Physics Theory

Mathamatical equations behind the simulations

Classical Mechanics


Newton's laws of motion

First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by an external force.

F = ma
Newton's Second Law: Force equals mass times acceleration

Third Law: For every action, there is an equal and opposite reaction.

Kinematics Equations

These equations describe motion with constant acceleration, fundamental to projectile motion and falling objects.

v = v₀ + at
Final velocity equals initial velocity plus acceleration times time
x = x₀ + v₀t + ½at²
Position as a function of time with constant acceleration
v² = v₀² + 2a(x − x₀)
Velocity–position relationship (time-independent)

Kinetic Energy

Energy of motion

K = ½mv²

Potential Energy

Potential energy near Earth's surface

Ep = mgh

Work–Energy Theorem

Work done equals change in kinetic energy

W = ΔK

Momentum

Momentum of an object

p = mv

Conservation of Momentum

Total momentum remains constant

pbefore = pafter

Centripetal Force

Force required for circular motion

F = mv2 / r

Simple Harmonic Motion

Motion where the restoring force is proportional to displacement and directed toward equilibrium.

F = −kx

Momentum

Momentum of an object

p = mv

Conservation of Momentum

Total momentum remains constant

pbefore = pafter

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Waves & Optics


Wave Speed Equation

Wave speed equals frequency times wavelength

v = fλ

Traveling Wave Equation

Describes the shape and motion of a traveling wave

y(x,t) = A sin(kx − ωt)

Wave Number

Spatial frequency of a wave

k = 2π / λ

Angular Frequency

Rate of oscillation in radians per second

ω = 2πf

Refractive Index

Measures how much light slows down in a medium

n = c / v

Snell’s Law

Governs refraction at a boundary

n₁ sinθ₁ = n₂ sinθ₂

Law of Reflection

Angle of incidence equals angle of reflection

θᵢ = θᵣ

Double-Slit Interference

Condition for constructive interference

d sinθ = mλ

Thin Lens Equation

Relates focal length, object distance, and image distance

1 / f = 1 / u + 1 / v

Magnification

Ratio of image size to object size

m = v / u

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Electromagnetism


Coulomb's Law

Electrostatic force between two point charges

F = keq1q2 / r2

Electric Field

Force per unit charge

E = F / q

Electric Field of a Point Charge

Field strength around a single charge

E = keq / r2

Electric Potential Energy

Energy stored in an electric field

U = keq1q2 / r

Electric Potential

Potential energy per unit charge

V = U / q

Capacitance

Ability to store charge

C = Q / V

Energy Stored in a Capacitor

Electrical energy stored

U = ½CV2

Ohm's Law

Relationship between voltage, current, and resistance

V = IR

Electric Power

Rate of electrical energy transfer

P = IV

Resistors in Series

Total resistance adds directly

Rtotal = R1 + R2 + R3 + ...

Resistors in Parallel

Reciprocal of total resistance

1 / Rtotal = 1 / R1 + 1 / R2 + 1 / R3 + ...

Magnetic Force on Moving Charge

Lorentz force on a charged particle

F = qvB sinθ

Magnetic Force on Current

Force on a current-carrying wire

F = BIL sinθ

Faraday's Law of Induction

Induced EMF from changing magnetic flux

ε = −dΦB / dt

Magnetic Flux

Measure of magnetic field through a surface

ΦB = BA cosθ

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Thermodynamics


Ideal Gas Law

Relationship between pressure, volume, temperature, and amount of gas

PV = nRT

First Law of Thermodynamics

Energy conservation in thermal systems

ΔU = Q − W

Heat Transfer

Heat required to change temperature

Q = mcΔT

Specific Heat Capacity

Heat capacity per unit mass

c = Q / (mΔT)

Latent Heat

Energy required for phase change

Q = mL

Thermal Expansion (Linear)

Change in length due to temperature change

ΔL = αL0ΔT

Thermal Expansion (Volume)

Change in volume due to temperature change

ΔV = βV0ΔT

Heat Conduction

Rate of heat transfer through a material

Q / t = kA(T2 − T1) / d

Stefan-Boltzmann Law

Power radiated by a black body

P = σAT4

Efficiency of a Heat Engine

Ratio of work output to heat input

η = W / QH

Carnot Efficiency

Maximum theoretical efficiency

ηCarnot = 1 − TC / TH

Internal Energy of Ideal Gas

Total kinetic energy of gas molecules

U = (3/2)nRT

Work Done by Gas

Work during expansion or compression

W = PΔV

Entropy Change

Measure of disorder in a system

ΔS = Q / T

Boltzmann's Entropy Formula

Entropy in terms of microstates

S = kB ln(Ω)