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Work and power in rotation
Intermediate
Work equals torque times angle; power equals torque times ω.
P = τωW = τθ, P = τω. Motors give constant power: higher speed means lower torque.
A 2 kW motor at 100 rad/s gives 20 N·m.
Gear ratios trade speed for torque.
In more detail
Work done by a torque through an angle is τθ, and the power delivered is τω. These are the rotational analogues of linear work and power.
Real-world uses
- Engine power in cars is calculated from torque and engine speed.
- Electric motors are rated by the torque they deliver at a given speed.
- An engine's power output is the torque it delivers times its angular speed, which is how car power ratings are calculated.
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Frequently asked questions
How is torque related to power?
Power equals torque times angular velocity.
Does a high torque always mean high power?
No. Power depends on both torque and speed.
Why are engines rated in kilowatts and horsepower?
These are both power units, and the torque-times-speed relation gives the power at any engine speed.
Related topics in Rotational Motion
Rolling without slipping · Rolling down an incline · Race of rolling bodies · Angular momentum of a particle · Angular momentum of rigid body · Torque and angular momentum