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Formulas

Formula Library

Learn from categorized formulas

Showing 24 of 341 formulas Page 6 of 15

Surface Tension Formula

Physics → Fluid Mechanics → Properties of Liquids → Surface Tension
$$\gamma = \frac{F}{L}$$
The force per unit length exerted parallel to the surface of a liquid.
📖 Physics 📚 Properties of Liquids

Binomial Probability Formula

Math → Statistics → Probability Distributions → Binomial Distribution
$$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$
The probability of exactly $k$ successes in $n$ independent Bernoulli trials.
📖 Math 📚 Probability Distributions

Root Mean Square Velocity

Chemistry → Physical Chemistry → Gaseous State → Molecular Speeds
$$v_{rms} = \sqrt{\frac{3RT}{M}}$$
The average speed of gas particles as determined by their kinetic energy.
📖 Chemistry 📚 Gaseous State

Terminal Velocity

Physics → Mechanics → Dynamics → Drag Force
$$v_t = \sqrt{\frac{2mg}{\rho AC_d}}$$
The constant speed reached by a falling object when the drag force equals the gravitational force.
📖 Physics 📚 Dynamics

Young's Double Slit (Fringe Width)

Physics → Optics → Wave Optics → Interference
$$\beta = \frac{\lambda D}{d}$$
Calculates the distance between two consecutive bright or dark fringes in an interference pattern.
📖 Physics 📚 Wave Optics

Area of a Trapezoid

Math → Geometry → 2D Shapes → Quadrilaterals
$$A = \frac{1}{2}(a+b)h$$
Calculates the area of a quadrilateral with at least one pair of parallel sides.
📖 Math 📚 2D Shapes

Self-Inductance of a Solenoid

Physics → Electromagnetism → Induction → Inductors
$$L = \frac{\mu_0 N^2 A}{l}$$
Calculates the inductance of a long solenoid.
📖 Physics 📚 Induction

Coulomb's Constant Formula

Physics → Electromagnetism → Electrostatics → Constants
$$k_e = \frac{1}{4\pi\epsilon_0}$$
Relates the SI units of charge to the electrostatic force.
📖 Physics 📚 Electrostatics

Henry's Law

Chemistry → Physical Chemistry → Solutions → Gas Solubility
$$C = kP$$
The solubility of a gas in a liquid is proportional to the partial pressure of the gas above the liquid.
📖 Chemistry 📚 Solutions

Kinetic Energy of Rotation

Physics → Mechanics → Rotational Motion → Energy
$$K_{rot} = \frac{1}{2}I\omega^2$$
Energy of a rigid body due to its rotation about an axis.
📖 Physics 📚 Rotational Motion

Heat Capacity Formula

Physics → Thermodynamics → Calorimetry → Specific Heat
$$Q = mc\Delta T$$
Calculates the amount of heat energy required to change the temperature of a substance.
📖 Physics 📚 Calorimetry

Van der Waals Equation

Chemistry → Physical Chemistry → States of Matter → Real Gases
$$\left(P + a\frac{n^2}{V^2}\right)(V - nb) = nRT$$
An equation of state for real gases that accounts for molecular size and intermolecular forces.
📖 Chemistry 📚 States of Matter

Ampere's Circuital Law

Physics → Electromagnetism → Magnetism → Magnetic Fields
$$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$$
Relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
📖 Physics 📚 Magnetism

Integration of Exponential Function

Math → Calculus → Integrals → Basic Integration
$$\int e^{ax} \, dx = \frac{1}{a} e^{ax} + C$$
The integral of the natural exponential function with a linear exponent constant.
📖 Math 📚 Integrals

Kinetic Energy of a Photoelectron

Physics → Modern Physics → Photoelectric Effect → Stopping Potential
$$eV_s = hf - \Phi$$
Relates stopping potential to the incident photon frequency and work function.
📖 Physics 📚 Photoelectric Effect

Bragg's Equation

Physics → Solid State → Crystallography → Diffraction
$$n\lambda = 2d \sin \theta$$
Explains why cleavage faces of crystals appear to reflect X-ray beams at certain angles.
📖 Physics 📚 Crystallography

Gibbs Free Energy and Equilibrium

Chemistry → Thermodynamics → Chemical Equilibrium → Spontaneity
$$\Delta G^\circ = -RT \ln K$$
Relates the standard Gibbs free energy change to the equilibrium constant.
📖 Chemistry 📚 Chemical Equilibrium

Magnetic Flux

Physics → Electromagnetism → Induction → Flux
$$\Phi_B = BA \cos \theta$$
A measure of the total magnetic field passing through a given surface area.
📖 Physics 📚 Induction

Pressure-Volume Work (Reversible Isothermal)

Physics → Thermodynamics → Gas Processes → Work Done
$$W = -nRT \ln\left(\frac{V_2}{V_1}\right)$$
Calculates work done by an ideal gas during a reversible isothermal expansion.
📖 Physics 📚 Gas Processes

Capacitors in Series

Physics → Electromagnetism → Capacitance → Circuit Combinations
$$\frac{1}{C_{eq}} = \sum \frac{1}{C_i}$$
Calculates the total capacitance of multiple capacitors connected in a single path.
📖 Physics 📚 Capacitance

Resistivity Formula

Physics → Electromagnetism → Current Electricity → Resistance
$$R = \rho \frac{L}{A}$$
Relates electrical resistance to the physical dimensions and material property of a conductor.
📖 Physics 📚 Current Electricity

Mean of a Discrete Random Variable

Math → Probability → Random Variables → Expectation
$$E(X) = \sum x_i P(x_i)$$
Calculates the expected value (average) of a discrete probability distribution.
📖 Math 📚 Random Variables

Surface Area of a Sphere

Math → Geometry → 3d Shapes → Surface Area
$$A = 4\pi r^2$$
The total area of the exterior of a sphere.
📖 Math 📚 3d Shapes

Stefan's Law (Radiant Intensity)

Physics → Thermodynamics → Heat Transfer → Radiation
$$I = \epsilon \sigma T^4$$
Power radiated per unit area of a body.
📖 Physics 📚 Heat Transfer
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