Sheet

Formulae

The compact kit. Every identity in the academy, grouped the way a first-year engineering exam is grouped. Print it in your head.

I. Kinematics

Velocity

v = dx/dt

m/s

Acceleration

a = dv/dt

m/s²

Constant a

v = v₀ + at

—

Displacement

Δx = v₀t + ½at²

—

Timeless

v² = v₀² + 2aΔx

—

Range

R = v₀² sin(2θ)/g

level ground

II. Forces

Second law

ΣF = ma

N = kg·m/s²

Weight

W = mg

g ≈ 9.81 m/s²

Kinetic friction

f_k = μk N

opposes slip

Angle of repose

θc = arctan μs

—

Ramp acceleration

a = g(sinθ − μk cosθ)

down the plane

III. Energy

Work

W = F Δr cosα

Power

P = F · v

W = J/s

Kinetic energy

KE = ½mv²

Gravitational PE

PE = mgh

datum-dependent

Spring PE

PE = ½kx²

IV. Momentum & rotation

Momentum

p = mv

kg·m/s

Impulse

J = Δp = F_avg Δt

N·s

Restitution

e = (v₂ − v₁)/(u₁ − u₂)

0…1

Torque

τ = r F sinθ

N·m

Rotation

τ = Iα

I in kg·m²

V. Oscillation & waves

SHM

ω = √(k/m)

rad/s

Pendulum

T = 2π√(L/g)

small angle

Wave identity

v = fλ

—

String speed

v = √(T/μ)

μ = kg/m

String harmonics

f_n = nv/(2L)

fixed-fixed

VI. Applied physics

Hydrostatic

P = P₀ + ρgh

Buoyancy

F_b = ρ V g

Bernoulli

P + ρgh + ½ρv² = const

streamline

Continuity

A₁v₁ = A₂v₂

incompressible

Carnot

η = 1 − T_C/T_H

kelvin

Ohm

V = IR

V, A, Ω

Electrical power

P = IV = I²R