How are torque and rotational speed related to the mechanical power supplied to a generator?

The mechanical power supplied to an electric generator is directly proportional to the product of the shaft's torque and its rotational, or angular, velocity.1

This relationship is expressed by the fundamental principle that power is the product of turning force and speed. In the context of a generator, the mechanical energy provided by a prime mover—such as a turbine or engine—is converted into electricity through this rotating shaft.21

Mathematically, if $P$ represents mechanical power, $\tau$ represents torque, and $\omega$ represents angular velocity, the relationship is:

$$P=\tau \times \omega$$

While rotational speed is often measured in revolutions per minute (rpm) in engineering, it is expressed in radians per second for physical calculations. Because power is defined by these two factors, any change in the torque applied by the prime mover or the speed at which the shaft rotates directly impacts the total mechanical power available for conversion into electrical energy.312