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Work in rotation
Intermediate
Torque times angle turned.
W = τθFor a torque τ turning through an angle θ, the work is W = τθ (θ in radians), analogous to F·d. Power P = τω.
A 10 N·m torque through 2 rad does 20 J.
Use radians.
In more detail
In rotation, work is done by torque acting through an angle, W = τθ. The rotational work-energy theorem links this to the change in rotational kinetic energy.
Real-world uses
- Motors do work by applying torque to rotate shafts.
- Brakes on a wheel do negative rotational work to slow it down.
- A motor shaft turning through a set angle does work equal to the torque times that angle.
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Frequently asked questions
What is the rotational version of power?
Power equals torque times angular velocity, P = τω.
Is torque work done when the torque is zero?
No work is done when torque is zero, since there is no turning effect.
How is rotational work like linear work?
Torque plays the role of force and angle plays the role of displacement, so W = τθ is the rotational version of W = Fd.
Related topics in Work, Energy & Power
Energy and power bills · Power of engines and climbers · Escape from a potential well · Rotational kinetic energy · Rolling without slipping energy · Work done by gravity on incline