PAT Flashcards
shuit??? No
Period vs Freq
Period is the number of seconds per wave
Frequency is the number of waves per second
Wave velocity, energy, angular velocity
λf = v
hv/λ = E
0 Kelvin in C
To convert from C to Kelvin, add 273
To convert from Kelvin to C, subtract 273
Inverse Square Law
Intensity (apparent brightness) = L / 4πr²
Lenz’s Law Ratio
Vs/Vp = Ns/Np
The ratio of the voltage over the secondary coil and the voltage over the primary coil is equivalent to the ratio of the number of loops in the secondary and primary coils.
sin cos tan approximations
x
1 - (x^2/2)
x
Power
Fv = VI = V²/R = I²R = P
Energy
mgh = 1/2mv^2 = 1/2 k(deltax)^2
specific heat capacity
J = mCdeltaT
how much energy is needed to change 1kg of some material’s temperature by 1K
capacitance
Q = cV
capacitors store energy, so current is lost when a capacitor is connected.
current is lost in
Rc = t
c = kA
Kepler’s Laws
1st - orbits are ellipses
2nd - orbits sweep equal area at all times (approximate using squares)
3rd - T^2 = kr^3
Simple harmonic motion
T = 2pi x sqrt(m/k)
w = vA
xuvat
v = u + at
x = ut + at²/2
x = vt - at²/2
v² = u² + 2ax
x = (v-u)/(2) x t
coeff of restitution
e = (v1-v2)/(u2-u1)
waves between media
flipped
v1/v2 = n2/n1
notflipped
n1sin(thetac) = n2sin(thetar)
mechanical advantage
count how many pulleys there are
ratio between the tensions (less force needed to produce more)
coulomb’s and newton’s law
F = ke (abs(Q1Q2))/(r²)
F = G (M1M2)/(r²)
point charge
point charge produces a force
F = qE
like charges have positive displacement and opposite
water displacement
if an object is at rest on the surface: the same WEIGHT of water is displaced
if an object is submerged under the surface: the same VOLUME of water is displaced
Derivation techniques
Chain Rule
y = f(g(x)) = f(u)
dy/dx = dy/du x du/dx
Product Rule
y = f(x)g(x) = uv
dy/dx = u(dv/dx) + v(du/dx)
Quotient Rule
y = f(x)/g(x) = u/v
dy/dx = (v(du/dx) - u(dv/dx))/v^2
Integration techniques
Substitution
y = f(g(x)) x d(g(x))/dx = f(u) x du/dx
∫ydx = ∫f(u)du
By parts
y = f(x)g(x) = uv
u∫vdx - ∫(du/dx)x∫vdx dx
uxintegral - allintegralderivativexintegral
Combinations & Permutations
n!/(n-r)! = permutations
order doesn’t matter
n! = permutations with repeats
n!/r!(n-r)! = combinations
order matters
areas/volumes of ball, cone/pyramid, triangle, equilateral
4/3 pir^3
4pir^2
1/3 x pir^2h
pir^2 + pirl
1/2 absinx
xh/2
sqrt(3)/4 x^2
trigonometric functions for all values
can be defined by rpi + n2pi (don’t forget there are two y for each x)
Resistance/Temperature graphs
Wire
Linear with some intercept
Resistors/filament lamps
Concave quadratic with some intercept [starts horizontal]
Thermistors/LDRs
Concave quadratic approaching zero with some [high] intercept
Current/Voltage graphs
Wire
Linear with no intercept
Resistors/filament lamps
Concave quadratic with no intercept [ends horizontal]
Diodes
Current only passes after threshold voltage is reached where shoots up with high gradient
General formula for wavelength
y(x,t) = Acos((2pi/lambda)x+wt)
you can use partial derivatives to get max velocity and acceleration
max velocity & acceleration in circular motion
v = wA
a = w^2 * A
conditional probability
P(A|B) = P(AuB)/P(B)
for P(B), forget about any other conditions, just the probability of that even occuring and the P(AuB) is the probability of both events occuring at the same time.
Graph transformations weird
for f(-x+a), the graph moves in the positive direction and otherwise
Elastic motion
Ek is fully conserved when changing direction of motion, e=1
Function ranges
always multiply by f(x)^2
if not remember that x-a can be -ive or +ive
if applicable, find limits, asymptotes, turning points
Summation
Can be manipulated the same as integrals, lay out the start and end points clearly and !!substitute!!
Circle arc and sector
theta r
(theta r^2)/2
Total energy
ALWAYS equals U + Ek (unless dissapative forces not ignored)
Coulomb’s Constant
1/(4pi permittivityconstant)
-ive and +ive electrostatic potential energy
If electrostatic energy is negative, it means the system is bound and needs energy to be “broken”
If positive, the system repels.
Projectile Trajectories
On level ground, the displacement of a projectile is maximised by a 45 degree angle.
Downhill, the displacement is maximised by <45 degree angle.
Uphill, the displacement is maximised by >45 degree angle.
Equation governance
When substituting values into an equation for graphing, check which values will make the biggest difference to the result.
For products and sums, the greater number will always govern the result.
For quotients and differences, it depends on the position of the bigger number but you can figure it out.
g
Unless the question specifies it’s on Earth, don’t use g=10ms^-2 DUMMY
Half-life questions
ALWAYS start out with equating the number of atoms after the half life time passes in both forms (N(0)/2 and the expression)
Mechanical Advantage
For pulleys, the “input” force < weight of the mass because of the multiple segments of the rope.
Same goes for distance, the “input” distance < distance one segment travels because the input distance is the sum of the segments.
Gravitational Potential Energy
Use mgh when near the surface of a planet, use -GMm/r when far away.
It’s negative for the same reason as electrostatic potential, energy needs to be put in to break the system.
Phase change at reflection
180 degrees
Constructive and destructive conditions
Constructive: d = mλ
Destructive d = (2m-1)/2 * λ
Q1 ≠ Q2
Q1 = nQ2
Circuits
POWER is constant over both sides of a transformer
RESISTANCE is constant for a component (unless temp isn’t)
CURRENT is constant in series and splits in parallel in ratio equal to resistance
PD is constant in parallel and splits over components in ratio equal to resistance
