Work-Energy Balance
Work-energy balance
The initial kinetic energy of the rigid body at state 1 plus the work done on the rigid body between state 1 and state 2 equals the final kinetic energy of the rigid body at state 2. This relationship is the same for rigid bodies as it was for particles.
T1 + U1-2 = T2
Work (U1-2) may be broken up into conservative (U1-2,con) and non-conservative work (U1-2,non). The conservative work done on the body is equal to the body's change in potential energy.
T1 + V1 + U1-2,non = T2 + V2
Work and energy for a system of rigid bodies
Energies are additive. Therefore, the total kinetic energy of a system of rigid bodies is just the sum of the individual bodyies' kinetic energies. The same principle applies to potential energy.
T = ∑ Ti
V = ∑ Vi
Conservation of energy
When there are no non-conservative forces performing work on the rigid body or system of rigid bodies, energy is conserved.
T1 + V1 = T2 + V2