Physics

Mechanics, energy, waves, electricity and light

Physics brings together the core formulas used to describe how the world moves, behaves, and transfers energy, from mechanics and kinematics to electricity, waves, and light. It’s a practical reference for students studying for exams, and for anyone applying physics in real-world problem solving, because these equations help you calculate forces, motion, power, momentum, and more with confidence.

Newton's Second Law

F = ma

Force equals mass times acceleration.

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.