Equation List Constant Velocity x = position v=x/t Δ x = vaverage t

Varsity Physics - Berg t = time xf - xo = Δ x vaverage = (vo + vf ) / 2

Accelerated Motion a = acceleration v f = v0 + a t (vf ) 2 = (vo )2 + 2 a Δx

a=v/t a = (vf – vo)/  t Δ x = vo t + ½ a t2 Δ x = ½ (vf + vo ) t Acceleration due to gravity on Earth = 9.8 m/s 2

xo = original position x = xo + vt

Projectile Motion Range = [Vo2 sin(2)] / g

v = velocity xf = final position

v = vf – vo

hypotenuse Opposite

Forces And Newton’s Laws side F = force m = mass Tan θ = Opposite side / Adjacent side Sin θ = Opposite side / hypotenuse Cos θ = Adjacent side / hypotenuse Fnet = m a Fg = m (9.8 m/s2) k = spring constant Ff = μk Fn Ff ≤ μs Fn μs > μk

θ Adjacent side

F=kx

(Hooke’s Law)

Circular Motion and Universal Gravitation ac = centripetal acceleration ac = v2 / r v = 2r / T

Fc = centripetal force Fc = ( 42 r m )/ T2 Fg = (G m1 m2)/ r2

r = radius (distance) Fc = (m v2)/ r G = 6.67 x 10-11 Nm2 / kg2

Momentum p = momentum (p)before = (p)after V1,f = [(m1 - m2) / (m1 + m2)] V1,0

Ft = m v p = mv V2,f = [(2m1) / (m1 + m2)] V1,0

Ft = impulse Va – Vb = V b’ – Va’

Ek = ½ mv 2 Power = change in Energy/ time

Eg = mgΔy Power = work / time

Energy E = energy Work = (Force)(distance) Thermal Physics Q = Thermal Energy Hf = Heat of Fusion Q = mcΔT Constants Csilver = 230 J / kg K Ccopper = 390 J / kg K Clead = 130 J / kg K Water Silver Iron

c = specific heat Hv = Heat of Vaporization Q = mHf Csteam = 2010 J/ kg K Ciron = 450 J / kg K Cprotein = 1700 J / kg K

Hf = 334,000 J/kg Hf = 88,000 J/kg Hf = 289,000 J/kg

T = temperature (K) Pressure = force/ area Q = mHv

Cice = 2100 J/ kg K Cglass = 840 J / kg K

PV = nrT

Cwater = 4180 J / kg K CAluminum = 900 J/kg K

Hv =2,260,000 J/kg Hv =2,300,000 J/kg Hv =6,340,000 J/kg

Mechanical Waves, SHM and Sound λ = wavelength f = frequency Speed = λf Speed = λ / T Speed of sound = 331 m/s + 0.6 m/s/ºC (temp) f'’ = f (vwave  v obs) / (vwave ∓ vsource) T = 2(L/g) T = 2(m/k) Static Electricity Felectric = electric force q = charge Felectric = (k q1 q2) / r2 k = 9x10 9 Nm2 / c2 E = V / d (parallel plates = constant field) V = Eelectric / q V x q = Eelectric Electric Circuits R = resistance R = R1 +R2 + R3 + … P = IV 1 kWh = 3,600,000 J

Ee = ½ kx2

T = period f = 1/ T T = 1/f f beat = f1 – f2

r = distance

V = voltage I = current 1/R = 1/R1 +1/R2 + 1/R3 + … P = I2R P = V2 / R v = I (R + r)

E = Electric Field E = Fe / q Eelectric = Electric Potential Energy Eelectric = Fe x distance P = Power V= IR

Rotational Physics τ = F r sinθ I = Σmr2 τ = Iα ω = 2πf ωf = ωo + αt ωf2 = ωo2 + 2αθ θ = ωot + 1/2αt2 L=I ω EK (Rot) = ½ I ω2 ISphere = 2/5 mr2 IHoop = mr2 (axis through center) 2 ISolid cylinder = ½ mr (through center) IHollow Cylinder = ½ m (r12 + r22) (through center; r1 = inner radius, r2 = outer) 2 IRod = (1/12) m length (Uniform rod; through center) IRod = (1/3) m length2 (Uniform rod; through end) 2 2 IRectangular Plane = (1/12) m (length + width ) (through center) Advanced Waves and Optics n = index of refraction n = speed of light in vacuum / Speed of light in material n1 sini = n2 sint i = r Speed of light = 3x 108 m/s f = focal length do = object distance di = image distance M = magnification factor ho = object height hi = image height 1/f = 1/do + 1/di M = -di / do = hi/ ho I = Io cos2θ sin  = / b (single slit interference) b =slit width d sin  = m (constructive Interference) m = 0,1,2,3,4… d = distance between slits d sin  = (m+ ½) (destructive Interference) 2d sin θ = n λ 2nt = m λ 2nt = (m+½) λ 2nt cos φ = m λ 2nt cos φ = (m+½) λ Environmental Physics Wind Power = ½Aρv3 Wave Power per length = ½ A2ρgv P = eσAT4 I = power / Area

ρ = density (kg/m3) Hydro Power = QρgΔy (Q= flow rate in m 3/s) λmax (meters) = 2.90x10-3 / T (Kelvin) Albedo = Total scattered power / total incident power

Fields Gravitation Field F = (G m1m2)/ r2 g=F/m ΔV = Δ E g / m V = - Gm / r g = - ΔV / Δr

Electric Field F = (k q1q2)/ r2 E=F/q ΔV = Δ Eelectric / q V = kq / r = q / 4πε or E = - ΔV / Δx

(Forces) (Field strength) (Change in Potential) (Potential) (Field based on Potential)

Magnetism F = force q = charge v = velocity B = Magnetic Field I = current L = length of wire r = radial distance μo = 4π x 10-7 (T m)/ A  = angle between field and charge movement F = qvB sin F = BIL sin B = (μo/2π) (I / r) Φ = B A cos θ (Magnetic Flux based on field (B) and area (A) and angle between area and field) ε = Bvl ε = - N (ΔΦ/Δt) (Creating EMF electromotive force (voltage)) Is/ Ip = Vp / Vs = N p / Ns (Transformers) Irms = (Io ) / √2 Vrms = (Vo ) / √2 R = Vo/Io = Vrms/ Irms R = (ρL) / A Pmax = IoVo Pav = ½ IoVo Atomic, Nuclear and Quantum Physics h = Planck’s Constant = 6.63 x 10 -34 Js hc = 1.99 x 10-25 J m = 1.24 x 10-6 eV m E = hf λ = hc / E p = h/λ EK = (n2h2) / 8meL2 ΔxΔp ≥ h /(4π) ΔEΔT ≥ h /(4π) N = Noe-λt T½ = (ln 2) / λ Astrophysics L = σ A T4 d (parsec) = 1/ p (arc-seconds) m – M = 5 log(d/10) Δλ / λ ≈ v / c

e = elementary charge = 1.60 x 10-19 C E = mc2

hf = φ + Emax

A = - (ΔN) / (Δt)

A = λN =λ Noe-λt

λmax (meters) = (2.90 x 10-3) / T (Kelvin) b = L / 4πd2 L ∝ mn where 3 < n < 4 v = Ho d

hf =hfo + eV