How are torque and horsepower related in a mechanical drive?

• A. HP = Torque × RPM / 5252
• B. HP = Torque × RPM × 5252
• C. HP = Torque ÷ RPM
• D. HP = Torque × 5252 / RPM

Answer: (A)

Power in a mechanical drive is the rate at which work is done, and for rotation it comes from how hard the shaft can twist (torque) and how fast it turns (speed). When torque is measured in pound-feet and speed in revolutions per minute, the standard relationship to horsepower is HP = Torque × RPM / 5252. This factor 5252 comes from converting the torque and rotational speed into the same power unit (horsepower) by tying in the definitions of horsepower and the conversion between revolutions per minute and radians per second.

So, at a fixed torque, increasing RPM increases horsepower; at a fixed RPM, increasing torque increases horsepower. The other forms would misplace the factors or invert the relation, which would not match how power scales with torque and speed.