In mechanics, the main conservation laws are the following:
- energy conservation law
- momentum conservation law
- angular momentum conservation law
All these conservation laws are fundamental if we correctly apply them.
For example, the energy conservation law is valid if take into accout all types of energy. There is no fundamental conservation law of mechanical energy, which is the sum of potential energy and kinetic energy. If the system is isolated and there is no friction, then we have conservation of mechanical energy of the system. But if there is a friction, then we have conservation law of total energy: the sum of mechanical energy and thermal energy.
In relation to the conservation law of total energy, the work-energy theorem is introduced. Accoding to this theorem, the change of mechanical energy is equal to the work produced by all forces acting on object. For example, if there is only the friction force then the energy-work theorem says that
where is the final mechanical energy of the system, is the initial mechanical energy of the system, and is the work produced by the friction. The work produced by the friction is negative, which means that the net mechanical energy decreases. At the same time the work produced by the friction can be expressed as the change of the thermal energy of the system (which is related to the temperature of the system - increase of the temperature):
If we combine above equations, we obtain conservation of the total energy:
The momentum conservation law is also fundamental law. Usually we apply the momentum conservation law for collision of the objects. When we apply this conservation law we need to be careful: we should apply this law for time instances just before and just after the colision. It is important that even if we have friction during the collision we still have momentum conservation law. In this case (with friction) we do not have conservation of mechanical energy, but we have conservation of momentum.
Below you can find animations of different concepts related to conservation laws.