kinematics equations

V = at + Vo

X = 1/2 a t^2 + Vo t + Xo

∆X=1/2 (Vo+V)t

V^2 = 2a∆X + Vo^2

force of gravity

F = G (m1m2)/r^2

angular symbols

∅ = x (radians or degrees

w = v

α = accelaration

T = torch = force

I = moment of inertia = center of mass

L = angular momentum = momentum

linear to angular equations

v = rw

a = rα

a = v^2/r

KE = 1/2mv^2 = Iw^2

s=r∅

torch

T = F*r sin∅

T = rma = rm(r∝)=r^2 m∝=αI

angular momentum

(L)=(mv)r=Iw I=mr^2

degrees to radians

degrees(π) = radians(180)

Spring

F = k * 1/2x

W = k * 1/2x^2

compression 3 - 8 inches : W = k* 1/2 (8^2 - 3^2)

center of mass

((Σmx/Σm))/Σx=center mass ratio

Multiply by the length of the object to find the location of the center of mass

conservation of momentum

mv=mv

fluids

p = m/V

buoyant F = pVg (pV = m)

weight of liquid displaced P = Po + pgh

F1/A1 = F2/A2

Bernoulli: P1 + pgh + 1/2pv^2 = P2 + pgh + 1/2pv^2

∆V/∆t = π/8 (r^4/n) (p1-p2)/L

n = viscosity P = pressure surface tension Y = F/L

speed of a wave

v = λf

speed of wave on string=(Ft/u)^(-2)

Ft = tension force u = mass/length

Speed of sound faster when molecules are closer together Ultrasound = 20,000Hz + infrasound = 20Hz -

de/constructive interference

constructive = phase of the wave lines up and increases in amplitude destructive = waves are out of phase and cancel each other out

power sound

P = I(4πr^2)

Intensity by the surface area of the sphere with the radius equal to the distance

decibels

dB = (10dB)log I/Io

increasing intensity by factor of 10 doubles the loudness Io=1x10^(-12) W/m^2

doppler effect

change in frequency when source or observer are moving towards/away from each other

f' = f (v+/-vo)/(v+/-vs)

moving towards each other = increase frequency moving away from each other = decreased frequency

harmonic motion

F=-kx

motion of spring: x = A x sin(2πt/T) = A x sin(2πft) = A x sin(wt)

w= angular frequency = (k/m)^(-2) energy:

E = 1/2mv^2 = 1/2kA^2 (A = amplitude)

energy equations

Total E = KE + PE

KE = 1/2mv^2 = 1/2kA^2 (harmonic A = amplitude)

KE = Iw^2 (angular motion)

PE = mgh W = k * 1/2x^2 (spring)

induction

inducing a charge in a object without touching it

electric field & voltage equations

F = 1/(4πεo ) x (q1 q2)/r^2

E = F/q = (1/(4πε0 )) x q/r^2

V = (1/(4πε0 ))*q/r Va-Vb = Wab/qo

electric field vs voltage

Vb-Va = Wab/qo E = delta(V)/delta(s)

electric field = amount of force a particle would experience per unit charge voltage = when force is not constant, amount of work to move 1 unit positive charge between A and B.

flux

ΦE=EA charge per m^2 (charge through an area)

q = ε0EA A = (4πr^2) sphere

current

I = Q/t = ∆q/∆t = nA(eV)

n= density charge

Current density j = i/A = nA(ev)

circuits equations

V=IR P = VI = V^2/R

P = I^2 R(heat loss)

R = p(L/A) p = resistivity AC

Power P = (Vmax Imax)/(2)^.5 C = Q/V = (ε0 A)/d

Resistance

R = p(L/A)

p = resistivity

V=IR P = VI = V^2/R P = I^2 R(heat loss)

capacitor

ability to store charge. build up of charge on a plate causing the opposite charge to accumulate on the other plate. measured in farad.

C = Q/V = (ε0 A)/d increase c with shorter distance between plates and more area. ε0 = 8.9x10^-12 F/m

ε0

ε0 = 8.9x10^-12 F/m

AC/DC current

direct current/alternating current average of sin wave = root mean square of maximum

Pavg = Vmax/2^.5 x Imax/2^.5 diode

converts AC to DC (only allows current to flow in 1 directions) half/full wave rectifier - diodes.

generator

rotating coil in a magnetic field induces a current to oppose the change in magnetic field through the wire as it rotates. make it stronger by: increase number of turns in coil rotate coils faster use stronger permanent magnets add soft Iron core in the coil to increase the magnetic field

parallel and series

parallel: C = C1 +C2 +C3... R = 1/R1 + 1/R2 + 1/R3..... series: C = 1/C1 + 1/C2 + 1/C3..... R = R1 + R2 + R3.....

magnetic force

F = qvB = 1/2mv^2 (centripetal F when charge moves in circle)

RHR: qv (hand) B(fingers) F (thumb)

mass spectrometer equation

breaks molecules into ions and shoots through magnetic field and measure the amount of bend in trajectory.

m = (qB^2r^2)/(2V)

magnetic field and current

RHR: current (thumb) magnetic field (fingers)

B = (Uo*I)/(2πr)

solenoids

loop of wire conducting a current that creates a strong magnetic field in the center of the loop. The strength depends on the number of loops (N)

first faraday's law

magnet through a loop: current only occurs when the magnet is moving current is directly proportional to the strength of the magnet and the speed direction of the current depends on the N-S orientation

second faraday's law

a loop with a battery next to a sensing loop with a galvanometer current seen only during opening or closing of switch induced current is proportional to the number of loops in either and the rate of change in current in the driving coil

lenz's law

current induced in a loop creates a magnetic field that opposes the change in magnetic field through the loop

light equations

n1 sinΦ1 = n2 sinΦ2

n=c/Vmedium

n= index of refraction

dispersion

prism effect from index of refraction (n) being different for different wavelengths n1 sinΦ1 = n2 sinΦ2

polarization

light with electric vectors going in same direction orientation of light wave (magnetic and electric field are at right angles) ^ electric field ^ o direction >magnetic field o >

reflect/refract polarization

light polarizes when angle of reflection and refraction are 90 degrees n(air)

sin⍬=n(water)

cos⍬ and tan⍬ = n(water)/n(air) if water and air ⍬ = 53

diffraction

what happens when light hits an object single and double slit: light must be polarized and have a single frequency

double slit

Y(m)/L=mλ/d

sin⍬=mλ/d

d = distance between slits

m = 1 constructive m = .5 destructive

single slit

Y(m)/L = mλ/a

sin⍬ = mλ/a

a = width of opening

m = .5 constructive m = 1 destructive

lense and mirror equations

1/o+1/i=1/f f=r/2 M=h(o)/h(i) =-i/o

mirrors

lateral inversion, virtual image front = + back = -

concave mirror )

inverted, closer o is to f the farther away i is, i is always positive

convex mirror (

up-right, closer o is to mirror the closer i is to mirror, i is always negative

converging lenses ()

f = + (between f-2f =>magnified other side)

(between f-m => same side)

diverging lenses )(

f = - image on same side

electron radii

r = (hεo)/(πme^2 ) n^2

r =ao n^2 ao = ??

quantum energy

En = 13.6ev/n^2

(Ei-Ef)/h =13.6ev/h * (1/(nf^2 ) - 1/(ni^2 ))

energy at radii n

En = 13.6ev/n^2

energy emitted by change in radii

f = (Ei-Ef)/h =13.6ev/h * (1/(nf^2 ) - 1/(ni^2 ))

plank's constant

h = 6.636 10^-34 Js h = 9.14 10^-15 eVs

fission

heavier nuclei splitting and releasing energy in the form of heat

fusion

two nuclei fuse together, specific elements release energy

radioactive decay

R = (delta)N/t = λN

λ = proportionality constant (+ = growth, - = decay)

N=No e^ λt (N = daughter, No = parent)

T = -ln2/ λ

R = Ro r^n

half life

T = -ln2/ λ

decay particles

alpha (α 4 ^2) beta (β 0 ^(+/- 1)) gamma (γ 0^0)

amount of decay material

N=No e^ λt (N = daughter, No = parent)

radiation per second

R = Ro r^n

n = number of counts

r = distance from source

Ro = initial radiation per second