Laws

Newton's Laws of Motion

  • First Law (Law of Inertia):

    • An object remains at rest or moves straight at constant speed unless acted on by a resultant external force.

  • Second Law:

    • Acceleration is directly proportional to resultant force, inversely proportional to mass.

    • Formula: ( F = ma )

  • Third Law:

    • For every action, there is an equal and opposite reaction.

Law of Gravitation

  • Newton’s Law of Universal Gravitation:

    • Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square distance between their centers.

    • Formula: ( F = GMm/ r^2)

Hooke's Law

  • The force needed to extend/compress a spring is directly proportional to the extension/compression, provided elastic limit is not exceeded.

  • Formula: ( F = kx )

Kepler's Laws of Planetary Motion

  • First Law (Law of Ellipses):

    • Planets move in elliptical orbits with the Sun at one focus.

  • Second Law (Law of Equal Areas):

    • A line connecting a planet to the Sun sweeps out equal areas in equal times.

  • Third Law (Harmonic Law):

    • The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

    • Formula: ( T^2 = k r^3 )

Coulomb's Law

  • The magnitude of electrostatic force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance.

  • Formula: ( F = Qq/4pie epsilon0 r squared )

Ohm's Law

  • Current through a conductor is directly proportional to the voltage across the two points, temperature remaining constant.

  • Formula: ( V = IR )

Kirchhoff's Laws

  • First Law (Current/Junction Rule):

    • Total current entering a junction equals total current leaving.

    • Formula: ( sum of I in = sum of I out)

  • Second Law (Voltage/Loop Rule):

    • The sum of potential differences = sum of EMFs in a closed loop.

    • Formula: ( EMF = V )

The Principle of Superposition (for Waves)

  • Resultant displacement at any point equals the vector sum of individual waves' displacements.

Snell’s Law (Law of Refraction)

  • The ratio of the sines of incidence and refraction angles is constant for given media.

  • Formula: ( n1 sin1 = n2 sin2)

The First Law of Thermodynamics

  • Change in internal energy equals heat added minus work done.

  • Formula: ( change energy = Q - W )

The Second Law of Thermodynamics

  • Heat cannot flow spontaneously from a colder to a hotter body.

  • Total entropy of an isolated system cannot decrease.

Boyle’s Law (Gas Law)

  • Pressure of a fixed mass of gas at constant temperature is inversely proportional to volume.

  • Formula: ( P = k/v)

Charles’s Law

  • Volume of gas at constant pressure is directly proportional to its absolute temperature.

  • Formula: ( V = kt )

Stefan-Boltzmann Law

  • Total energy radiated per unit area of a black body is proportional to the fourth power of its temperature.

  • Formula: ( P = sigma A T^4 )

Wien’s Displacement Law

  • Wavelength at maximum emission of black body radiation is inversely proportional to its absolute temperature.

  • Formula: ( lambda max = k/T)

Lenz’s Law

  • Direction of induced current opposes the change in magnetic flux causing it.

Faraday’s Law of Electromagnetic Induction

  • Induced electromotive force (EMF) in a loop equals rate of change of magnetic flux.

  • Formula: ( EMF = - Change inFlux linkage/ change in time )

Ampère’s Law

  • Magnetic field around a loop is proportional to the total current passing through.

The Doppler Effect

  • Change in frequency/wavelength of a wave in relation to an observer moving relative to wave source.

  • Formula (for sound): ( f' = f (v+v0/v-vs) )

The Photoelectric Effect (Einstein’s Equation)

  • Energy of a photon is proportional to its frequency; can eject electrons if energy exceeds work function.

  • Formula: ( E = hf = ke max + work function)

De Broglie Hypothesis

  • Every particle has an associated wavelength inversely proportional to its momentum.

  • Formula: ( lambda = h/p)