Power from Torque
Mechanical power from torque and angular speed.
Formula
Variables
Example
Engine power output
How it works
This formula says that a rotating machine delivers power when a torque acts through an angular speed. It comes from the work done by a torque: a small rotational work amount is dW = au d, so dividing by time gives P = dW/dt = au(d/dt) = au. In SI units, torque is in newton-metres and angular velocity is in radians per second, so the result is watts.
When to use it
Use this when you know how hard a shaft is being twisted and how fast it is spinning, such as in motors, gearboxes, turbines, or rotating test rigs. It is especially useful for converting rotational measurements into output power.
Worked example, step by step
A drill motor applies a torque of 12 Nm while rotating at 150 rad/s. P = au = 12 150 P = 1800 W So the mechanical power output is 1800 W, or 1.8 kW.
Common mistakes to avoid
- Using revolutions per minute directly instead of converting to rad/s
- Forgetting that torque and angular velocity must be from the same shaft or rotating part
- Mixing up mechanical power with electrical power without accounting for losses
Did You Know?
An engine's power is torque times rotational speed, which is why gearboxes trade one for the other.
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