PAT Equations

Question 1

Arithmetic series sum
Sn=

Answer 1

Sn = (n(2a+(n-1)d)/2a

Question 2

Geometric series sum
Sn=

Answer 2

Sn = a(1-r^n)/(1-r)

Question 3

Sum to infinity S=
What conditions is this true for?

Answer 3

S = a/(1-r)
Geometric series that converges (-1<r<1)

Question 4

What is the formula for an even function?
Simplifying in integration top tips?

Answer 4

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

Question 5

What is the formula for an odd function?
Simplifying in integration top tips?

Answer 5

Odd function:
f(-x)=-f(x)
Simplifying, it will be zero if the interval is equal either side of the y axis

Question 6

Moment=?

Answer 6

Force x perpendicular distance from line of action of force to point of rotation/axis

Question 7

Momentum=
Units?

Answer 7

p=mv
kgm/s

Question 8

(related to momentum)
F=?

Answer 8

F=change in momentum/time

Question 9

What is an impulse?
Equation?
Units?

Answer 9

Change in momentum
F x (change in time)
Ns

Question 10

W=?
What about at an angle of x?

Answer 10

W=Fs
W=Fscosx

Question 11

(Springs)
F=?

Answer 11

F=kx

Question 12

For springs in parallel:
What happens to the spring constant?

Answer 12

kt=k1+k2+…
(It adds up, gets bigger)

Question 13

For springs in series:
What happens to the spring constant?

Answer 13

1/kt = 1/k1 + 1/k2 +…
(It gets smaller)

Question 14

For springs in parallel:
What happens to extension?

Answer 14

It gets smaller

Question 15

For springs in series:
What happens to extension?

Answer 15

It gets bigger

Question 16

(For springs)
Ep = ?

Answer 16

Ep= 1/2 Fx and F=kx
So…
Ep= 1/2 kx^2

Question 17

frequency= ?

Answer 17

1/T (time period)

Question 18

Constructive interference:

Answer 18

nλ

Question 19

Destructive interference:

Answer 19

(n+1/2)λ

Question 20

Double slit:

Answer 20

w= (λD)/s

Question 21

Single slit:

Answer 21

dsinx = nλ

Question 22

Snells law:

Answer 22

n1sinx1 = n2sinx2

Question 23

n (refractive index) =?

Answer 23

n =c(speed of light in vacuum) /cs (speed of light in substance)

Question 24

Critical angle?

Answer 24

sin xc = n2/n1 where n2>n1

Question 25

Angular frequency =

Answer 25

w=2 pi f

Question 26

Circular motion: a = ?

Answer 26

a=v^2/r and a=w^2r

Question 27

Circular motion: F= ?

Answer 27

F=(mv^2)/r and F=mw^2r

Question 28

Circular motion: v=?

Answer 28

v=wr

Question 29

SHM: x=?

Answer 29

x=Acos(wt)

Question 30

SHM: a=?

Answer 30

a=-w^2x

Question 31

SHM: vmax = ? amax= ?

Answer 31

vmax= wA amax= w^2 A

Question 32

SHM: Pendulum T=?

Answer 32

T= 2 pi sqrt(L/g)

Question 33

SHM: Mass spring system=?

Answer 33

T= 2 pi sqrt(m/k)

Question 34

Energy of accelerated electron beam = ? Velocity of accelerated electron = ?

Answer 34

Ek = 2ev v= sqrt(2ev/m)

Question 35

Capacitance: C=?

Answer 35

C=Q/V or C=(ErE0A)/d

Question 36

Capacitors in parallel:

Answer 36

CT=C1+C2+...

Question 37

Capacitors in series:

Answer 37

1/CT = 1/C1 + 1/C2 + ...

Question 38

Capacitance: W=?

Answer 38

W=1/2 QV W= 1/2 (Q^2/C) W=1/2 CV^2

Question 39

For a charging capacitor: I=? V=?

Answer 39

I=I0 e^(-t/RC) V= V0 (1-e^(-t/RC)) (Q like V)

Question 40

For a discharging capacitor: I=? V=? R=?

Answer 40

All the same: X=X0 e^(-t/RC)

Question 41

Electricity: V=?

Answer 41

V=IR

Question 42

Electricity: EMF =

Answer 42

EMF = E/Q

Question 43

Electricity: W=?

Answer 43

W= QV

Question 44

Electricity: Power equations

Answer 44

P=IV P=E/t P=I^2R P=V^2/R E=Itv

Question 45

Electricity: I in = ?

Answer 45

I in = I out

Question 46

Electricity: EMF =?

Answer 46

EMF = total voltage EMF = I (R+r)

Question 47

Electricity: Resistors in parallel

Answer 47

1/RT = 1/R1 + 1/R2 + ..

Question 48

Electricity; Resistors in series

Answer 48

RT = R1 + R2 + ...

Question 49

Electricity: Resistivity =

Answer 49

p = RA/L

Question 50

Gravitational fields: F=?

Answer 50

F=GMm/r^2

Question 51

Gravitational field strength g=?

Answer 51

g= F/m g= -GM/r^2

Question 52

Gravitational potential =?

Answer 52

Vg = -GM/r

Question 53

Gravitational potential energy =?

Answer 53

E = -GMm/r

Question 54

Kepler's third law

Answer 54

T proportional to r^3 where T is an orbital period

Question 55

Electric fields: E =?

Answer 55

E = F/Q E=V/d

Question 56

Coulomb's law

Answer 56

F= (1/4piE0)(Qq/r^2)

Question 57

Electric Potential

Answer 57

E=Q/(4piE0r^2)

Question 58

Electric potential energy

Answer 58

E= Qq/(4piE0r)

Question 59

Transformers equation

Answer 59

Is/Ip = Vp/Vs = Np/Ns