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Important-Equations-in-A-level-Physics-CIE

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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
πœƒ=
π‘™π‘’π‘›π‘”π‘‘β„Ž π‘œπ‘“ π‘Žπ‘Ÿπ‘ 𝑠
=
π‘Ÿπ‘Žπ‘‘π‘–π‘’π‘ 
π‘Ÿ
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
πœ”=
34
567
567
;<=>?;@ ABCD?;EFGF<H
HBGF H;IF<
34
=
or
or
βˆ†K
βˆ†H
4
897
897
4
=
34
L
=2πœ‹π‘“
speed = angular velocity × radius ⟹ 𝑣 = πœ”π‘Ÿ =
34@
L
3
𝑣
= πœ”3 π‘Ÿ
π‘Ÿ
π‘šπ‘£ 3
𝐹=
= π‘šπ‘Ÿπœ”3
π‘Ÿ
π‘Ž=
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 π‘π‘š3 𝐾𝑔Z3
πΊπ‘€π‘š
π‘Ÿ3
𝐹 𝐺𝑀
𝑔= = 3
π‘š
π‘Ÿ
The gravitational potential at a point is the work done per unit
mass in bringing a mass from the infinity to the point
𝐺𝑀
πœ™=−
π‘Ÿ
πΊπ‘€π‘š
𝑔. 𝑝. 𝑒. = −
π‘Ÿ
𝐹=
Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 –
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17
18
𝑣3 =
Orbital speed v
ab
@
𝑇3 =
Orbital period
or 𝑣 =
34@
L
3
4πœ‹
π‘Ÿ5
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.
π‘₯ = π‘₯7 sin πœ”π‘‘ or π‘₯ = π‘₯7 cos πœ”π‘‘
22
Acceleration of an oscillator
π‘Ž = −πœ”3 π‘₯
23
Velocity of an oscillator
or 𝑣 = 𝑣7 cos πœ”π‘‘ or 𝑣 = ±πœ” π‘₯73 − π‘₯ 3
24
Maximum velocity of an
oscillator
𝑣 = πœ”π‘₯7
25
Kinetic energy
26
Potential energy
27
Phase difference
e
1
𝐸 = π‘šπœ”3 (π‘₯73 − π‘₯ 3 )
2
1
𝐸 = π‘šπœ”3 π‘₯ 3
2
π‘₯
𝑑
∅ = 2πœ‹ π‘œπ‘Ÿ ∅ = 2πœ‹
πœ†
𝑇
Communication (Unit 16 syllabus)
28
Attenuation
29
Attenuation per unit length
30
Signal to noise ratio
31
π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝑑𝐡 = 10π‘™π‘œπ‘”
wHHF<>;HBx< Ay
zF<=H{ xe |;}?F (~G)
10π‘™π‘œπ‘”
tu
tv
8
tu
z
tv
= 10π‘™π‘œπ‘”
π‘†π‘–π‘”π‘›π‘Žπ‘™ π‘ƒπ‘œπ‘€π‘’π‘Ÿ
π‘π‘œπ‘–π‘ π‘’ π‘ƒπ‘œπ‘€π‘’π‘Ÿ
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
Δπ‘ˆ = π‘ž + 𝑀
32 First law of Thermodynamics
33
Specific Heat Capacity
𝐸 = π‘šπ‘βˆ†πœƒ
34
Specific Latent Heat
𝐸 = π‘šπΏ
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 –
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8
L
36
Ideal gas equation
37
Pressure
38
𝑝𝑉 = 𝑛𝑅𝑇
1 π‘π‘š 𝑐 3 1
𝑝=
= πœŒπ‘3
3
𝑉
3
1
3π‘˜π‘‡
𝑅
𝐸= π‘šπ‘3=
(π‘˜ = )
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=
•4Ε½• @ v
𝑉=
Œ
•4Ε½• @ v
𝑄
4πœ‹πœ€7 π‘Ÿ
𝐸=
43 Field Strength (uniform field)
π‘Š
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
𝐢=
𝑄
𝑉
1
1
1 𝑄3
π‘Š = 𝑄𝑉 = 𝐢𝑉 3 =
2
2
2 𝐢
𝑄HxH;? = 𝑄8 + 𝑄3 + 𝑄5 + β‹―
𝐢HxH;? = 𝐢8 + 𝐢3 + 𝐢5 + β‹―
1
𝐢HxH;?
Electronics (Unit 21 syllabus)
=
1
1
1
+ + +β‹―
𝐢8 𝐢3 𝐢5
𝐢 = 4πœ‹πœ€7 π‘Ÿ
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 –
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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
𝐡=
𝐹
𝐼𝐿
𝐹 = 𝐡𝐼𝐿 sin πœƒ
𝐡=
π‘šπ‘£
π‘žπ‘Ÿ
𝐹 = 𝐡𝑄𝑣
π‘šF 𝑣 3
= 𝐡𝑒𝑣
π‘Ÿ
𝐸
𝑣=
𝐡
𝐡𝐼
𝑉— =
π‘›π‘‘π‘ž
𝑒
2𝑉E;
= 3 3
π‘šF π‘Ÿ 𝐡
1
π‘šπ‘£ 3 = 𝑒𝑉E;
2
Electromagnetic induction (Unit 23 syllabus)
61
Magnetic flux F through area A
62
Faraday’s law
63
Magnetic flux linkage
𝑁𝛷 = 𝑁𝐡𝐴 cos πœƒ
64
Motional e.m.f
πœ€ = 𝐡𝑙𝑣
𝛷 = 𝐡𝐴
𝐸=
βˆ†(𝑁𝛷)
βˆ†π‘‘
Electromagnetic induction (Unit 24 syllabus)
65
Sinusoidal alternating current
𝐼 = 𝐼7 sin πœ”π‘‘
66
Sinusoidal alternating e.m.f.
𝑉 = 𝑉7 sin πœ”π‘‘
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 –
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Quantum Physics (Unit 25 syllabus)
𝐸 = β„Žπ‘“ or 𝐸 =
{E
69
Energy of a photon
70
Kinetic energy of a particle of charge e accelerated
through a voltage V
1
𝑒𝑉 = π‘šπ‘£ 3
2
71
Einstein’s photoelectric equation
β„Žπ‘“ = 𝛷 + π‘˜. 𝑒.G;•
72
De Broigle wavelength
πœ†=
73
Difference in energy between two levels when a photon is
either emitted or absolved
βˆ†πΈ = 𝐸8 − 𝐸3 = β„Žπ‘“ =
œ
β„Ž
π‘šπ‘£
β„Žπ‘
πœ†
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 = π‘šπ‘ 3
βˆ†π‘
= −πœ†π‘
βˆ†π‘‘
𝐴=
π‘₯ = π‘₯7 𝑒 (ZœH)
𝑑8
3
=
ln 2 0.693
=
πœ†
πœ†
Medical Imaging (Unit 22 and 25 syllabus)
𝑒𝑉
β„Ž
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
π‘‡β„Žπ‘–π‘π‘˜π‘›π‘’π‘ π‘  π‘œπ‘“ π‘π‘œπ‘›π‘’ =
84
Lamour frequency
85
Frequency f0 of the processing nuclei
π‘₯8
3
=
•
ln 2
πœ‡
𝑍 = πœŒπ‘£
𝐼H
𝑍3 − 𝑍8
=
𝐼7
𝑍3 + 𝑍8
3
3
𝑍3 − 𝑍8
=
𝑍3 + 𝑍8
3
π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’ π‘‘π‘Ÿπ‘Žπ‘£π‘’π‘™π‘™π‘’π‘‘ 𝑏𝑦 π‘’π‘™π‘‘π‘Ÿπ‘Žπ‘ π‘œπ‘’π‘›π‘‘
𝑐Δ𝑑
=
2
2
πœ”7 = 𝛾𝐡7
𝑓7 =
πœ†π΅7
2πœ‹
Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 –
5
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