motor power is torque times angular velocity which equals N.m.rad/s, and in base units kg.m.m.rad/s³
Simplifying gives kg.m².rad/s³
In the SI system the radian is dimensionless, ie, it has no units and is just a number, so in base units we get the power of the motor as proportional to kg.m²/s³ which is power in watts.
Following on from SoD’s comment that a stepper motor can give torque at zero speed so can an induction motor using vector control. There are two basic types of vector control, open-loop and closed loop. In open loop there is no rotor position sensor. This limits the minimum speed to around 0.8Hz. In closed loop, with knowledge of rotor position, an induction motor can give full torque at zero speed. Although the rotor is not rotating the magnetic field from the poles is, at the appropriate slip frequency.
The ability to have full torque at zero speed is important in electric vehicles as it is the equivalent of slipping the clutch for a hill start.
Julie