USEFUL FORMULAE

Units

• I Pm = 1015 m, I Tm = 109 m, I Gm = 109 m, I Mm = 106 m, 1 km = 1000 m = 103 m,1 cm = 10−2 m, 1 mm = 10−3 m, 1 µm = 10−6m, 1 nm = 10−9 m, 1 pm = 10−12 m, 1 fm = 10−15 m

• 1 mile = 1,609.3 m = 1.6093 km• 1 ft = 12 inches = 0.305 m, 1 inches = 0.025 m; mph - miles per hours = miles/hr• 1 N = 1 kg m/s2, 1 J = 1 N·m

Geometry / Vector

• Circle - Circumference: C = 2πr, Area A = πr2

• Sphere - Surface Area: Asphere = 4πr2, Volume: Vsphere = 43πr

3

• Pythagorean theorem: a2 + b2 = h2

• sin θ = ah , cos θ = b

h , tan θ = ab

Constants in Physics

Solar System Mass Radius Orbital Radius Orbital PeriodEarth 5.98 × 1024kg 6, 400km 1.50 × 1011 m 365.2564 daysMoon 7.35 × 1022kg 1, 700km 384, 403 km 27.322 daysSun 1.99 × 1030kg 6.96 × 108m − -

Formulae in Physics

Kinematical Variables Definition or FormulaPosition x(t)

Displacement ∆x = x(t) − x0 =∫v(t)dt

Velocity v(t) = dx(t)dt = v0 +

∫a(t)dt

Acceleration a(t) = dv(t)dt

• Density ρ = mV