Frame invariant and conserved are two completely independent concepts. KE is frame variant, it has different values in different frames. But in all frames energy is conserved, its value stays the same over time.Leo Liu said:I am doubtful that one can apply the conservation of energy to a "moving" system because the kinetic energies of the same object measured at different observers are different. Is this method valid?
Conservation of energy in a CM (center of mass) system moving at constant velocity means that the total energy of the system remains constant, even as the individual components may exchange energy with each other. This is because the total kinetic energy of the system is equal to the total potential energy, and as the system moves at a constant velocity, there is no change in kinetic or potential energy.
Conservation of energy is important in a CM system because it helps us understand and predict the behavior of the system. It allows us to determine the total energy of the system at any given point and how that energy is distributed among its components. This is crucial in many scientific fields, such as mechanics and thermodynamics, and helps us make accurate calculations and predictions.
Conservation of energy applies to real-world situations in many ways. For example, in a simple pendulum, the potential energy at the highest point is equal to the kinetic energy at the lowest point, demonstrating conservation of energy. In more complex systems, such as a car moving at a constant speed, the energy of the car (kinetic energy) is equal to the energy of the fuel (chemical potential energy) being used to power it.
The main factor that can affect conservation of energy in a CM system moving at constant velocity is external forces acting on the system. These forces, such as friction or air resistance, can cause energy to be lost or gained by the system, leading to a change in its total energy. However, if the system is isolated with no external forces, conservation of energy will still hold true.
Conservation of energy is closely related to the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or transformed. In a CM system moving at constant velocity, the total energy remains constant, demonstrating the first law of thermodynamics. Additionally, the second law of thermodynamics states that the total entropy (disorder) of a closed system will always increase over time, which can also affect the total energy of a system.