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Formulas

Formula Library

Learn from categorized formulas

Showing 24 of 341 formulas Page 12 of 15

Gravitational Potential Energy (Universal)

Physics → Mechanics → Gravitation → Energy
$$U = -\frac{G M m}{r}$$
Work done in bringing a mass from infinity to a point in a gravitational field.
📖 Physics 📚 Gravitation

Orbital Velocity

Physics → Mechanics → Gravitation → Satellite Motion
$$v_o = \sqrt{\frac{GM}{r}}$$
Velocity required for a satellite to stay in a circular orbit.
📖 Physics 📚 Gravitation

Kepler's Third Law

Physics → Mechanics → Gravitation → Planetary Motion
$$T^2 \propto R^3$$
The square of the time period of a planet is proportional to the cube of the semi-major axis.
📖 Physics 📚 Gravitation

Stress

Physics → Properties of Matter → Mechanical Properties of Solids → Elasticity
$$\sigma = \frac{F}{A}$$
Restoring force per unit area developed inside a body.
📖 Physics 📚 Mechanical Properties of Solids

Strain

Physics → Properties of Matter → Mechanical Properties of Solids → Elasticity
$$\epsilon = \frac{\Delta L}{L}$$
Ratio of change in dimension to original dimension.
📖 Physics 📚 Mechanical Properties of Solids

Surface Tension

Physics → Properties of Matter → Mechanical Properties of Fluids → Surface Phenomena
$$S = \frac{F}{l}$$
Force per unit length acting in the plane of the interface.
📖 Physics 📚 Mechanical Properties of Fluids

Bernoulli's Theorem

Physics → Properties of Matter → Mechanical Properties of Fluids → Fluid Dynamics
$$P + \frac{1}{2}\rho v^2 + \rho gh = \text{Constant}$$
Conservation of energy for a flowing non-viscous fluid.
📖 Physics 📚 Mechanical Properties of Fluids

Equation of Continuity

Physics → Properties of Matter → Mechanical Properties of Fluids → Fluid Dynamics
$$A_1 v_1 = A_2 v_2$$
Mass flow rate remains constant in a tube of varying cross-section.
📖 Physics 📚 Mechanical Properties of Fluids

Ideal Gas Equation

Physics → Thermodynamics → Kinetic Theory of Gases → Gas Laws
$$PV = nRT$$
Equation of state for an ideal gas.
📖 Physics 📚 Kinetic Theory of Gases

Adiabatic Process Equation

Physics → Thermodynamics → Thermodynamics → Thermodynamic Processes
$$PV^\gamma = \text{Constant}$$
Relationship between P and V where no heat is exchanged.
📖 Physics 📚 Thermodynamics

Carnot Engine Efficiency

Physics → Thermodynamics → Thermodynamics → Heat Engines
$$\eta = 1 - \frac{T_L}{T_H}$$
Maximum possible efficiency for any heat engine.
📖 Physics 📚 Thermodynamics

RMS Speed of Gas Molecules

Physics → Thermodynamics → Kinetic Theory of Gases → Molecular Speeds
$$v_{rms} = \sqrt{\frac{3RT}{M}}$$
The square root of the average of the squares of molecular speeds.
📖 Physics 📚 Kinetic Theory of Gases

Law of Equipartition of Energy

Physics → Thermodynamics → Kinetic Theory of Gases → Energy Distribution
$$E = \frac{1}{2} k_B T \text{ per degree of freedom}$$
Total energy is shared equally among all degrees of freedom.
📖 Physics 📚 Kinetic Theory of Gases

Simple Harmonic Motion (Displacement)

Physics → Oscillations → Oscillations → SHM
$$x = A \sin(\omega t + \phi)$$
Equation describing the position of a particle in SHM.
📖 Physics 📚 Oscillations

Time Period of Spring-Mass System

Physics → Oscillations → Oscillations → SHM Examples
$$T = 2\pi \sqrt{\frac{m}{k}}$$
Time period of a mass $m$ oscillating on a spring of constant $k$.
📖 Physics 📚 Oscillations

Speed of Sound in Solids

Physics → Waves → Waves → Sound Waves
$$v = \sqrt{\frac{Y}{\rho}}$$
Velocity of longitudinal waves in a long solid rod.
📖 Physics 📚 Waves

Newton-Laplace Equation (Sound in Gas)

Physics → Waves → Waves → Sound Waves
$$v = \sqrt{\frac{\gamma P}{\rho}}$$
Corrected speed of sound in a gas considering adiabatic conditions.
📖 Physics 📚 Waves

Power (Instantaneous)

Physics → Mechanics → Work, Energy, and Power → Power
$$P = \vec{F} \cdot \vec{v}$$
The rate of doing work expressed as the dot product of force and velocity.
📖 Physics 📚 Work, Energy, and Power

Viscosity (Newton's Law)

Physics → Properties of Matter → Mechanical Properties of Fluids → Viscosity
$$F = -\eta A \frac{dv}{dx}$$
Viscous force between fluid layers is proportional to area and velocity gradient.
📖 Physics 📚 Mechanical Properties of Fluids

Pressure in a Fluid Column

Physics → Properties of Matter → Mechanical Properties of Fluids → Hydrostatics
$$P = P_0 + \rho gh$$
Total pressure at a depth $h$ in a static fluid.
📖 Physics 📚 Mechanical Properties of Fluids

Work Done in Stretching a Wire

Physics → Properties of Matter → Mechanical Properties of Solids → Elasticity
$$W = \frac{1}{2} \times \text{Stress} \times \text{Strain} \times \text{Volume}$$
Energy stored in a wire when stretched within elastic limit.
📖 Physics 📚 Mechanical Properties of Solids

Escape Velocity from Earth surface

Physics → Mechanics → Gravitation → Gravity
$$v_e = \sqrt{2gR}$$
Minimum velocity required to escape Earth's gravity.
📖 Physics 📚 Gravitation

Variation of g with Altitude

Physics → Mechanics → Gravitation → Gravity
$$g_h = g\left(1 - \frac{2h}{R}\right)$$
How gravity decreases as you move above Earth's surface.
📖 Physics 📚 Gravitation

Torricelli's Law (Efflux Speed)

Physics → Properties of Matter → Mechanical Properties of Fluids → Fluid Dynamics
$$v = \sqrt{2gh}$$
Speed of efflux of liquid from an orifice.
📖 Physics 📚 Mechanical Properties of Fluids
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