Physics Laws and Theorems Summarized

For each of the basic principles of physics, there are several important laws or theorems that we should all become familiar with. Here’s a breakdown of the key laws and theorems associated with each principle:

1. Motion and Forces

  • Newton’s Laws of Motion:
    • First Law (Law of Inertia): Explains that an object will maintain its state of motion unless acted upon by an external force.
    • Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma).
    • Third Law: For every action, there is an equal and opposite reaction.
  • Law of Universal Gravitation (Newton’s Law of Gravity): Every mass attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers (F = G (m1 × m2) / r²).

2. Energy

  • Conservation of Energy (First Law of Thermodynamics): Energy cannot be created or destroyed; it can only change forms (e.g., potential energy to kinetic energy).
  • Work-Energy Theorem: The work done on an object is equal to the change in its kinetic energy (W = ΔKE).
  • Law of Conservation of Mechanical Energy: In a closed system without non-conservative forces (like friction), the total mechanical energy (sum of kinetic and potential energy) remains constant.

3. Work and Power

  • Hooke’s Law (for elastic forces): The force needed to extend or compress a spring by a distance x is proportional to that distance (F = -kx).
  • Law of Machines: Mechanical advantage (MA) is the ratio of output force to input force, used to calculate efficiency and work in machines.

4. Heat and Temperature

  • Second Law of Thermodynamics: Heat naturally flows from hotter objects to colder ones, and processes that convert heat energy to work have limitations (entropy always increases in an isolated system).
  • Zeroth Law of Thermodynamics: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
  • Third Law of Thermodynamics: As the temperature of a system approaches absolute zero, the entropy of the system approaches a constant minimum.
  • Boyle’s Law (Gas Laws): At constant temperature, the pressure of a gas is inversely proportional to its volume (P1V1 = P2V2).
  • Charles’s Law (Gas Laws): At constant pressure, the volume of a gas is directly proportional to its temperature (V1/T1 = V2/T2).

5. Waves

  • Law of Reflection: The angle of incidence of a wave equals the angle of reflection.
  • Snell’s Law (Law of Refraction): Describes how light bends when passing from one medium to another with a different refractive index (n1 sin(θ1) = n2 sin(θ2)).
  • Principle of Superposition: When two or more waves overlap, the resulting wave displacement is the sum of the individual displacements.

6. Electricity and Magnetism

  • Ohm’s Law: The current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance (V = IR).
  • Coulomb’s Law: The electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them (F = k(q1q2) / r²).
  • Faraday’s Law of Electromagnetic Induction: A changing magnetic field within a closed loop of wire induces an electromotive force (EMF) in the wire.
  • Ampère’s Law: The magnetic field in space around an electric current is proportional to the current that flows through a wire.
  • Gauss’s Law: The electric flux through any closed surface is proportional to the total charge enclosed within the surface.

7. Light and Optics

  • Huygens’ Principle: Every point on a wavefront acts as a source of wavelets that spread out in the forward direction at the same speed as the wave itself.
  • Snell’s Law (also mentioned under Waves): Governs the refraction of light when passing between media.
  • Law of Reflection: The angle of reflection of light is equal to the angle of incidence.
  • Lensmaker’s Equation: Describes the focal length of a lens in terms of its curvature and refractive index.
  • Planck’s Law (related to light as electromagnetic radiation): Describes the energy of photons emitted by objects at a given temperature.

8. Sound

  • Doppler Effect: The observed frequency of a wave depends on the relative speed of the source and observer (explains pitch changes in moving sources).
  • Hooke’s Law (for oscillations): Describes the force in springs and can be applied to simple harmonic motion.

9. Matter and Its Properties

  • Archimedes’ Principle: A body submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the body.
  • Pascal’s Law: A change in pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid.
  • Bernoulli’s Principle: For a fluid in motion, an increase in speed occurs simultaneously with a decrease in pressure or potential energy.
  • Boyle’s Law and Charles’s Law (mentioned under Heat and Temperature) also apply here to the behavior of gases.

10. Scientific Method

  • Occam’s Razor: When presented with competing hypotheses, the one with the fewest assumptions should be selected.
  • Falsifiability Principle (Karl Popper): A scientific hypothesis must be falsifiable, meaning it can be tested and potentially proven wrong.