Principle of Work and Energy for the Plane Motion of Rigid Bodies

The principle of work and energy for a rigid body in obtained by adding the equations of work and energy for each of the particles that make up the rigid body, which gives

where T₁ and T₂ are the total kinetic energies of all the particles that make up the body and U_1-2 is the total work done by all external forces and couples acting on the body.

One can also express the principle of work and energy as

where U^(o)_1-2 is the work done by all non-conservative forces.

When two or more rigid bodies are connected by inextensible cords or by frictionless pins, the above work and energy equations can be written for each body. When the resulting equations are added together, the work done by the connection forces will cancel in pairs. Therefore, the above equations are also valid for a system of connected rigid bodies!