Theorem
The Work Energy Theorem States that
where
Derivation
So
Interpretation and Information
As shown in the derivation, the work energy theorem is simply Newton’s Second Law (See Newton’s Laws) in Energy Form.
The work energy theorem is an invariant law, meaning that it is the same in all reference frames.
The Work Energy only applies to individual particles and not Systems of Particles. Each part of the object should behave in exactly the same way.
For example, in a car crash, different parts of the car act differently in response to the crash and there is internal energy moving with the bending of the car, so we cannot apply the Work-Energy Theorem exactly.
This also applies to friction; friction is complicated and is generally not correct to apply the work-energy theorem to particles undergoing frictional forces.