Physics

Kinetic Energy

KE = \frac{1}{2}mv^2

Energy of a moving object.

Gravitational Potential Energy

PE = mgh

Energy stored due to height in a gravitational field.

Work Done

W = F d \cos\theta

Work done by a force over a distance.

Power

P = \frac{W}{t}

Rate of doing work.

Momentum

p = mv

Quantity of motion of an object.

Impulse

J = F\Delta t = \Delta p

Change in momentum from a force over time.

Kinematics: Velocity

v = u + at

Final velocity under constant acceleration.

Kinematics: Displacement

s = ut + \frac{1}{2}at^2

Displacement under constant acceleration.

Kinematics: v²

v^2 = u^2 + 2as

Velocity–displacement relation under constant acceleration.

Ohm's Law

V = IR

Voltage equals current times resistance.

Electrical Power

P = VI = I^2R

Power dissipated in an electrical component.

Mass–Energy Equivalence

E = mc^2

Energy equivalent of mass.

Wave Speed

v = f\lambda

Speed of a wave from frequency and wavelength.

Coulomb's Law

F = k\frac{q_1 q_2}{r^2}

Electrostatic force between two charges.

Snell's Law

n_1\sin\theta_1 = n_2\sin\theta_2

Refraction of light between two media.

Newton's Gravitation

F = G\frac{m_1 m_2}{r^2}

Attractive force between two masses.

Hooke's Law

F = -kx

Restoring force of a spring.

Simple Pendulum Period

T = 2\pi\sqrt{\frac{L}{g}}

Period of a simple pendulum.

Centripetal Force

F = \frac{mv^2}{r}

Force needed to keep an object in circular motion.

Density

\rho = \frac{m}{V}

Mass per unit volume.

Pressure

P = \frac{F}{A}

Force per unit area.

Heat Energy

Q = mc\Delta T

Heat needed to change temperature of a substance.

Doppler Effect

f' = f\frac{v \pm v_o}{v \mp v_s}

Observed frequency shift due to relative motion.

Speed

v = \frac{d}{t}

Speed equals distance divided by time.

Acceleration

a = \frac{\Delta v}{t}

Rate of change of velocity.

Weight

W = mg

The gravitational force on a mass.

Frequency and Period

f = \frac{1}{T}

Frequency is the inverse of the period.

Mechanical Advantage

MA = \frac{F_{out}}{F_{in}}

Force amplification of a simple machine.

Energy of a Photon

E = hf

Energy of a photon from its frequency.

Weight

W = mg

Gravitational force on a mass near Earth.

Hooke Law

F = -kx

Restoring force of a spring proportional to displacement.

Impulse

J = F\Delta t = \Delta p

Change in momentum from a force over time.

Torque

\tau = rF\sin\theta

Rotational effect of a force about a pivot.

Angular Momentum

L = I\omega

Rotational analog of linear momentum.

Rotational Kinetic Energy

KE = \frac{1}{2}I\omega^2

Kinetic energy of a rotating body.

Gravitational Potential Energy (General)

U = -\frac{GMm}{r}

Potential energy of two masses at distance r.

Orbital Velocity

v = \sqrt{\frac{GM}{r}}

Speed needed for a circular orbit.

Escape Velocity

v_e = \sqrt{\frac{2GM}{r}}

Minimum speed to escape a gravitational field.

Spring Oscillation Period

T = 2\pi\sqrt{\frac{m}{k}}

Period of a mass on a spring.

Friction Force

f = \mu N

Resistive force between surfaces.

Terminal Velocity

v_t = \sqrt{\frac{2mg}{\rho A C_d}}

Constant fall speed when drag balances gravity.

Projectile Range

R = \frac{v^2\sin 2\theta}{g}

Horizontal distance of a projectile on level ground.

Centripetal Force

F = \frac{mv^2}{r}

Inward force needed for circular motion.

Power from Work

P = \frac{W}{t}

Rate of doing work.

Elastic Potential Energy

U = \frac{1}{2}kx^2

Energy stored in a stretched or compressed spring.