Important Equations in A Level Physics CIE
P2: Planning, analysis and evaluation
1
Choice of axes for
straight-line graphs
Relationship
Graph
y = mx+c
y against x
ln y against
ln x
lg y against
lg x
y = axn
3
4
m
c
n
ln a
lg a
Because...
ln y = n ln
x + ln a
lg y = kx +
ln a
Always add uncertainties, never subtract. Where quantities are:
• Added or subtracted, then add absolute uncertainties;
• Multiplied or divided, then add percentage uncertainties.
y = aekx
2
Intercept on yaxis
Gradient
Combining
uncertainties
Uncertainties and
logarithms
Error in gradient
ln y against x
k
ln a
logarithm likely value - logarithm smallest/largest value
error = (gradient of the best fit line) – (gradient of worst acceptable line)
Circular Motion (Unit 7 syllabus)
5
6
7
Angle in radians
𝜃=
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 𝑠
=
𝑟𝑎𝑑𝑖𝑢𝑠
𝑟
To convert from degrees to radians, multiply by
To convert from radians to degrees, multiply by
8
Angular velocity
9
Relating velocity and angular
velocity
10
Centripetal acceleration
11
Centripetal force
𝜔=
34
567
567
;<=>?;@ ABCD?;EFGF<H
HBGF H;IF<
34
=
or
or
∆K
∆H
4
897
897
4
=
34
L
=2𝜋𝑓
speed = angular velocity × radius ⟹ 𝑣 = 𝜔𝑟 =
34@
L
3
𝑣
= 𝜔3 𝑟
𝑟
𝑚𝑣 3
𝐹=
= 𝑚𝑟𝜔3
𝑟
𝑎=
Gravitational Fields (Unit 8 syllabus)
12
Gravitational constant G
13
Newton’s law of gravitation
14
Gravitational field strength g
15
Gravitational potential
16
Gravitational potential
energy
𝐺 = 6.67 × 10Z88 𝑁𝑚3 𝐾𝑔Z3
𝐺𝑀𝑚
𝑟3
𝐹 𝐺𝑀
𝑔= = 3
𝑚
𝑟
The gravitational potential at a point is the work done per unit
mass in bringing a mass from the infinity to the point
𝐺𝑀
𝜙=−
𝑟
𝐺𝑀𝑚
𝑔. 𝑝. 𝑒. = −
𝑟
𝐹=
Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 –
1
17
18
𝑣3 =
Orbital speed v
ab
@
𝑇3 =
Orbital period
or 𝑣 =
34@
L
3
4𝜋
𝑟5
𝐺𝑀
Oscillations (Unit 13 syllabus)
8
19
Period
Time (T) for a complete oscillation 𝑇 =
20
Frequency
Frequency (f) is the number of oscillations per unit time 𝑓 =
21
Equations of s.h.m.
𝑥 = 𝑥7 sin 𝜔𝑡 or 𝑥 = 𝑥7 cos 𝜔𝑡
22
Acceleration of an oscillator
𝑎 = −𝜔3 𝑥
23
Velocity of an oscillator
or 𝑣 = 𝑣7 cos 𝜔𝑡 or 𝑣 = ±𝜔 𝑥73 − 𝑥 3
24
Maximum velocity of an
oscillator
𝑣 = 𝜔𝑥7
25
Kinetic energy
26
Potential energy
27
Phase difference
e
1
𝐸 = 𝑚𝜔3 (𝑥73 − 𝑥 3 )
2
1
𝐸 = 𝑚𝜔3 𝑥 3
2
𝑥
𝑡
∅ = 2𝜋 𝑜𝑟 ∅ = 2𝜋
𝜆
𝑇
Communication (Unit 16 syllabus)
28
Attenuation
29
Attenuation per unit length
30
Signal to noise ratio
31
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝐵 = 10𝑙𝑜𝑔
wHHF<>;HBx< Ay
zF<=H{ xe |;}?F (~G)
10𝑙𝑜𝑔
tu
tv
8
tu
z
tv
= 10𝑙𝑜𝑔
𝑆𝑖𝑔𝑛𝑎𝑙 𝑃𝑜𝑤𝑒𝑟
𝑁𝑜𝑖𝑠𝑒 𝑃𝑜𝑤𝑒𝑟
Thermal Physics (Unit 12 syllabus)
The internal energy of a system is the sum of the random
Internal Energy
distribution of kinetic and potential energies of its atoms or
molecules
Δ𝑈 = 𝑞 + 𝑤
32 First law of Thermodynamics
33
Specific Heat Capacity
𝐸 = 𝑚𝑐∆𝜃
34
Specific Latent Heat
𝐸 = 𝑚𝐿
Ideal Gases (Unit 10 syllabus)
35
Boyle´s Law
pV=constant or 𝑝8 𝑉8 = 𝑝3 𝑉3
Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 –
2
8
L
36
Ideal gas equation
37
Pressure
38
𝑝𝑉 = 𝑛𝑅𝑇
1 𝑁𝑚 𝑐 3 1
𝑝=
= 𝜌𝑐3
3
𝑉
3
1
3𝑘𝑇
𝑅
𝐸= 𝑚𝑐3=
(𝑘 = )
2
2
𝑁w
Mean translational kinetic energy E
of a particle of an ideal gas
Coulomb’s Law (Unit 17 syllabus)
39
Œu Œv
𝐹=
Coulomb´s Law
40
Work done in moving a charge from the
negative to the positive plate
41
Electric Field Strength
𝐸=
42
Electric Potential
𝑉=
•4Ž• @ v
𝑉=
Œ
•4Ž• @ v
𝑄
4𝜋𝜀7 𝑟
𝐸=
43 Field Strength (uniform field)
𝑊
𝑄
“
A
Capacitance (Unit 18 syllabus)
44
Capacitance
45
Work done in charging a capacitor
46
Capacitors in parallel
(all have same voltage)
47
Capacitors in series
(all have same charge)
48
Capacitance of isolated bodies
𝐶=
𝑄
𝑉
1
1
1 𝑄3
𝑊 = 𝑄𝑉 = 𝐶𝑉 3 =
2
2
2 𝐶
𝑄HxH;? = 𝑄8 + 𝑄3 + 𝑄5 + ⋯
𝐶HxH;? = 𝐶8 + 𝐶3 + 𝐶5 + ⋯
1
𝐶HxH;?
Electronics (Unit 21 syllabus)
=
1
1
1
+ + +⋯
𝐶8 𝐶3 𝐶5
𝐶 = 4𝜋𝜀7 𝑟
𝑅e
𝑉x>H
=−
𝑉B<
𝑅B<
𝑉x>H
𝑅8
𝐺=
=1+
𝑉B<
𝑅3
+
If V is slightly greater in magnitude than V-, then Vout
will have a magnitude equal to the positive power
supply voltage.
+
If V is slightly smaller in magnitude than V-, then Vout
will have a magnitude equal to the negative power
supply voltage.
𝐺=
49
Inverting Amplifier
50
Non-inverting Amplifier
51
The op-amp as a comparator
Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 –
3
52
53
54
55
Magnetic Fields (Unit 22 syllabus)
Magnetic Flux Density for a uniform
magnetic field
Magnetic Force on a current-carrying
conductor
Magnetic flux density for charged particles
Charged particles (Unit 22 syllabus)
Magnetic force on a moving particle at right angles to a
magnetic field
56
Electron traveling in a uniform magnetic field
57
Velocity of an undeflected charged particle in a region
where electric and magnetic fields are at right angles
58
Hall Voltage
59
Charge-to-mass ratio
60
Kinetic energy of electrons leaving the anode in a
deflection tube
𝐵=
𝐹
𝐼𝐿
𝐹 = 𝐵𝐼𝐿 sin 𝜃
𝐵=
𝑚𝑣
𝑞𝑟
𝐹 = 𝐵𝑄𝑣
𝑚F 𝑣 3
= 𝐵𝑒𝑣
𝑟
𝐸
𝑣=
𝐵
𝐵𝐼
𝑉— =
𝑛𝑡𝑞
𝑒
2𝑉E;
= 3 3
𝑚F 𝑟 𝐵
1
𝑚𝑣 3 = 𝑒𝑉E;
2
Electromagnetic induction (Unit 23 syllabus)
61
Magnetic flux F through area A
62
Faraday’s law
63
Magnetic flux linkage
𝑁𝛷 = 𝑁𝐵𝐴 cos 𝜃
64
Motional e.m.f
𝜀 = 𝐵𝑙𝑣
𝛷 = 𝐵𝐴
𝐸=
∆(𝑁𝛷)
∆𝑡
Electromagnetic induction (Unit 24 syllabus)
65
Sinusoidal alternating current
𝐼 = 𝐼7 sin 𝜔𝑡
66
Sinusoidal alternating e.m.f.
𝑉 = 𝑉7 sin 𝜔𝑡
67
Root-mean-square of an alternating current
𝐼@GC = 𝐼7 / 2
68
Transformers
𝑉C 𝑁›
=
𝑉D 𝑁D
𝐼D 𝑉D = 𝐼C 𝑉C
Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 –
4
Quantum Physics (Unit 25 syllabus)
𝐸 = ℎ𝑓 or 𝐸 =
{E
69
Energy of a photon
70
Kinetic energy of a particle of charge e accelerated
through a voltage V
1
𝑒𝑉 = 𝑚𝑣 3
2
71
Einstein’s photoelectric equation
ℎ𝑓 = 𝛷 + 𝑘. 𝑒.G;•
72
De Broigle wavelength
𝜆=
73
Difference in energy between two levels when a photon is
either emitted or absolved
∆𝐸 = 𝐸8 − 𝐸3 = ℎ𝑓 =
œ
ℎ
𝑚𝑣
ℎ𝑐
𝜆
Nuclear Physics (Unit 26 syllabus)
74
Einstein energy-mass equation
75
Activity of a radioactive sample
76
Exponential decrease of a quantity (A/R/N)
77
Half-life
𝐸 = 𝑚𝑐 3
∆𝑁
= −𝜆𝑁
∆𝑡
𝐴=
𝑥 = 𝑥7 𝑒 (ZœH)
𝑡8
3
=
ln 2 0.693
=
𝜆
𝜆
Medical Imaging (Unit 22 and 25 syllabus)
𝑒𝑉
ℎ
78
Maximum X-ray frequency
𝑓G;• =
79
Attenuation of X-rays as they pass a uniform
material
𝐼 = 𝐼7 𝑒 Z
80
Half thickness
81
Acoustic impedance of a material
82
Fraction of the intensity of an ultrasound wave
reflected at a boundary
83
Thickness of bone
𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑏𝑜𝑛𝑒 =
84
Lamour frequency
85
Frequency f0 of the processing nuclei
𝑥8
3
=
•
ln 2
𝜇
𝑍 = 𝜌𝑣
𝐼H
𝑍3 − 𝑍8
=
𝐼7
𝑍3 + 𝑍8
3
3
𝑍3 − 𝑍8
=
𝑍3 + 𝑍8
3
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑏𝑦 𝑢𝑙𝑡𝑟𝑎𝑠𝑜𝑢𝑛𝑑
𝑐Δ𝑡
=
2
2
𝜔7 = 𝛾𝐵7
𝑓7 =
𝜆𝐵7
2𝜋
Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 –
5