Equations

Core Additional Higher Level
 

Topic 1 - Physics and physical measurement

 

     AH = A cosq

      AV = A cosq

 

 
 

 

 

Topic 7  Measurement and uncertainties

      If y = a + b, then  

      Dy = Da + Db

 

      If y = ab/c, then

      Dy/y = Da/a + Db/b + Dc/c

 

 

Topic 2 Mechanics

 

      vav  = Ds/Dt

      aav  = Dv/Dt

      v = u + at

      s = (u + v)/2 t

      s = ut +1/2at2

      v2 = u2 + 2as

      s: displacement

      t: time

      u: initial speed

      v: final speed

      a: acceleration

      F = ma

      p = mv

     F = Dp/Dt

     Impulse = FDt = mDv

     W = Fs cosq

  Ek = 1/2mv2

    Ek = p2/2m    

     DEp = mgDh

     F = kx

     Eelas = 1/2kx2

     power = work/time = Fv

     a = v2/r = 4p2r/T2

 

 

Topic 8  Mechanics

 

      g = F/m 

      g = G(m/r2)

      F = -G(m1m2/r)

      V = -G(m/r)

      T2/R3 = constant

      Ffr < msFN

      Ffr = mkFN

       t = Frsinq

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Topic 3  Thermal Physics

 

      p = F/A

      DQ = mcDT

      DQ = mL

      pV = nRT

 

 

 

 

 

 

Topic 9  Thermal Physics

 

      DW = pDV

      DQ = DU + DW

      +DQ = thermal energy transferred to the system

      +DU = increase in internal energy of the system

      +DW = work done by the system

      efficiency = (Qh - Qc)/Qh

      Qh/Th = Qc/Tc   (Carnot cycle)

      efficiency = (Th - Tc)/Th  (Carnot cycle)

 

 

Topic 4  Waves

 

      f = 1/T

      v = fl

      sinq1/sinq2 = v1/v2

      n1sinq1 = n2sinq2

      n = c/v

 

 

Topic 10 Waves

 

      f' = f(1/(1 + vs/v) )   Moving source

      f' = f(1 + (v0/v))    Moving observer

      Fbeat = |f1 - f2|

      d sinq = nl

      s = lD/d

 

 

Topic 5  Electricity and Magnetism

 

  F = k(q1q2/r2) = (1/4pe0)(q1q2/r2)

  E = F/q

  E = kq/r2

  E = V/d

  I = Dq/Dt

  R = V/I

  P = VI = I2R = V2/R

  R = R1 + R2

  1/R = 1/R1 + 1/R2

  F = qvB sinq

  F = IlB sinq

  B = m0I/(2pr)

  B = m0(NI/l) = monI

  F/l = (m0/2p)(I1I2/r)

 

 

Topic 11 Electromagnetism

 

  V = kq/r = (1/4pe0)(q/r)

  E = -DV/Dx

     F = BA cosqf

     e = Bvl

     e = -NDf/Dt

  Vp/Vs = Np/Ns

  Irms = I0/Ö2

  Vrms = V0/Ö2

 

 

 

 

 

 

 

 

 

Topic 6  Atomic and nuclear physics

 

  E = mc2

 

 

 

 

 

 

 

Topic 12  Quantum physics and nuclear physics

 

  E = hf

  hf = f + Ek(max)

  hf = hf0 + eVs

  p = h/l

  N = N0e-lt

  T1/2 = ln 2/l

 

 

Options Standard Level

 

  Option A  Mechanics Extension

 

  g = F/m

  g = G(m/r2)

  F = G(m1m2/r2)

  Ep = -G(m1m2/r2)

  V = -G(m/r)

  T2/R3 = constant

  Ffr < msFn

  Ffr = mkFn

   t = Fr sinq

 

 

  Option B  Quantum physics and nuclear physics

 

  E = hf

  hf = f + Ek(max)

  hf = hf0 + eVs

  p = h/l

  N = N0e-lt

  T1/2 = ln 2/l

 

 

  Option C  Energy extension

 

      DW = pDV

      DQ = DU + DW

      +DQ = thermal energy transferred to the system

      +DU = increase in internal energy of the system

      +DW = work done by the system

      efficiency = (Qh - Qc)/Qh

      Qh/Th = Qc/Tc   (Carnot cycle)

      efficiency = (Th - Tc)/Th  (Carnot cycle)

      power = 1/2rAv3

 

 

Options Standard Level/Higher Level

Core(SL + HL) Extension (HL only)
 

  Option D  Biomedical Physics

 

  b = 10log(I/I0) where I0 = 10-12Wm-2

  I = I0e-mx

  x1/2 = ln 2/m

 

 

 

 

 

 

Mechanical Advantage = load / effort

Velocity Ratio = distance moved by effort / distance moved by load

Absorbed dose = Absorbed energy / mass

Exposure = total charge / mass

Dose equivalent = quality factor X Absorbed dose

1/TE = (1/TB) + (1/TR)

 

  Option E  The history and development of physics

 

Any formulas required will be found in the core topics

 

 

 

 

 

 

 

  1/l = RH((1/n2) - (1/m2))

  DxDp > h/2p

  DEDt > h/2p

Any other formulas required will be found in the AHL topics

 

 

  Option F  Astrophysics

 

  L = sAT4

  lmax (metres) = (2.90 X 10-3)/T (Kelvin)

  d (parsec) = 1/p (arc-second)

  b = L/(4pd2)

 

 

 

 

     v = Hd

     Dl/l = v/c 

 

 

 

  

  Option G Relativity

 

      g = 1/Ö(1 - (v2/c2))

     Dt = gDt0

  L = L0/g

  u'x = (ux - v)/(1 - (uxv/c2))

  m = gm0

  E0 = m0c2

  E = mc2

 

 

  p = gm0u

  E2 = p2c2 + m02c4

     Df/f = gDh/c2

  RSch = 2GM/c2

 

 

 

 

  

  Option  H   Optics

 

  n1sinq1 = n2sinq2

  n = 1/sinqc

  1/f = 1/u + 1/v

  m = hi/ho = v/u

  M = qi/qo

 

 

     q = l/b

     q = 1.22(l/b)

  dsinq = nl