# Work

The definition of work and the previous equations used to calculate work may still be used when analyzing a rigid body. However, keep in mind that a rigid body has size and the forces may be applied at an offset to the body's center of mass (G). This means that each applied force may move through a different distance.

### Work done by a force

The work done by a force may be calculated as discussed in the *Work* section of the module on *Particle Work and Energy* or the work may be calculated by considering the moment resulting from the force application.

Depending on whether or not the force is constant with respect to the displacement and in what direction the force is applied, one of the following equations may be used to calculate the work performed by the force.

U = ∫F⋅dr

U = F⋅r = Fd cosθ

U =Fd

If the body is undergoing **pure rotation**, the work performed by force (F) may be calculated using the moment induced and the angular displacement.

U = ∫F_{⊥}rdθ = ∫M dθ

### Work done by a moment

If a pure moment is applied to the body, the following equation may be used to calculate the work performed by the moment (M).

U = ∫M⋅dθ