Mechanics formulas

57 relations, each one a node in the derivation graph. Every symbol carries a declared base dimension, so every one of them can be checked.

• Angular Frequency From Period — ω = 2·π / T
• Angular Momentum (Point Mass) — L = m·v·r
• Angular Velocity From Tangential Speed — ω = v / r
• Average Power — P = W / t
• Center of Mass (1D) — x_cm = Σ(m_i·x_i) / Σ(m_i)
• Centripetal Force — F_c = m·v^2/r
• Coefficient of Restitution (1D) — e = (v2p - v1p) / (v1 - v2)
• Elastic Collision 1D Final Velocity of Body 1 — v1p = ((m1 - m2)·v1 + 2·m2·v2) / (m1 + m2)
• Elastic Collision 1D Final Velocity of Body 2 — v2p = ((m2 - m1)·v2 + 2·m1·v1) / (m1 + m2)
• Elastic Potential Energy — U = (1 / 2)·k·x^2
• Escape Velocity — v = sqrt(2·G·M / r)
• Surface Gravitational Acceleration — g_surf = G·M / R^2
• Gravitational Potential Energy — U = m·g·h
• Gravitational Potential Energy (General) — U = -(G·M·m) / r
• Hooke's Law — F = -k·x
• Impulse-Momentum Theorem — J = F·Δt
• Kepler's Third Law (Orbital Period) — T = 2·π·sqrt(r^3 / (G·M))
• Kinematics (3D Position Vector) — r = (x, y, z)
• Kinematics (3D Velocity Squared) — v^2 = vx^2 + vy^2 + vz^2
• Kinematics (3D Velocity Vector) — v = (vx, vy, vz)
• Kinematics (Δx = ½(v+v₀)t) — Δx = (1/2)·(v_f + v_o)·t
• Kinematics (Δx = v₀t + ½at²) — Δx = v_o·t + (1/2)·a·t^2
• Kinematics (v = v₀ + at) — v_f = v_o + a·t
• Kinematics (v² = v₀² + 2aΔx) — v_f^2 = v_o^2 + 2·a·Δx
• Kinetic Energy — KE = 1/2·m·v^2
• Moment Of Inertia Of A Point Mass — I = m·r^2
• Moment Of Inertia Of A Rod About Its Center — I = (1/12)·m·L^2
• Moment Of Inertia Of A Solid Disk — I = (1/2)·m·R^2
• Moment Of Inertia Of A Solid Sphere — I = (2/5)·m·R^2
• Linear Momentum — p = m·v
• Newton's Second Law — F = m·a
• Total Orbital Energy — E = -(G·M·m) / (2·r)
• Circular Orbital Velocity — v = sqrt(G·M / r)
• Parallel Axis Theorem — I = I_cm + m·d^2
• Simple Pendulum Frequency — f = (1 / (2·π))·sqrt(g / L), g = 9.80665 m/s^2
• Simple Pendulum Period — T = 2·π·sqrt(L/g)
• Perfectly Inelastic Collision Final Velocity — vf = (m1·v1 + m2·v2) / (m1 + m2)
• Poisson Equation (Gravity) — laplacian(φ) = 4·π·G·ρ
• Mechanical Power — P = W/t = F·v
• Pressure — P = F/A
• Projectile Maximum Height — H = (v0^2·sin(θ)^2) / (2·g)
• Projectile Range — R = (v0^2·sin(2·θ)) / g
• Projectile Time of Flight — t = (2·v0·sin(θ)) / g
• Reduced Mass — μ = (m1·m2) / (m1 + m2)
• Rotational Kinetic Energy — KE = (1/2)·I·ω^2
• Newton's Second Law For Rotation — τ = I·α
• SHM Angular Frequency Of A Spring — ω = sqrt(k / m)
• SHM Frequency Of A Spring — f = (1 / (2·π))·sqrt(k / m)
• SHM Maximum Acceleration — a_max = ω^2·A
• SHM Maximum Velocity — v_max = ω·A
• SHM Period Of A Spring — T = 2·π·sqrt(m / k)
• SHM Total Energy — E = (1 / 2)·k·A^2
• Torque — τ = r·F·sin(θ)
• Newton's Law of Gravitation — F = G·m1·m2 / r^2
• Work from Force and Displacement — W = F·s·cos(θ)
• Work-Energy Theorem — W = ΔKE = KE_f - KE_i
• Work (Force · Displacement) — W = F·s

Derive through any of them in the explorer — no account needed.