PAT Equations Flashcards
(94 cards)
1
Q
Volume of a sphere
A
4/3 πr^3
2
Q
Plank’s Constant
A
6.63*10^-34
3
Q
Free space permittivity
A
8.85*10^-12
4
Q
electron rest mass
A
9.11*10^-31
5
Q
sphere surface area
A
4πr^2
6
Q
Equation linking momentum, force, time
A
F = p/t Force = momentum/time
7
Q
Equation linking velocity, power, force
A
P = Fv
8
Q
Equations for energy stored by a spring (E)
A
E = 1/2 K x^2
or E = 1/2Fx
9
Q
Equation for stress
A
σ = F/A
10
Q
Equation for strain
A
ε = x/L
11
Q
Equation for young’s modulus
A
E = σ/ε
12
Q
Electricity equations for work done?
A
W = VQ (Work Done = p.d. * charge) W = VIt (because Q = It)
13
Q
Equation linking current, time, electric charge
A
Q = It Charge = Current * time
14
Q
The resistivity-resistance equation
A
R = pL/A
15
Q
Internal resistance equation
A
E = IR + Ir (V + v)
16
Q
WAVE SPEEEEED
A
v = f λ
17
Q
Total internal refraction equation
A
sin(C)=n2/n1 (n2
18
Q
Snell’s law equation
A
n1sinθ1=n2sinθ2
19
Q
Equation for the refractive index
A
n = c/v
refractive index = speed of light in vacuum/speed of light in material
20
Q
Plank’s wavelength equation
A
λ = h/p
21
Q
Quantum energy equations
A
E = hf E = hc/λ
22
Q
Work function equation
A
hf = φ + KEmax
23
Q
Centripetal force equation
A
F = mv^2/r F = mrω^2 F = mvω
24
Q
Centripetal acceleration equations
A
a = v^2/r a = rω^2 a = vω
25
Velocity of a centripetal particle thing
v = rω
26
angular velocity equation
```
ω = 2Pi/T
ω = 2fPi
```
27
Gravitational potential (Vg)
Vg = -GM/r
28
Units for gravitational potential
J per Kg
29
Electric field strength
E = F/Q
30
gravitational field strength
g = -GM/r^2
31
Force due to gravity
F = -GMm/r^2
32
Energy due to gravity
E = -GMm/r (from Vg which is J per Kg (hence * small m))
33
Equation relating voltage, charge and capacitance
C = Q/V Capacitance = charge/p.d.
34
Capacitance from a radius
C = 4πε0r
35
Equation for electric potential (in volts V)
V = Q/4πε0r
36
Equation for energy due to the electric field between charges
E = Qq/4πε0r
37
Equations for electric filed strength
```
E = V/d
E = Q/4πε0r^2
```
38
Equation for force acting between two point charges
F = Qq/4πε0r^2
39
integral of 1/x
ln(mod(x))+c
40
differential of ln(kx)
1/x (no matter what k is the result is 1/x)
41
differential of a^kx
a^kx * kln(a)
42
differential of cosec(kx)
-k*cosec(kx)cot(k)
43
differential of sec(kx)
k*sec(kx)tan(kx)
44
differential of cot(kx)
-k*cosec^2(kx)
45
integral of e^x
e^x + c
46
cos(2A) =
cos^2(A) - sin^2(A)
47
sin(2A) =
2sin(A)cos(A)
48
ln(1) =
0
49
ln(0) =
can't be done
50
equation for force from momentum
F = dp/dt
51
kepler's law equation
T^2 = (4π^2/GM)*r^3
52
nCr equation
n!/r!(n-r)!
53
value of the 'deci' (d) prefix
10^-1
54
value of the micro (μ) prefix
10^-6
55
value of the nano (n) prefix
10^-9
56
value of the pico (p) prefix
10^-12
57
Critical angle equation
sin(C) = 1/n
58
Alpha particle consists of...
2 neutrons 2 protons
59
equation for arc length
rθ
60
area of a sector (when θ is in radians)
1/2 * r^2 * θ
61
pressure equations
```
p = F/A
p = hρg
```
62
Current in a wire equation
I = Anqv
63
Equation for voltage out from a potential divider
Vout = Vin * R2/(R1+R2)
64
potential divider ratio
V1/V2 = R1/R2
65
Equation linking capacitance, cross-sectional area and distance
C = εA/d
66
cos(90-x) =
sin(x)
67
Acceleration of an object oscillating under simple harmonic motion
```
a = -ω^2*x
a(max) = -ω^2*A
```
68
Velocity of an object oscillating under simple harmonic motion
```
v = +-ω* sqrt(A^2 - x^2)
v(max) = ωA
```
69
Displacement of an object oscillating under simple harmonic motion
```
x = Acos(ωt), If the time is measured from when the displacement was at a MAXIMUM
x = Asin(ωt), If the time is measured from when the displacement was at the MIDPOINT
```
70
Equations for angular frequency
```
ω = 2πf
ω = 2π/T
```
71
Equation for intensity
I = P/A
72
Equation for double-slit experiment
λ = ax/D
73
log(1/x) =
-log(x) - works for any base
74
log_a_(b) =
(log_c_(b))/(log_c_(a))
75
What is the equation for newton's experimental law?
v2-v1 = -e(u2-u1)
76
Implulse equations
I = F*t
| I =mv - mu
77
Sn for an algebraic sequence
Sn = n/2 * (2a + (n-1)d)
or
Sn = n/2 * (a+L)
78
Sn for a geometric sequence
Sn = a(1-r^n)/(r-1)
79
Sum to infinity for a geometric sequence
S∞ = a/(1-r)
80
formula for nth term of an arithmetic sequence?
un = a + (n-1)d
81
small angle approximation for:
tanθ
cosθ
sinθ
```
tanθ = θ
cosθ = 1 - θ^2/2
sinθ = θ
```
82
units for electric potential
Volts - V
83
What is kepler's first law?
The orbit of a planet is an ellipse with the sun at one of two foci
84
What is Kepler's second law?
A line segment joining a planet and sun sweeps out equal areas during equal intervals of time
85
What is Kepler's third law?
It's the one about t2 = r3 something not sure how it goes
86
Units of resistivity
The Ohm-metre!
87
Equation for charge/current/pd of a discharging capacitor
x = x0 * e^(-t/RC) for all
88
Equation for charge/current/PD of a charging capacitor
```
x = x0 * (1-e^(-t/RC) for V and Q
x = x0 * e^(-t/RC) for I (Current)!!!
```
89
What is the time taken for a capacitor to charge dully?
5RC
90
Up quark charge
+2/3 e
91
Down quark charge
-1/3 e
92
Strange quark charge
-1/3 e
93
Power, p.d, current
```
P = VI
P = I^2 R
P = V^2 / R
```
V = IR
94
Magnetic field equatuons
```
F = BILsin(theta)
F = BQv
```
