PAT Equations Flashcards
Volume of a sphere
4/3 πr^3
Plank’s Constant
6.63*10^-34
Free space permittivity
8.85*10^-12
electron rest mass
9.11*10^-31
sphere surface area
4πr^2
Equation linking momentum, force, time
F = p/t Force = momentum/time
Equation linking velocity, power, force
P = Fv
Equations for energy stored by a spring (E)
E = 1/2 K x^2
or E = 1/2Fx
Equation for stress
σ = F/A
Equation for strain
ε = x/L
Equation for young’s modulus
E = σ/ε
Electricity equations for work done?
W = VQ (Work Done = p.d. * charge) W = VIt (because Q = It)
Equation linking current, time, electric charge
Q = It Charge = Current * time
The resistivity-resistance equation
R = pL/A
Internal resistance equation
E = IR + Ir (V + v)
WAVE SPEEEEED
v = f λ
Total internal refraction equation
sin(C)=n2/n1 (n2
Snell’s law equation
n1sinθ1=n2sinθ2
Equation for the refractive index
n = c/v
refractive index = speed of light in vacuum/speed of light in material
Plank’s wavelength equation
λ = h/p
Quantum energy equations
E = hf E = hc/λ
Work function equation
hf = φ + KEmax
Centripetal force equation
F = mv^2/r F = mrω^2 F = mvω
Centripetal acceleration equations
a = v^2/r a = rω^2 a = vω
Velocity of a centripetal particle thing
v = rω
angular velocity equation
ω = 2Pi/T ω = 2fPi
Gravitational potential (Vg)
Vg = -GM/r
Units for gravitational potential
J per Kg
Electric field strength
E = F/Q
gravitational field strength
g = -GM/r^2
Force due to gravity
F = -GMm/r^2
Energy due to gravity
E = -GMm/r (from Vg which is J per Kg (hence * small m))
Equation relating voltage, charge and capacitance
C = Q/V Capacitance = charge/p.d.
Capacitance from a radius
C = 4πε0r
Equation for electric potential (in volts V)
V = Q/4πε0r
Equation for energy due to the electric field between charges
E = Qq/4πε0r
Equations for electric filed strength
E = V/d E = Q/4πε0r^2
Equation for force acting between two point charges
F = Qq/4πε0r^2
integral of 1/x
ln(mod(x))+c
differential of ln(kx)
1/x (no matter what k is the result is 1/x)
differential of a^kx
a^kx * kln(a)
differential of cosec(kx)
-k*cosec(kx)cot(k)
differential of sec(kx)
k*sec(kx)tan(kx)
differential of cot(kx)
-k*cosec^2(kx)
integral of e^x
e^x + c
cos(2A) =
cos^2(A) - sin^2(A)
sin(2A) =
2sin(A)cos(A)
ln(1) =
0
ln(0) =
can’t be done
equation for force from momentum
F = dp/dt
kepler’s law equation
T^2 = (4π^2/GM)*r^3
nCr equation
n!/r!(n-r)!
value of the ‘deci’ (d) prefix
10^-1
value of the micro (μ) prefix
10^-6
value of the nano (n) prefix
10^-9
value of the pico (p) prefix
10^-12
Critical angle equation
sin(C) = 1/n
Alpha particle consists of…
2 neutrons 2 protons
equation for arc length
rθ
area of a sector (when θ is in radians)
1/2 * r^2 * θ
pressure equations
p = F/A p = hρg
Current in a wire equation
I = Anqv
Equation for voltage out from a potential divider
Vout = Vin * R2/(R1+R2)
potential divider ratio
V1/V2 = R1/R2
Equation linking capacitance, cross-sectional area and distance
C = εA/d
cos(90-x) =
sin(x)
Acceleration of an object oscillating under simple harmonic motion
a = -ω^2*x a(max) = -ω^2*A
Velocity of an object oscillating under simple harmonic motion
v = +-ω* sqrt(A^2 - x^2) v(max) = ωA
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
Equations for angular frequency
ω = 2πf ω = 2π/T
Equation for intensity
I = P/A
Equation for double-slit experiment
λ = ax/D
log(1/x) =
-log(x) - works for any base
log_a_(b) =
(log_c_(b))/(log_c_(a))
What is the equation for newton’s experimental law?
v2-v1 = -e(u2-u1)
Implulse equations
I = F*t
I =mv - mu
Sn for an algebraic sequence
Sn = n/2 * (2a + (n-1)d)
or
Sn = n/2 * (a+L)
Sn for a geometric sequence
Sn = a(1-r^n)/(r-1)
Sum to infinity for a geometric sequence
S∞ = a/(1-r)
formula for nth term of an arithmetic sequence?
un = a + (n-1)d
small angle approximation for:
tanθ
cosθ
sinθ
tanθ = θ cosθ = 1 - θ^2/2 sinθ = θ
units for electric potential
Volts - V
What is kepler’s first law?
The orbit of a planet is an ellipse with the sun at one of two foci
What is Kepler’s second law?
A line segment joining a planet and sun sweeps out equal areas during equal intervals of time
What is Kepler’s third law?
It’s the one about t2 = r3 something not sure how it goes
Units of resistivity
The Ohm-metre!
Equation for charge/current/pd of a discharging capacitor
x = x0 * e^(-t/RC) for all
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)!!!
What is the time taken for a capacitor to charge dully?
5RC
Up quark charge
+2/3 e
Down quark charge
-1/3 e
Strange quark charge
-1/3 e
Power, p.d, current
P = VI P = I^2 R P = V^2 / R
V = IR
Magnetic field equatuons
F = BILsin(theta) F = BQv
