Relationship between torque and power
If a force is allowed to act through a distance, it is doing mechanical work. Similarly, if torque is allowed to act through a rotational distance, it is doing work. Power is the work per unit time. However, time and rotational distance are related by the angular speed where each revolution results in the circumference of the circle being travelled by the force that is generating the torque. This means that torque that is causing the angular speed to increase is doing work and the generated power may be calculated as:
Mathematically, the equation may be rearranged to compute torque for a given power output. However in practice there is no direct way to measure power whereas torque and angular speed can be measured directly.
Consistent units must be used. For metric SI units power is watts, torque is newton-metres and angular speed is radians per second (not rpm and not even revolutions per second).
