Formulae Flashcards
1
Q
acceleration due to gravity
A
9.81 m s-2
on formula sheet
2
Q
elementary charge
A
1.60 * 10^-19 C
on formula sheet
3
Q
speed of light in a vacuum
A
3.00 * 10^8 m s-1
on formula sheet
4
Q
Planck’s constant
A
6.63 * 10^-34 J s
on formula sheet
5
Q
Avogadro’s constant
A
6.02 * 10^23 mol-1
on formula sheet
6
Q
molar gas constant
A
8.31 J mol-1 K-1
on formula sheet
7
Q
Boltzmann constant
A
1.38 * 10^-23 J K-1
on formula sheet
8
Q
gravitational constant
A
6.67 * 10^-11 N m2 kg-2
on formula sheet
9
Q
permittivity of free space
A
8.85 * 10^-12 C2 N-1 m-2 (F m-1)
on formula sheet
10
Q
electron rest mass
A
9.11 * 10^-31 kg
on formula sheet
11
Q
proton rest mass
A
1.673 * 10^-27 kg
on formula sheet
12
Q
neutron rest mass
A
1.675 * 10^-27 kg
on formula sheet
13
Q
alpha particle rest mass
A
6.646 * 10^-27 kg
on formula sheet
14
Q
Stefan constant
A
5.67 * 10^-8 W m-2 K-4
on formula sheet
15
Q
up quark charge
A
+2/3e
on formula sheet
16
Q
down quark charge
A
-1/3e
on formula sheet
17
Q
strange quark charge
A
-1/3e
on formula sheet
18
Q
unified atomic mass unit to kg
A
1 u = 1.661 * 10^-27 kg
on formula sheet
19
Q
electronvolt to J
A
1 eV = 1.60 * 10^-19 J
on formula sheet
20
Q
day to s
A
1 day = 8.64 * 10^4 s
on formula sheet
21
Q
year to s
A
1 year ≈ 3.16 * 10^7 s
on formula sheet
22
Q
light year to m
A
1 light year ≈ 9.5 * 10^15 m
on formula sheet
23
Q
parsec to m
A
1 parsec ≈ 3.1 * 10^16 m
on formula sheet
24
Q
arc length
A
r𝜃
on formula sheet
25
circumference of a circle
2πr
| on formula sheet
26
area of a circle
πr^2
| on formula sheet
27
curved surface area of a cylinder
2πrh
| on formula sheet
28
surface area of a sphere
4πr^2
| on formula sheet
29
area of a trapezium
1/2(a + b)h
| on formula sheet
30
volume of a cylinder
πr^2h
| on formula sheet
31
volume of a sphere
4/3πr^3
| on formula sheet
32
Pythagoras' theorem
a^2 = b^2 + c^2
| on formula sheet
33
cosine rule
a^2 = b^2 + c^2 - 2cos(A)
| on formula sheet
34
sine rule
a/sin(A) = b/sin(B) = c/sin(C)
| on formula sheet
35
logarithms multiplication rule
log(AB) = log(A) + log(B)
| on formula sheet
36
logarithms division rule
log(A/B) = log(A) - log(B)
| on formula sheet
37
logarithms powers rule
log(x^n) = n*log(x)
| on formula sheet
38
vectors trigonometry
Fx = F*cos(𝜃)
Fy = F*sin(𝜃)
on formula sheet
39
suvat equations
```
v = u + a*t
s = 1/2*(u + v)*t
s = u*t + 1/2 *a*t^2
v^2 = u^2 + 2*a*s
s = displacement (m)
u = initial velocity (m s-1)
v = final velocity (m s-1)
a = acceleration (m s-2)
t = time (s)
on formula sheet
```
40
force (using momentum)
```
F = Δp/Δt
F = force (N)
Δp = change in momentum (kg m s-1)
Δt = change in time
on formula sheet
```
41
force (using acceleration)
```
F = m*a
F = force (N)
m = mass (kg)
a = acceleration (m s-2)
NOT ON FORMULA SHEET
```
42
momentum (using mass)
```
p = m*v
p = momentum (kg m s-1)
m = mass (kg)
v = velocity (m s-1)
on formula sheet
```
43
moment
moment = F*x
F = force (N)
x = perpendicular distance from pivot (m)
on formula sheet
44
torque
torque = F*d
F = force (N)
d = distance between forces across the pivot (m)
on formula sheet
45
density
```
ρ = m/V
ρ = density (kg m-3)
m = mass (kg)
V = volume (m3)
on formula sheet
```
46
pressure (using force)
```
p = F/A
p = pressure (N m-2)
F = force (N)
A = area (m2)
on formula sheet
```
47
pressure (using fluid density)
```
p = h*ρ*g
p = pressure (N m-2)
h = depth (m)
ρ = fluid density (kg m-3)
g = acceleration due to gravity (9.81 m s-2)
on formula sheet
```
48
work (using an angle)
```
W = F*x*cos(𝜃)
W = work (J)
F = force (N)
x = displacement (m)
𝜃 = angle between the force and the direction of motion (°)
on formula sheet
```
49
efficiency
efficiency = (useful energy output)/(total energy input) * 100%
on formula sheet
50
power (using work done)
```
P = W/t
P = power (W)
W = work done (J)
t = time (s)
on formula sheet
```
51
power (using force and velocity)
```
P = F*v
P = power (W)
F = force (N)
v = velocity (m s-1)
on formula sheet
```
52
Hooke's law
```
F = k*x
F = force (N)
k = force constant (N m-1)
x = extension (m)
on formula sheet (not labelled)
```
53
energy (using force and extension)
```
E = 1/2*F*x
E = elastic potential energy (J)
F = force (N)
x = extension (m)
on formula sheet
```
54
energy (using the force constant)
```
E = 1/2*k*x^2
E = elastic potential energy (J)
k = force constant (N m-1)
x = extension (m)
on formula sheet
```
55
stress
```
σ = F/A
σ = stress (N m-2)
F = force (N)
A = area (m2)
on formula sheet (not labelled)
```
56
strain
```
ε = x/L
ε = strain (no units)
x = extension (m)
L = original length (m)
on formula sheet (not labelled)
```
57
Young's modulus (using stress and strain)
```
E = σ/ε
E = Young's modulus (N m-2)
σ = stress (N m-2)
ε = strain (no units)
on formula sheet (not labelled)
```
58
Young's modulus (using force and extension)
```
E = (F*L)/(A*x)
E = Young's modulus (N m-2)
F = force (N)
L = original length (m)
A = area (m2)
x = extension (m)
NOT ON FORMULA SHEET but easy to find from information you are given
```
59
charge
```
ΔQ = I*Δ*t
ΔQ = change in charge (C)
I = current (A)
Δt = chage in time (s)
on formula sheet
```
60
current (using cross-sectional area)
I = A*n*e*v
I = current (A)
A = cross-sectional area of wire (m2)
n = number of electrons per unit volume (m-3)
e = charge of an electron (1.602 * 10^-19 C)
v = mean drift velocity of the electrons (m s-1)
on formula sheet
61
work done (using potential difference and charge)
```
W = V*Q
W = work done (J)
V = potential difference (V)
Q = charge (C)
on formula sheet
```
62
work done (using e.m.f and charge)
```
W = ε*Q
W = work done (J)
ε = e.m.f (V)
Q = charge (C)
on formula sheet
```
63
work done (using potential difference, current and time)
```
W = V*I*t
W = work done (J)
V = potential difference (V)
I = current (A)
t = time (s)
on formula sheet
```
64
resistors in series
R = R1 + R2 +...
R = total resistance (Ω)
Rn = resistance of component n (Ω)
on formula sheet (not labelled as 'in series')
65
resistors in parallel
1/R = 1/R1 + 1/R2 +...
R = total resistance (Ω)
Rn = resistance of component n (Ω)
on formula sheet (not labelled as 'in parallel')
66
resistance (using resistivity)
```
R = (ρ*L)/A
R = resistance (Ω)
ρ = resistivity (Ω m)
L = length of wire (m)
A = cross-sectional area (m2)
on formula sheet
```
67
power (using potential difference and current)
```
P = V*I
P = power (W)
V = potential difference (V)
I = current (A)
on formula sheet
```
68
power (using current and resistance)
```
P = I^2 * R
P = power (W)
I = current (A)
R = resistance (Ω)
on formula sheet
```
69
power (using potential difference and resistance)
```
P = V^2 / R
P = power (W)
V = potential difference (V)
R = resistance (Ω)
on formula sheet
```
70
e.m.f (using Resistance)
```
ε = I*(R+r)
ε = e.m.f (V)
I = current (A)
R = external resistance (Ω)
r = internal resistance (Ω)
on formula sheet
```
71
e.m.f (using potential difference)
```
ε = V + I*r
ε = e.m.f (V)
V = potential difference (V)
I = current (A)
r = internal resistance (Ω)
on formula sheet
```
72
potential divider formula (using Vin and Vout)
Vout = (R2/(R1 + R2))*Vin
Vout = potential difference measured across R2 (V)
R1 = resistance of component 1 (Ω)
R2 = resistance of component 2 (Ω)
Vin = potential difference across R1 and R2 (V)
on formula sheet
73
potential divider formula (using V1 and V2)
```
V1/V2 = R1/R2
V1 = potential difference across R1 (V)
V2 = potential difference across R2 (V)
R1 = resistance of componenet 1 (Ω)
R2 = resistance of componenet 2 (Ω)
on formula sheet
```
74
current (using potential difference and resistance)
```
I = V/R
I = current (A)
V = potential difference (V)
R = resistance (Ω)
NOT ON FORMULA SHEET
```
75
potential difference (using current and resistance)
```
V = IR
V = potential difference (V)
I = current (A)
R = resistance (Ω)
NOT ON FORMULA SHEET
```
76
resistance (using potential difference and current)
```
R = V/I
R = resistance (Ω)
V = potential difference (V)
I = current (A)
NOT ON FORMULA SHEET
```
77
wave velocity
```
v = f*λ
v = wave velocity (m s-1)
f = frequency (Hz)
λ = wavelength (m)
on formula sheet
```
78
frequency
f = 1/T
f = frequency (Hz)
T = time period (s)
on formula sheet
79
Intensity
```
I = P/A
I = intensity (W m-2)
P = power (W)
A = area (m2)
on formula sheet
```
80
wavelength (using double slit experiment)
```
λ = (a*x)/D
λ = wavelength (m)
a = slit separation (m)
x = fringe separation (m)
D = distance between the slits and the screen (m)
on formula sheet
```
81
wavelength (using diffraction grating)
```
n*λ = d*sin(𝜃)
n = order of the maximum (no unit)
λ = wavelength (m)
d = slit separation (m)
𝜃 = angle between normal to the grating and the beam of light (°)
NOT ON FORMULA SHEET
```
82
refraction (using the speed of light)
```
n = c/v
n = refravtive index (no units)
c = speed of light in a vacuum (3.00 * 10^8 m s-1)
v = speed of light in material (m s-1)
on formula sheet
```
83
refraction (using a constant)
```
n*sin(𝜃) = constant
n = refravtive index (no units)
𝜃 = angle between normal to the material and the beam of light (°)
constant = n2*sin(𝜃2)
on formula sheet
```
84
refraction (using the critical angle)
sin(C) = 1/n
C = critical angle, point at which total internal reflection begins (°)
n = refractive index (no units)
on formula sheet
85
energy of a photon (using frequency)
```
E = h*f
E = energy of a photon (J)
h = Planck's constant (6.626 * 10^-34 J s)
f = frequency (Hz)
on formula sheet
```
86
energy of a photon (using wavelength)
E = (h*c)/λ
E = energy of a photon (J)
h = Planck's constant (6.626 * 10^-34 J s)
c = speed of light in a vacuum (3.00 * 10^8 m s-1)
λ = wavelength (m)
on formula sheet
87
wavelength (using Planck's constant)
```
λ = h/p
λ = wavelength (m)
h = Planck's constant (6.626 * 10^-34 J s)
p = momentum (kg m s-1)
on formula sheet
```
88
energy of a photon (using kinetic energy)
```
E = h*f
h*f = Φ + KEmax
E = energy of a photon (J)
h = Planck's constant (6.626 * 10^-34 J s)
f = frequency (Hz)
Φ = work function (J)
KEmax = kinetic energy of electrons once released (J)
on formula sheet
```
89
force (using acceleration due to gravity)
```
F = m*g
F = force (N)
m = mass (kg)
g = acceleration due to gravity (9.81 m s-2)
NOT ON FORMULA SHEET
```
90
acceleration (using force)
```
a = F/m
a = acceleration (m s-2)
F = force (N)
m = mass (kg)
NOT ON FORMULA SHEET
```
91
mass (using acceleration)
```
m = F/a
m = mass (kg)
F = force (N)
a = acceleration (m s-2)
NOT ON FORMULA SHEET
```
92
Drag
Fd = 1/2*ρ*Cd*A*v
Fd = drag (N)
ρ = fluid density (kg m-3)
Cd = coefficient of drag (no units)
A = cross-sectional area of the moving object (m2)
v = velocity of the moving object (m s-1)
NOT ON FORMULA SHEET
93
Kinetic energy (using velocity)
```
KE = 1/2*m*v^2
KE = kinetic energy (J)
m = mass (kg)
v = velocity (m s-1)
NOT ON FORMULA SHEET
```
94
thinking distance
```
thinking distance (m) = reaction time (s) * velocity of the car (m s-1)
NOT ON FORMULA SHEET
```
95
relationship between braking distance and velocity
braking distance ∝ (velocity)^2
| NOT ON FORMULA SHEET
96
stopping distance
stopping distance = thinking distance + braking distance
| NOT ON FORMULA SHEET
97
thermal energy
```
E = m*c*ΔT
E = thermal energy (J)
m = mass (kg)
c = specific heat capacity (J kg °C-1)
ΔT = change in temperature (K or °C)
NOT ON FORMULA SHEET
```
98
nuclear energy
```
E = m*c^2
E = nuclear energy (J)
m = mass (kg)
c = speed of light in a vacuum (3.00 * 10^8 m s-1)
NOT ON FORMULA SHEET
```
99
weight (using acceleration due to gravity)
```
w = m*g
w = weight (N)
m = mass (kg)
g = acceleration due to gravity (m s-2)
NOT ON FORMULA SHEET
```
100
gravitational potential energy
```
GPE = m*g*Δh
m = mass (kg)
g = acceleration due to gravity (m s-2)
Δh = change in height (m)
NOT ON FORMULA SHEET
```
101
relationship between gravitational potential energy and kinetic energy
```
kinetic energy (J) ↓ , gravitational potential energy (J) ↑
kinetic energy (J) ↑ , gravitational potential energy (J) ↓
NOT ON FORMULA SHEET
```
102
relationship between intensity and amplitude
intensity (W m-2) ∝ (amplitude (m))^2
| NOT ON FORMULA SHEET
103
energy (using power)
```
E = P*t
E = energy (J)
P = power (W)
t = time (s)
NOT ON FORMULA SHEET
```
104
impulse
```
I = F*Δt
I = impulse (N s)
F = force (N)
Δt = change in time (s)
NOT ON FORMULA SHEET
```
105
power (using force and distance)
```
P = (F*d)/t
P = power (W)
F = force (N)
d = distance (m)
t = time (s)
NOT ON FORMULA SHEET
```
106
work done (using force and distance)
```
W = F*d
W = work done (J)
F = force (N)
d = distance (m)
NOT ON FORMULA SHEET
this is the same as W = F*d*cos(θ) but θ is 0° so cos(θ) = 1
```
107
work done (using acceleration due to gravity)
```
W = m*g*h
W = work done (J)
m = mass (kg)
g = acceleration due to gravity (9.81 m s-1)
h = height (m)
NOT ON FORMULA SHEET
```
108
e.m.f (using energy transferred)
e.m.f (V) = energy transferred (J) / charge (C)
| NOT ON FORMULA SHEET
109
energy (using work done)
energy (J) = work done (J)
| NOT ON FORMULA SHEET
110
potential difference (using work done)
```
V = W/Q
V = potential difference (V)
W = work done (J)
Q = charge (C)
NOT ON FORMULA SHEET
```
111
relationship between resistivity and temperature
ρT = ρ0[1 + ∝(T - T0)]
ρT = resistivity of material at temperature T (Ω m)
ρ0 = resistivity of material at temperature T0
∝ = the temperature coefficient
T = temperature of the material (K or °C)
T0 = reference temperature at which the resistivity of the material is quoted (K or °C)
NOT ON FORMULA SHEET
112
percentage uncertainty from absolute uncertainty
percentage uncertainty = (absolute uncertainty / measured value)*100%
NOT ON FORMULA SHEET
113
y = a*b
| % uncertainty of y from % uncertainties of a and b
% uncertainty of y = % uncertainty of a + % uncertainty of b
| NOT ON FORMULA SHEET
114
y = a/b
| % uncertainty of y from % uncertainties of a and b
% uncertainty of y = % uncertainty of a + % uncertainty of b
| NOT ON FORMULA SHEET
115
y = a^n
| % uncertainty of y from % uncertainty of a
% uncertainty of y = % uncertainty of a * n
| NOT ON FORMULA SHEET
116
percentage uncertainty from a gradient
percentage uncertainty = (absolute uncertainty / gradient of line of best fit)*100%
NOT ON FORMULA SHEET
117
percentage uncertainty from a y-intercept
percentage uncertainty = (absolute uncertainty / 'best' y-intercept)*100%
NOT ON FORMULA SHEET
118
absolute uncertainty form gradients
absolute uncertainty = gradient of best fit line - gradient of worst fit line
NOT ON FORMULA SHEET
119
absolute uncertainty form y-intercepts
absolute uncertainty = best y-intercept - worst y-intercept
| NOT ON FORMULA SHEET
120
average speed
```
average speed (m s-1) = distance (m) / time (s)
NOT ON FORMULA SHEET
```
121
average velocity
```
average velocity (m s-1) = total displacement (m) / time (s)
NOT ON FORMULA SHEET
```
122
acceleration (using change in velocity)
acceleration (m s-2) = change in velocity (m s-1) / time (s)
NOT ON FORMULA SHEET
this can be found by rearranging v =u + a*t
123
1 kilowatt-hour
1 kilowatt-hour = 1000 watts * 3600 seconds
1 kilowatt-hour = 3600 000 Joules
NOT ON FORMULA SHEET
124
cost of energy
cost = number of kilowatt-hours * cost per kilowatt-hour
| NOT ON FORMULA SHEET
125
distance between nodes in a stationary wave
λ/2
λ = wavelength (m)
NOT ON FORMULA SHEET
126
distance between anti-nodes in a stationary wave
λ/2
λ = wavelength (m)
NOT ON FORMULA SHEET
127
distance between nodes and anti-nodes in a stationary wave
λ/4
λ = wavelength (m)
NOT ON FORMULA SHEET
128
Kirchhoff's first law
ΣIin = ΣIout
sum of currents entering a junction (A) = sum of currents exiting a junction (A)
NOT ON FORMULA SHEET
129
Kirchhoff's second law
Σε = ΣI*R
sum of the e.m.f (V) = sum of the products of current and resistance of each component in series (V)
NOT ON FORMULA SHEET
130
maximum kinetic energy of electrons emitted as a result of the photoelectric effect
maximum kinetic energy (J) = charge of an electron (1.602 * 10^-19 C) * stopping potential (V)
NOT ON FORMULA SHEET
131
Snell's law
n1 * sin(θ1) = n2 * sin(θ2)
n1 = refractive index of material 1 (no units)
θ1 = angle between normal to material 1 and the beam of light in material 1 (°)
n2 = refractive index of material 2 (no units)
θ2 = angle between normal to material 2 and the beam of light in material 2 (°)
132
critical angle between two materials
```
sin(C) = n1/n2
C = critical angle (°)
n1 = refractive index of material 1 (no units)
n2 = refractive index of material 2 (no units)
```
133
In the suvat equations, what does s denote?
Displacement (m)
134
In the suvat equations, what does u denote?
Initial Velocity (m s-1)
135
In the suvat equations, what does v denote?
Final Velocity (m s-1)
136
In the suvat equations, what does a denote?
Acceleration (m s-2)
137
In the suvat equations, what does t denote?
Time (s)
138
What equation would you use to find final velocity given initial velocity, acceleration and time?
v = u + a*t
139
What equation would you use to find final velocity given initial velocity, acceleration and displacement?
v^2 = u^2 + 2*a*s
140
What equation would you use to find displacement given initial velocity, final velocity and time?
s = 1/2*(u + v)*t
141
What equation would you use to find displacement given initial velocity, acceleration and time?
s = u*t + 1/2*a*t^2
142
Rearrange v = u + a*t for u
u = v - a*t
143
Rearrange v = u + a*t for a
a = (v - u)/t
144
Rearrange v = u + a*t for t
t = (v - u)/a
145
Rearrange v^2 = u^2 + 2*a*s for u^2
u^2 = v^2 - 2*a*s
146
Rearrange v^2 = u^2 + 2*a*s for a
a = (v^2 - u^2)/(2*s)
147
Rearrange v^2 = u^2 + 2*a*s for s
s = (v^2 - u^2)/(2*a)
148
Rearrange s = 1/2*(u + v)*t for u
u = (s/t)*2 - v
149
Rearrange s = 1/2*(u + v)*t for v
v = (s/t)*2 - u
150
Rearrange s = 1/2*(u + v)*t for t
t = (2*s)/(u + v)
151
Rearrange s = u*t + 1/2*a*t^2 for u
u = (s - 1/2*a*t^2)/t
152
Rearrange s = u*t + 1/2*a*t^2 for a
a = 2*(s - u*t)/t^2
153
Rearrange s = u*t + 1/2*a*t^2 for t
t = ((2*a*s + u^2)^(1/2) - u)/a
