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Showing 24 of 341 formulas Page 7 of 15

Volume of a Cone

Math β†’ Geometry β†’ 3d Shapes β†’ Volume
$$V = \frac{1}{3} \pi r^2 h$$
Amount of space occupied by a right circular cone.
πŸ“– Math πŸ“š 3d Shapes

Malus's Law

Physics β†’ Optics β†’ Wave Optics β†’ Polarization
$$I = I_0 \cos^2 \theta$$
Determines the intensity of a beam of polarized light after passing through a polarizer.
πŸ“– Physics πŸ“š Wave Optics

Escape Speed from Earth

Physics β†’ Mechanics β†’ Gravitation β†’ Planetary Motion
$$v = \sqrt{2gr}$$
A simpler form of escape velocity using surface gravity.
πŸ“– Physics πŸ“š Gravitation

Standard Cell Potential

Chemistry β†’ Electrochemistry β†’ Redox β†’ Voltage
$$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$
Calculates the maximum voltage of an electrochemical cell under standard conditions.
πŸ“– Chemistry πŸ“š Redox

Magnetic Force on a Current-Carrying Wire

Physics β†’ Electromagnetism β†’ Magnetism β†’ Lorentz Force
$$F = BIl \sin \theta$$
Force exerted on a conductor carrying current in a magnetic field.
πŸ“– Physics πŸ“š Magnetism

Work-Energy Theorem (Rotational)

Physics β†’ Mechanics β†’ Rotation β†’ Energy
$$W = \Delta K_{\text{rot}} = \frac{1}{2} I \omega_f^2 - \frac{1}{2} I \omega_i^2$$
The net work done by all torques acting on a rigid body is equal to the change in its rotational kinetic energy.
πŸ“– Physics πŸ“š Rotation

Change in Entropy (Reversible Process)

Physics β†’ Thermodynamics β†’ Second Law β†’ Entropy
$$\Delta S = \int \frac{dQ_{\text{rev}}}{T}$$
Definition of entropy change for a system during a reversible process.
πŸ“– Physics πŸ“š Second Law

Pressure at Depth in Fluid

Physics β†’ Fluid Mechanics β†’ Hydrostatics β†’ Pressure
$$P = P_0 + \rho gh$$
Calculates the total pressure at a certain depth in a liquid.
πŸ“– Physics πŸ“š Hydrostatics

Bohr's Radius

Physics β†’ Atomic Physics β†’ Atoms β†’ Bohr Model
$$r_n = \frac{\epsilon_0 h^2 n^2}{\pi m e^2}$$
Calculates the allowed radii for an electron in a hydrogen atom.
πŸ“– Physics πŸ“š Atoms

Standard Reaction Quotient

Chemistry β†’ Physical Chemistry β†’ Equilibrium β†’ Reaction Quotient
$$Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}$$
Calculates the relative amounts of products and reactants at any point during a reaction.
πŸ“– Chemistry πŸ“š Equilibrium

Derivative of Sine

Math β†’ Calculus β†’ Differentiation β†’ Trig Derivatives
$$\frac{d}{dx} \sin x = \cos x$$
The instantaneous rate of change of the sine function.
πŸ“– Math πŸ“š Differentiation

Wave Velocity

Physics β†’ Waves β†’ Oscillations β†’ Wave Motion
$$v = f \lambda$$
Relates the speed of a wave to its frequency and wavelength.
πŸ“– Physics πŸ“š Oscillations

Elastic Potential Energy

Physics β†’ Mechanics β†’ Energy β†’ Potential Energy
$$U = \frac{1}{2} k x^2$$
Energy stored as a result of deforming an elastic object.
πŸ“– Physics πŸ“š Energy

Area of a Sector

Math β†’ Geometry β†’ Circles β†’ Sectors
$$A = \frac{1}{2} r^2 \theta$$
Calculates the area of a 'pizza slice' part of a circle.
πŸ“– Math πŸ“š Circles

Brewster's Law

Physics β†’ Optics β†’ Polarization β†’ Reflections
$$\tan \theta_p = \frac{n_2}{n_1}$$
An angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface.
πŸ“– Physics πŸ“š Polarization

Kinetic Energy (Relativistic)

Physics β†’ Modern Physics β†’ Relativity β†’ Energy
$$K = (\gamma - 1)mc^2$$
Calculates kinetic energy when speeds approach the speed of light.
πŸ“– Physics πŸ“š Relativity

Law of Reciprocal Proportions

Chemistry β†’ General Chemistry β†’ Basic Concepts β†’ Laws Of Chemical Combination
$$W_{AB} = \frac{W_{AC} \times W_{BC}}{W_C}$$
If two different elements combine separately with a fixed mass of a third element, the ratio of the masses in which they do so are either the same as or a simple multiple of the ratio of the masses in which they combine with each other.
πŸ“– Chemistry πŸ“š Basic Concepts

Average Acceleration

Physics β†’ Mechanics β†’ Kinematics β†’ Motion
$$a_{avg} = \frac{v_f - v_i}{t_f - t_i}$$
The rate at which an object changes its velocity over a period of time.
πŸ“– Physics πŸ“š Kinematics

Inductive Reactance

Physics β†’ Electromagnetism β†’ AC Circuits β†’ Impedance
$$X_L = 2\pi f L$$
The opposition that an inductor offers to the flow of alternating current.
πŸ“– Physics πŸ“š AC Circuits

Density of States (3D)

Physics β†’ Solid State β†’ Free Electron Model β†’ Fermi Gas
$$g(E) = \frac{V}{2\pi^2} \left(\frac{2m}{\hbar^2}\right)^{3/2} \sqrt{E}$$
The number of states per unit energy interval for a 3D system.
πŸ“– Physics πŸ“š Free Electron Model

Faraday's Second Law of Electrolysis

Chemistry β†’ Electrochemistry β†’ Electrolysis β†’ Chemical Equivalents
$$\frac{m_1}{m_2} = \frac{E_1}{E_2}$$
Masses of different substances deposited by the same amount of electricity are proportional to their chemical equivalent weights.
πŸ“– Chemistry πŸ“š Electrolysis

Period of a Simple Pendulum

Physics β†’ Mechanics β†’ Oscillations β†’ SHM
$$T = 2\pi \sqrt{\frac{L}{g}}$$
Calculates the time for one full swing of a pendulum.
πŸ“– Physics πŸ“š Oscillations

Integration of a Constant

Math β†’ Calculus β†’ Integrals β†’ Basic Integration
$$\int k \, dx = kx + C$$
The antiderivative of a constant value.
πŸ“– Math πŸ“š Integrals

Volume of a Rectangular Prism

Math β†’ Geometry β†’ 3d Shapes β†’ Volume
$$V = lwh$$
The amount of space inside a rectangular box.
πŸ“– Math πŸ“š 3d Shapes
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