Examples of law of conservation of energy in the following topics:

 To solve a conservation of energy problem determine the system of interest, apply law of conservation of energy, and solve for the unknown.
 If you know the potential energies ($PE$) for the forces that enter into the problem, then forces are all conservative, and you can apply conservation of mechanical energy simply in terms of potential and kinetic energy.
 The equation expressing conservation of energy is: $KE_i+PE_i=KE_f+PE_f$.
 If you know the potential energy for only some of the forces, then the conservation of energy law in its most general form must be used:
 Once you have solved a problem, reexamine the forms of work and energy to see if you have set up the conservation of energy equation correctly.

 The first law of thermodynamics is a version of the law of conservation of energy specialized for thermodynamic systems.
 The law of conservation of energy can be stated like this: The energy of an isolated system is constant.
 If we are interested in how heat transfer is converted into work, then the conservation of energy principle is important.
 The first law of thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy into and out of the system.
 The first law of thermodynamics is the conservationofenergy principle stated for a system where heat and work are the methods of transferring energy for a system in thermal equilibrium.

 Mechanical work done by an external force to produce motional EMF is converted to heat energy; energy is conserved in the process.
 Energy is conserved in the process.
 We learned in the Atom "Faraday's Law of Induction and Lenz' Law" that Lenz' law is a manifestation of the conservation of energy.
 (b) Lenz's law gives the directions of the induced field and current, and the polarity of the induced emf.
 Apply the law of conservation of energy to describe the production motional electromotive force with mechanical work

 Kirchhoff's circuit laws are two equations that address the conservation of energy and charge in the context of electrical circuits.
 Fundamentally, they address conservation of energy and charge in the context of electrical circuits.
 Kirchhoff's laws are extremely important to the analysis of closed circuits.
 The voltage law is a simplification of Faraday's law of induction, and is based on the assumption that there is no fluctuating magnetic field within the closed loop.
 Describe relationship between the Kirchhoff's circuit laws and the energy and charge in the electrical circuits

 This relationship is known as Faraday's law of induction.
 The minus sign in Faraday's law of induction is very important.
 Lenz' law is a manifestation of the conservation of energy.
 In fact, if the induced EMF were in the same direction as the change in flux, there would be a positive feedback that would give us free energy from no apparent source—conservation of energy would be violated.
 Express the Faraday’s law of induction in a form of equation

 The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.
 These examples have the hallmarks of a conservation law.
 This is an expression for the law of conservation of angular momentum.
 An example of conservation of angular momentum is seen in an ice skater executing a spin, as shown in .
 Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum.

 In physics and chemistry there are many conservation laws—among them, the Law of Conservation of Nucleon Number, which states that the total number of nucleons (nuclear particles, specifically protons and neutrons) cannot change by any nuclear reaction.
 Chain reactions of nuclear fission release a tremendous amount of energy, but follow the Law of Conservation of Nucleon Number.
 Finally, nuclear fusion follows the Law of Conservation of Nucleon Number.
 It is well understood that the tremendous amounts of energy released by nuclear fission and fusion can be attributed to the conversion of mass to energy.
 However, the mass that is converted to energy is rather small compared to any sample, and never includes the conversion of a proton or neutron to energy.

 Conservation of mechanical energy states that the mechanical energy of an isolated system remains constant without friction.
 Conservation of mechanical energy states that the mechanical energy of an isolated system remains constant in time, as long as the system is free of all frictional forces.
 Let us consider what form the workenergy theorem takes when only conservative forces are involved (leading us to the conservation of energy principle).
 This equation is a form of the workenergy theorem for conservative forces; it is known as the conservation of mechanical energy principle.
 Remember that the law applies to the extent that all the forces are conservative, so that friction is negligible.

 Gravitational energy is the potential energy associated with gravitational force (a conservative force), as work is required to elevate objects against Earth's gravity.
 Gravitational potential energy near the Earth can be expressed with respect to the height from the surface of the Earth.
 (The surface will be the zero point of the potential energy. ) We can express the potential energy (gravitational potential energy) as:
 For the computation of the potential energy we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation (with respect to the distance r between the two bodies).
 Using that definition, the gravitational potential energy of a system of masses m and M at a distance r using gravitational constant G is:

 Recall that the potential energy (PE), stored in a spring that follows Hooke's Law is:
 Conservation of energy for these two forms is:
 This statement of conservation of energy is valid for all simple harmonic oscillators, including ones where the gravitational force plays a role.
 The conservation of energy principle can be used to derive an expression for velocity v.
 The conservation of energy for this system in equation form is thus: