PAT Equations Flashcards
Arithmetic series sum
Sn=
Sn = (n(2a+(n-1)d)/2a
Geometric series sum
Sn=
Sn = a(1-r^n)/(1-r)
Sum to infinity S=
What conditions is this true for?
S = a/(1-r)
Geometric series that converges (-1<r<1)
What is the formula for an even function?
Simplifying in integration top tips?
Even function:
f(x)=f(-x)
Simplifying, multiply from 0 to a by two if the interval is equal either side of the y axis
What is the formula for an odd function?
Simplifying in integration top tips?
Odd function:
f(-x)=-f(x)
Simplifying, it will be zero if the interval is equal either side of the y axis
Moment=?
Force x perpendicular distance from line of action of force to point of rotation/axis
Momentum=
Units?
p=mv
kgm/s
(related to momentum)
F=?
F=change in momentum/time
What is an impulse?
Equation?
Units?
Change in momentum
F x (change in time)
Ns
W=?
What about at an angle of x?
W=Fs
W=Fscosx
(Springs)
F=?
F=kx
For springs in parallel:
What happens to the spring constant?
kt=k1+k2+…
(It adds up, gets bigger)
For springs in series:
What happens to the spring constant?
1/kt = 1/k1 + 1/k2 +…
(It gets smaller)
For springs in parallel:
What happens to extension?
It gets smaller
For springs in series:
What happens to extension?
It gets bigger
(For springs)
Ep = ?
Ep= 1/2 Fx and F=kx
So…
Ep= 1/2 kx^2
frequency= ?
1/T (time period)
Constructive interference:
nλ
Destructive interference:
(n+1/2)λ
Double slit:
w= (λD)/s
Single slit:
dsinx = nλ
Snells law:
n1sinx1 = n2sinx2
n (refractive index) =?
n =c(speed of light in vacuum) /cs (speed of light in substance)
Critical angle?
sin xc = n2/n1 where n2>n1
Angular frequency =
w=2 pi f
Circular motion:
a = ?
a=v^2/r and a=w^2r
Circular motion:
F= ?
F=(mv^2)/r and F=mw^2r
Circular motion:
v=?
v=wr
SHM:
x=?
x=Acos(wt)
SHM:
a=?
a=-w^2x
SHM:
vmax = ?
amax= ?
vmax= wA
amax= w^2 A
SHM:
Pendulum T=?
T= 2 pi sqrt(L/g)
SHM:
Mass spring system=?
T= 2 pi sqrt(m/k)
Energy of accelerated electron beam = ?
Velocity of accelerated electron = ?
Ek = 2ev
v= sqrt(2ev/m)
Capacitance:
C=?
C=Q/V
or
C=(ErE0A)/d
Capacitors in parallel:
CT=C1+C2+…
Capacitors in series:
1/CT = 1/C1 + 1/C2 + …
Capacitance:
W=?
W=1/2 QV
W= 1/2 (Q^2/C)
W=1/2 CV^2
For a charging capacitor:
I=?
V=?
I=I0 e^(-t/RC)
V= V0 (1-e^(-t/RC))
(Q like V)
For a discharging capacitor:
I=?
V=?
R=?
All the same:
X=X0 e^(-t/RC)
Electricity:
V=?
V=IR
Electricity:
EMF =
EMF = E/Q
Electricity:
W=?
W= QV
Electricity:
Power equations
P=IV
P=E/t
P=I^2R
P=V^2/R
E=Itv
Electricity:
I in = ?
I in = I out
Electricity:
EMF =?
EMF = total voltage
EMF = I (R+r)
Electricity:
Resistors in parallel
1/RT = 1/R1 + 1/R2 + ..
Electricity;
Resistors in series
RT = R1 + R2 + …
Electricity:
Resistivity =
p = RA/L
Gravitational fields:
F=?
F=GMm/r^2
Gravitational field strength g=?
g= F/m
g= -GM/r^2
Gravitational potential =?
Vg = -GM/r
Gravitational potential energy =?
E = -GMm/r
Kepler’s third law
T proportional to r^3 where T is an orbital period
Electric fields:
E =?
E = F/Q
E=V/d
Coulomb’s law
F= (1/4piE0)(Qq/r^2)
Electric Potential
E=Q/(4piE0r^2)
Electric potential energy
E= Qq/(4piE0r)
Transformers equation
Is/Ip = Vp/Vs = Np/Ns
