Physics formulas

Most formula sheets are a wall of symbols. That is fine in an exam, where you already know what each line is for, and useless the week before, when the question is which line to reach for. The guides below are organized the way the decision actually goes: what the relationship says, what has to be true before you can use it, and a worked example with real numbers so you can see the method, not just the result. Each guide lists the open textbook pages it was checked against.

Mechanics

Motion, forces, energy, momentum and rotation. The formulas most courses start with and most exams lean on.

Formula	Says
Kinematics equations v = v₀ + at	The kinematics equations relate displacement, initial velocity, final velocity, acceleration and time for motion in a straight line.
Torque formula τ = rF·sin θ	Torque measures how effectively a force turns an object about an axis.
Impulse formula J = F_avg·Δt	Impulse is the average force on an object multiplied by the time that force acts, and it equals the object's change in momentum.
Work-energy theorem W_net = ΔKE = ½mv² - ½mv₀²	The work-energy theorem says the net work done on an object equals its change in kinetic energy.
Moment of inertia formula I = Σ mᵢrᵢ²	Moment of inertia is rotational mass: it measures how hard an object is to spin up about a chosen axis.
Tension formula T = mg	Tension is the pulling force carried along a rope, string or cable.
Momentum formula p = mv	Momentum is mass times velocity, a vector pointing the way the object moves.
Centripetal force formula F_c = mv² / r	Centripetal force is the net inward force that keeps an object on a circular path.
Newton's second law ΣF = ma	Newton's second law states that the net external force on an object equals its mass times its acceleration.
Projectile motion formulas v₀ₓ = v₀·cos θ₀ and v₀ᵧ = v₀·sin θ₀	Projectile motion splits into two independent problems.

Electricity and magnetism

Charges, fields, circuits and induction.

Formula	Says
Coulomb's law F = k·|q₁q₂| / r²	Coulomb's law gives the electrostatic force between two point charges: it is proportional to the product of the charges and falls off with the square of the distance between them.
Kirchhoff's laws ΣI_in = ΣI_out	Kirchhoff's two rules solve circuits that series and parallel shortcuts cannot.
Faraday's law of induction ε = -N·ΔΦ / Δt	Faraday's law says a changing magnetic flux through a loop induces an emf in that loop, sized by how fast the flux changes and by the number of turns.
Ohm's law V = IR	Ohm's law relates voltage, current and resistance: the current through a component equals the voltage across it divided by its resistance.

Waves and optics

How waves travel and how light bends.

Formula	Says
Wave speed equation v = fλ	The wave speed equation says a wave's speed equals its frequency times its wavelength.
Snell's law n₁·sin θ₁ = n₂·sin θ₂	Snell's law predicts how far a light ray bends when it crosses between two materials.

Thermodynamics and fluids

Gases, pressure and moving fluids.

Formula	Says
Bernoulli's equation p + ½ρv² + ρgy = constant	Bernoulli's equation is energy conservation written for a flowing fluid: pressure, kinetic energy per unit volume and gravitational potential energy per unit volume add to the same total everywhere along a streamline.
Pressure formula p = F / A	Pressure is the force pressing perpendicular to a surface divided by the area of that surface.
Ideal gas law pV = nRT	The ideal gas law ties pressure, volume, temperature and amount of gas into a single relation.

Modern physics

Decay and the ideas that broke classical physics.

Formula	Says
Half-life formula N = N₀ · (1/2)^(t / T½)	Half-life is the time for half the radioactive nuclei in a sample to decay.

How to use a formula sheet well

Start from the quantities you know and the one you want, then find the formula that contains exactly those and nothing you would have to guess. Check its conditions before the algebra, not after: constant acceleration, one straight line, an ideal gas. Write the units through every line, because a unit that does not cancel is the fastest way to catch a wrong formula. And keep one worked example per formula that you can reproduce from memory; that is what turns the sheet into a method.