Laws of Physics
Conservation laws
Conservation of mass law
The law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of a closed system (in the sense of a completely isolated system) will remain constant over time. This is much like the conservation of energy in the sense that both keep the energy or mass enclosed in the system (hence, "conservation").
(However, in special relativity, the conservation of mass does not apply if the system is open and energy escapes. However, it does continue to apply to closed systems.)
Conservation of energy law
The law of conservation of energy is an empirical law of physics. It states that the total amount of energy in an isolated system remains constant over time (is said to be conserved over time).
Conservation of momentum law
Momentum has the special property that, in a closed system, it is always conserved, even in collisions and separations caused by explosive forces. Kinetic energy, on the other hand, is not conserved in collisions if they are inelastic. Since momentum is conserved it can be used to calculate an unknown velocity following a collision or a separation if all the other masses and velocities are known. A common problem in physics that requires the use of this fact is the collision of two particles. Since momentum is always conserved, the sum of the momenta before the collision must equal the sum of the momenta after the collision:
where u1 and u2 are the velocities before collision, and v1 and v2 are the velocities after collision.
Determining the final velocities from the initial velocities (and vice versa) depend on the type of collision. There are two types of collisions that conserve momentum: elastic collisions, which also conserve kinetic energy, and inelastic collisions, which do not.
Conservation of angular momentum law
Angular momentum is conserved in a system where there is no net external torque.
The angular momentum of a system of particles (e.g. a rigid body) is the sum of angular momenta of the individual particles. For a rigid body rotating around an axis of symmetry (e.g. the fins of a ceiling fan), the angular momentum can be expressed as the product of the body's moment of inertia I (a measure of an object's resistance to changes in its rotation rate) and its angular velocity ω:
In this way, angular momentum is sometimes described as the rotational analog of linear momentum.
Charge conservation law
The change in the amount of electric charge in any volume of space is exactly equal to the amount of charge flowing into the volume minus the amount of charge flowing out of the volume. In essence, charge conservation is an accounting relationship between the amount of charge in a region and the flow of charge into and out of that region.
Mathematically, we can state the law as a continuity equation:
Q(t) is the quantity of electric charge in a specific volume at time t, QIN is the amount of charge flowing into the volume between time t1 and t2, and QOUT is the amount of charge flowing out of the volume during the same time period.
Gas Laws
Boyle's Law (pressure and volume of ideal gas)
Charles & Gay-Lussac (gases expand equally with the same change of temperature)
Ideal Gas Law : PV=nRT
Einstein's laws
Energy of photons - Energy equals Planck's constant multiplied by the frequency of the light.
Special Relativity
Constancy of the speed of light
Lorentz transformations - Transformations of Cartesian coordinates between relatively moving reference frame.
y' = y
z' = z
Mass-energy equivalence
(Energy = mass × speed of light2)
General Relativity
Energy-momentum (including mass via E=mc2) curves spacetime. This is described by the Einstein field equations:
Rab is the Ricci tensor, R is the Ricci scalar, gab is the metric tensor, Tab is the stress-energy tensor, and the constant is given in terms of π (pi), c (the speed of light) and G (the gravitational constant).
, where
Newton's laws
Newton's laws of motion - Replaced by relativity
1. Newton's First Law:
Every body remains in a state of constant velocity unless acted upon by an external unbalanced force. This means that in
the absence of a non-zero net force, the center of mass of a body either remains at rest, or moves at a constant velocity.
2. Newton's Second Law: A body of mass m subject to a net force F undergoes an acceleration a that has the same direction as the
force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e., F = ma. Alternatively,
the total force applied on a body is equal to the time derivative of linear momentum of the body:
. When the mass is constant, this implies .
3. Newton's Third Law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear. This means
that whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are
equal in magnitude and opposite in direction. This law is sometimes referred to as the action-reaction law, with F called the "action"
and −F the "reaction". The action and the reaction are simultaneous.
Law of heat conduction
General law of gravitation - Gravitational force between two objects equals the gravitational constant times the product of the masses divided by the distance between them squared. Newton's second law was gravity's effect on us humans.
This law is really just the low limit solution of Einstein's field equations and is not accurate with modern high precision gravitational measurements.
Electromagnetic laws
Coulomb's law - Force between any two charges is equal to the product of the charges divided by 4 pi times the vacuum permittivity times the distance squared between the two charges.
Ohm's Law
Kirchhoff's circuit laws (current and voltage laws)
Kirchhoff's law of thermal radiation
Maxwell's equations (electric and magnetic fields):
Name
Gauss's law :
Gauss's law for magnetism:
Faraday's law of induction:
Ampère's law + Maxwell's extension:
Partial Differential form
Thermodynamic laws
Zeroth law of thermodynamics
If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with one another.
First law of thermodynamics
The change in energy dU in a system is accounted for entirely by the heat δQ absorbed by the system and the work δW done by the system:
Second law of thermodynamics
Third law of thermodynamics
As the temperature T of a system approaches absolute zero, the entropy S approaches a minimum value C: as T → 0, S → C.
Onsager reciprocal relations - sometimes called the Fourth Law of Thermodynamics
;
.
Quantum laws
Heisenberg Uncertainty Principle - Uncertainty in position multiplied by uncertainty in momentum is equal to or greater than the reduced Planck constant divided by 2.
Matter wavelength - Laid the foundations of particle-wave duality and was the key idea in the Schrödinger equation.
Schrödinger equation - Describes the time dependence of a quantum mechanical system.
The Hamiltonian H(t) is a self-adjoint operator acting on the state space, ψ(t) is the instantaneous quantum state vector at time t, i is the unit imaginary number, is Planck's constant divided by 2π
It is thought that the successful integration of Einstein's field equations with the uncertainty principle and Schrödinger equation, something no one has achieved so far with a testable theory, will lead to a theory of quantum gravity, the most basic physical law sought after today.