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

 The first law of thermodynamics is a version of the law of conservation of energy, specialized for thermodynamical systems.
 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.
 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 .
 In equation form, the first law of thermodynamics is
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.
 heat (noun) energy transferred from one body to another by thermal interactions
 law of conservation of energy (noun) The law stating that the total amount of energy in any isolated system remains constant, and cannot be created or destroyed, although it may change forms.
 internal energy (noun) The sum of all energy present in the system, including kinetic and potential energy; equivalently, the energy needed to create a system, excluding the energy necessary to displace its surroundings.

 Identify steps necessary to solve a conservation of energy problem
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 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.
 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: KE_{i}+PE_{i}+W_{nc}+OE_{i}=KE_{f}+PE_{f}+OE_{f}, where OE stands for all other energies.
 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:
$KE_i+PE_i+W_{nc}+OE_i=KE_f+PE_f+OE_f$
where $OE$ stand for all other energies, and $W_{nc}$ stands for work done by nonconservative forces.
 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.
 conservative force (noun) A force with the property that the work done in moving a particle between two points is independent of the path taken.
 potential energy (noun) The energy an object has because of its position (in a gravitational or electric field) or its condition (as a stretched or compressed spring, as a chemical reactant, or by having rest mass)
 kinetic energy (noun) The energy possessed by an object because of its motion, equal to one half the mass of the body times the square of its velocity.

 Describe relationship between the Kirchhoff's circuit laws and the energy and charge in the electrical circuits
Kirchhoff's circuit laws are two equations that address the conservation of energy and charge in the context of electrical circuits.
 Kirchhoff's laws are special cases of conservation of energy and charge.
 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.
 electromotive force (noun) (EMF)—The voltage generated by a battery or by the magnetic force according to Faraday's Law.
It is measured in units of volts (not newtons, N; EMF is not a force).
 capacitor (noun) An electronic component consisting of two conductor plates separated by empty space (sometimes a dielectric material is instead sandwiched between the plates), and capable of storing a certain amount of charge.

 Formulate the law of conservation of energy and momentum as it is applied to the refraction
Identify conditions required for the refraction phenomenon in optics
Refraction is a surface phenomenon that occurs as the change in direction of a wave due to a change in its medium.
 Refraction is mainly in governance to the law of conservation of energy and momentum.
 Refraction is described by Snell's law, which states that for a given pair of media and a wave with a single frequency, $\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$.
 Essentially, it is a surface phenomenon—mainly in governance to the law of conservation of energy and momentum.
 Refraction is described by Snell's law, which states that for a given pair of media and a wave with a single frequency, the ratio of the sines of the angle of incidence θ1 and angle of refraction θ2 is equivalent to the ratio of phase velocities (v_{1}/v_{2}) in the two media, or equivalently, to the opposite ratio of the indices of refraction (n_{2}/n_{1}):
$\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$.
 refractive index (noun) The ratio of the speed of light in air or vacuum to that in another medium.
 Snell's law (noun) A formula used to describe the relationship between the angles of incidence and refraction.

 Describe the process of conversion of matter to energy during the nuclear fusion and fission
Formulate law of Conservation of Nuclear Number
Through radioactive decay, nuclear fusion and nuclear fission, the number of nucleons (sum of protons and neutrons) is always held constant.
 The law of Conservation of Nuclear Number states that the sum of protons and neutrons among species before and after a nuclear reaction will be the same.
 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.
 fission (noun) The process of splitting the nucleus of an atom into smaller particles; nuclear fission.
 nucleon (noun) One of the subatomic particles of the atomic nucleus (i.e., a proton or a neutron).
 fusion (noun) A nuclear reaction in which nuclei combine to form more massive nuclei with the concomitant release of energy.

 Apply the law of conservation of energy to describe the production motional electromotive force with mechanical work
Mechanical work done by an external force to produce motional EMF is converted to heat energy; energy is conserved in the process.
 Lenz' law guarantees that the motion of the rod is opposed, and therefore the law of energy conservation is not violated.
 (b) Lenz's law gives the directions of the induced field and current, and the polarity of the induced emf.
 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.
 Faraday’s law of induction (noun) A basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF).

 Kirchhoff's loop rule is a rule pertaining to circuits that is based upon the principle of conservation of energy.
 Kirchhoff's loop rule (otherwise known as Kirchhoff's voltage law (KVL), Kirchhoff's mesh rule, Kirchhoff's second law, or Kirchhoff's second rule) is a rule pertaining to circuits, and is based on the principle of conservation of energy.
 Conservation of energy—the principle that energy is neither created nor destroyed—is a ubiquitous principle across many studies in physics, including circuits.
 Mathematically, Kirchhoff's loop rule can be represented as the sum of voltages in a circuit, which is equated with zero:
We justify Kirchhoff's Rules from diarrhea and conservation of energy.
 Given that voltage is a measurement of energy per unit charge, Kirchhoff's loop rule is based on the law of conservation of energy, which states: the total energy gained per unit charge must equal the amount of energy lost per unit of charge.
illustrates the changes in potential in a simple series circuit loop.
 electromotive force (noun) (EMF)—The voltage generated by a battery or by the magnetic force according to Faraday's Law.
It is measured in units of volts, not newtons, and thus, is not actually a force.

 Consider observations of conservation law to explain angular momentum
Evaluate the implications of net torque on conservation of energy
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 .
 (I: rotational inertia, $\omega$: angular velocity)
Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum.
 quantum mechanics (noun) The branch of physics that studies matter and energy at the level of atoms and other elementary particles; it substitutes probabilistic mechanisms for classical Newtonian ones.
 angular momentum (noun) A vector quantity describing an object in circular motion; its magnitude is equal to the momentum of the particle, and the direction is perpendicular to the plane of its circular motion.
 torque (noun) A rotational or twisting effect of a force; (SI unit newtonmeter or Nm; imperial unit footpound or ftlb)

 Express the principle of the conservation of the mechanical energy in the form of an equation
Formulate the principle of the conservation of the mechanical energy
Conservation of mechanical energy states that the mechanical energy of an isolated system remains constant without friction.
 The conservation of mechanical energy can be written as "KE + PE = const".
 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.
 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.
 conservation (noun) A particular measurable property of an isolated physical system does not change as the system evolves.
 frictional force (noun) Frictional force is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.

 Kirchhoff's junction rule is an application of the principle of conservation of electric charge: current is flow of charge per time, and if current is constant, that which flows into a point in a circuit must equal that which flows out of it.
 Kirchhoff's junction rule, also known as Kirchhoff's current law (KCL), Kirchoff's first law, Kirchhoff's point rule, and Kirchhoff's nodal rule, is an application of the principle of conservation of electric charge.
 We justify Kirchhoff's Rules from diarrhea and conservation of energy.
 This law is founded on the conservation of charge (measured in coulombs), which is the product of current (amperes) and time (seconds).
 Because charge is conserved, the only way this is possible is if there is a flow of charge across the boundary of the region.
 electric charge (noun) A quantum number that determines the electromagnetic interactions of some subatomic particles; by convention, the electron has an electric charge of 1 and the proton +1, and quarks have fractional charge.
 current (noun) The time rate of flow of electric charge.