Physics Equations (PDF)

# 121 Equations **Kinematics:** * **r** is generic position vector * vavg = total distance / total time * v = dr/dt * aavg = Δv/Δt * a = dv/dt = d²r/dt² * **r**f = **r**i + **v**iΔt + 1/2 **a**(Δt)² * **v**f = **v**i + **a**Δt * **v**f² = **v**i² + 2**a**Δ**r** * **r** = √(x² + y²), θ = tan⁻¹(y/x)...

# 121 Equations **Kinematics:** * **r** is generic position vector * vavg = total distance / total time * v = dr/dt * aavg = Δv/Δt * a = dv/dt = d²r/dt² * **r**f = **r**i + **v**iΔt + 1/2 **a**(Δt)² * **v**f = **v**i + **a**Δt * **v**f² = **v**i² + 2**a**Δ**r** * **r** = √(x² + y²), θ = tan⁻¹(y/x) * s = rθ * T = 2πr / 2π * ω = dθ/dt * v = ωr * aτ = rα = ω²r * aτ = rα * a = aτ + a * α = dw/dt **Rotation:** * τ = rF sin θ * **τ** = **r** x **F** * Σ **τ** = I**α** * L = Iw = **r** x **p** * Σ **τ** = dL/dt * Fg = G Mm/r² * T² = (4π²r³/GM) * PEg = -G Mm/r **Moments of Inertia:** | Object | Axis | Moment of Inertia (I) | |---|---|---| | Hoop | Cylinder axis | MR² | | Annular cylinder (or ring) | Cylinder axis | M/2 (R₁² + R₂²) | | Solid cylinder (or disk) | Cylinder axis | MR²/2 | | Solid cylinder (or disk) | Central diameter | MR²/4 + ML²/12 | | Thin rod | Axis through center perpendicular to length | ML²/12 | | Thin rod | Axis through one end perpendicular to length | ML²/3 | | Solid sphere | Any diameter | 2MR²/5 | | Thin spherical shell | Any diameter | 2MR²/3 | | Hoop | Any diameter | MR²/2 | | Slab | Axis through center, perpendicular | M(a² + b²)/12 | **Work and Energy:** * Wnc = ΔKE + ΔPE * F = -dU/dr * P = dW/dt = F . **v** * XCM = (M1X1 + M2X2 + M3X3 + ...)/(m1 + m2 + m3 + ...) * I = Σ miri² * I = ∫r²dm * I = ICM + MD² * KErot = 1/2 Iw² **linear Momentum:** * Σ F = m ȧ * Fg = mg * Ff = μFN * p = mv̇ * p̄f = p̄i * Ī = F̄avg∆t = ∆p̄ * Σ F = dp/dt = mv̇ * KE = 1/2 mv² * PEg = mgh * PEs = 1/2 k (Δx)² * Fs = -kΔx * Vf1 = (m1 - m2)/(m1 + m2) Vi1 * Vf2 = (2m1/ (m1 + m2) Vi1 * Wnet = ΔKE * W = F . Δr = Fr cos θ **Other:** * Vsphere = 4/3πr³