Units & Measurements — Formula & Dimensions Sheet

UNITS & MEASUREMENTS — FORMULA & DIMENSIONS SHEET SI BASE UNITS length m · mass kg · time s · current A · temperature K · amount mol · luminous intensity cd COMMON DIMENSIONAL FORMULAE Velocity [L T^-1] · Acceleration [L T^-2] · Force [M L T^-2] · Momentum & Impulse [M L T^-1] Work, Energy, Torque [M L^2 T^-2] · Power [M L^2 T^-3] · Pressure, Stress [M L^-1 T^-2] Density [M L^-3] · Frequency [T^-1] · Charge [A T] · Gravitational constant G [M^-1 L^3 T^-2] Planck's constant h [M L^2 T^-1] · Surface tension [M T^-2] · Coefficient of viscosity [M L^-1 T^-1] DIMENSIONLESS QUANTITIES Strain, angle, solid angle, refractive index, relative density, Poisson's ratio, trigonometric ratios. ERROR PROPAGATION Sum/Difference Z = A ± B → ΔZ = ΔA + ΔB Product/Quotient Z = A·B or A/B → ΔZ/Z = ΔA/A + ΔB/B Powers Z = A^p B^q / C^r → (ΔZ/Z) = p(ΔA/A) + q(ΔB/B) + r(ΔC/C) Percentage error = (ΔZ/Z) × 100% SIGNIFICANT FIGURES Add/Subtract → answer keeps the least DECIMAL PLACES. Multiply/Divide → answer keeps the least SIGNIFICANT FIGURES. LEAST COUNT Vernier callipers: LC = 1 MSD − 1 VSD Screw gauge: LC = pitch / number of circular-scale divisions Reading = Main scale reading + (coinciding division × LC) − zero error HANDY CONVERSIONS 1 angstrom = 10^-10 m · 1 light year ≈ 9.46 × 10^15 m · 1 AU ≈ 1.496 × 10^11 m 1 atm ≈ 1.013 × 10^5 Pa · 1 eV = 1.6 × 10^-19 J