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)