IB Physics Formula Sheet (from the Physics Data Booklet)
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Topic 1: Measurement and uncertainties
1.1. Measurements in physics
1.3.Vectors and scalars
AH = A cos
AV = A sin
AV
A
1.2. Uncertainties and errors
If y = a ± b then ∆y = ∆a + ∆b
AH
If y = ab/c then ∆y/y = ∆a/a + ∆b/b + ∆c/c
If y = an then ∆y/y = |n ∆a/a|
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Topic 2: Mechanics
2.1. Motion
v = u + at
s = ut + (1/2)at2
v2 = u2 + 2as
s = (1/2)(v + u)/t
2.2. Forces
F = ma
Ff ≤ µsR
Ff ≤ µdR
2.3. Work, energy and power 2.4. Momentum and impulse
W = Fs cos
p = mv
EK = (1/2)mv2
F = p/t
2
EP = (1/2)kx
EK = p2/2m
EP = mgh
power = Fv
Efficiency = Wout/Win = Pout/Pin
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Topic 3: Thermal concepts
3.1. Thermal concepts
Q = mct
Q = mL
3.2. Modelling a gas
p = F/A
n = N/NA
pV = nRT
EK = (3/2)kBT = (3/2)RT/NA
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Topic 4: Waves
4.1. Oscillations
T = 1/f
4.3. Wave characteristics
I  A2
I  x-2
4.4. Wave behaviour 4.5. Standing waves
I = I0 cos
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Topic 5: Electricity and magnetism
5.1. Electric fields
I = q/t
F = kq1q2/r2
k= 1/(40)
V = W/q
E = F/q
I = nAvq
4.2. Travelling waves
c = f
5.2. Electric currents 5.3. Electric cells
5.4. Magnetic effects
V = 0 (loop)
 = I(R + r)
F = qvB sin
I= 0 (junction)
F = BIL sin
R = V/I
P = VI = I2R = V2/R
Rtotal = R1 + R2 + …
1/Rtotal = 1/R1 + 1/R2 + …
 = RA/L
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Topic 6: Circular motion and gravitation
6.1. Circular motion
6.2. Newton’s law of gravitation
v = r
F = GMm/r2
2
2
2
a = v /r = 4 r/T
g = F/m
2
2
F = mv /r = m r
g = GM/r2
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Topic 7: Atomic, nuclear and particle physics
7.1. Discrete energy and radioactivity
E = hf
 = hc/E
7.2. Nuclear reactions
E= m c2
7.3. The structure of matter
Charge
Quarks
Baryon number
(2/3)e
u
c
t
1/3
-(1/3)e
d
s
b
1/3
All quarks have a strangeness number of 0 except the
strange quark that has a strangeness number of -1
Charge
Leptons
-1e
e


0
e


All leptons have a lepton number of 1
and antileptons have a lepton
number of -1
Gravitational
Weak
Electromagnetic
Strong
Particles experiencing
All
Quarks, leptons
Charged
Quarks, gluons
Particles mediating
Graviton
W +, W - , Z 0
Gluons

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Topic 8: Energy production
8.1. Energy sources
Power = energy/time
Power = (1/2) Av3
8.2. Thermal energy transfer
P = eAT4
max = 2.9010-3/T
I = power/A
albedo = total scattered power / total incident power
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Topic 9: Simple harmonic motion
9.1. SHM
9.2. Single-slit
9.3. Interference
 = 2/T
 = /b
n = d sin
2
a = - x
Constructive interference: 2dn = (m + ½)
x = x0 sin t; x = x0 cos t;
Destructive interference: 2dn = m 
v = x0 cos t; v = -x0 sin t;
v = ± sqrt (x02 – x2)
9.4. Resolution
9.5. Doppler effect
2
2
2
EK = (1/2)m  (x0 – x )
 = 1.22 /b
Moving source: f ‘ = fv/(v ± us)
2 2
ET = (1/2)m  x0
R = (/∆) = mN
Moving observer: f ‘ = f(v ± uo)/v
Pendulum: T = 2 sqrt (l/g)
∆f/f = /∆  v/c
Mass-spring: T = 2 sqrt (m/k)
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Topic 10: Fields
10.1. Describing fields
W = q∆Ve
W = m∆Vg
10.2. Fields at work
Vg = -GM/r;
Ve = kq/r
g = -∆Vg/∆r;
E = -∆Ve/∆r
EP = mVg = -GMm/r
EP = qVe = kq1q2/r
2
FG = Gm1m2/r
FE = kq1q2/r2
Vesc = sqrt (2GM/r)
Vorbit = sqrt (GM/r)
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Topic 11: Electromagnetic induction
11.1. Induction

 = BA cos
 = -N ∆/∆t
 = Bvl
 = BvlN
11.2. Power generation
11.3. Capacitance
Irms = I0/2
C = q/V
Vrms = V0/2
Cparallel = C1 + C2 + …
 = RC
R = V0/I0 = Vrms/ Irms
1/Cseries = 1/C1 + 1/C2 + …
q = q0e-t/
Pmax = I0V0
C = 0A/d
I = I0e-t/
2
Pavg = (1/2) I0V0
E = (1/2)CV
V = V0e-t/
p/s = Np/Ns = Is/Ip
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Topic 12: Quantum and nuclear physics
12.1. Interaction of matter with radiation
12.2. Nuclear physics
2
E = hf
P(r) = || ∆V
R = R0A1/3
Emax = hf - 
∆x∆p  h/4
N = N0e-t
E = -13.6/n2 eV
∆E∆t h/4
A = N0e-t
mvr = nh/2
sin = /d
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Option A: Relativity
A.1. Beginnings of relativity
x’ = x – vt
u’ = u - v
A.2. Lorentz transformations
A.3. Spacetime diagrams
 = (1 – v2/c2)-1/2
 = tan-1(v/c)
x’ = (x – vt); ∆x’ = (∆x – v∆t)
t’ = (t – vx/c2); ∆t’ = (∆t – v∆x/c2)
u’ = (u – v)/(1 – uv/c2)
∆t = ∆t0
L = L0/
(ct’)2 – (x’)2 = (ct)2 – (x)2
A.4. Relativistic mechanics (HL only)
A.5. General relativity (HL only)
2
E = m0c
∆f/f =g∆h/c2
2
E0 = m0c
Rs = 2GM/c2
EK = ( - 1)m0c2
∆t = ∆t0/sqrt(1 – Rs/r)
p = m0v
E2 = p2c2 + m02c4
qV = ∆EK
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Option B: Engineering physics
B.1. Rigid bodies and rotational dynamics
 = Fr sin
 = 2f
I = mr2
f = I + t
 = I
f2 = I2 + 2
 = It + (1/2)t2
L = I
EKrot = (1/2)I2
B.2. Thermodynamics
Q = U + W
U = (3/2)nRT
S = Q/T
pV5/3 = const
W = pV
pV5/3 = const
W = pV
 = Wuseful/Einput
 carnot = 1 – Tcold/Thot
B.3. Fluids and fluid dynamics (HL only)
B.4. Forced vibrations and resonance (HL only)
B = fVfg
FD = 6rv
Q = 2(Estored/Edissipated/cycle)
P = P0 + fgd
R = vr/
Q = 2fres(Estored/Ploss)
Av = constant
(1/2) v2 + gz + p = const
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Option C: Imaging
C.1. Introduction to imaging
1/f = 1/v + 1/u
P = 1/f
m = hi/ho = -v/u
M = i/o
C.2. Imaging instrumentation
M = i/o
M = fo/fe
Mnear point = D/f + 1
Minfinity = D/f
C.3. Fibre optics
n = 1/sin c
attenuation = 10 log (I/I0)
C.4. Medical imaging (HL only)
Lf = 10 log (I1/I0)
I = I0 e-x
µx1/2 = ln 2
Z = pc
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Option D: Astrophysics
D.1. Stellar quantities
d(parsec) = 1/p(arc-second)
L = AT4
B = L/(4d2)
D.2. Stellar evolution
max = 2.910-3 m K
L  M3.5
D.3. Cosmology
z = /0  v/c
z = R/R0 – 1
v = H0d
T  1/H0
D.4. Stellar processes (HL only)
D.5. Further cosmology (HL only)
v = sqrt(4G/3) r
c = 3H2/(8G)
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