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Orders of magnitude
 powers of ten
 mult add exponents
 div subtract exponents
 powers multiply exponents

S and I Units
 MKS
 length meters
 mass kilograms
 time seconds

Sig Figs
 w/ decimal atlantic
 w/o decimal pacific
 adding/subtracting smallest decimal place
 multiply/dividing smalles # of sig figs

graphs (x,y)
 x  independent variable
 y  dependent variable

graph equations
 Δy/Δx
 slope=mx+b
 yintercept b=y_{2}mx_{2}


scalar
 a # can be  or +
 ex) time, age, temp

motion diagrams
 dots closer = slower
 dots farther apart = faster

average velocity
 V_{avg}= Δx / Δt
 displacement over time

motion with constant accelerations (equations)
 d=V_{i}t+1/2at^{2}
 V_{f}=V_{i}+at

conservation of energy
V_{f}^{2}=V_{i}^{2}+2aΔx

free fall equations
 d=V_{i}t+1/2at^{2}
 V_{f}=V_{i}+at
 V_{f}^{2}=V_{i}^{2}+2aΔy

dynamics
forces that cause motion

Newton's 1st Law
 "Law of inertia"
 an object at rest stays at rest
 an object in motion stays in motion

net force
act sto change an objects velocity

Newton's 2nd Law
F_{net}=ma [N]

gravitational force
 F_{g}
 attracts
 between masses

normal force
 F_{N}
 perpendicular force between surface and objects resting or moving along it

frictional force
 F_{f}
 parallel force btwn two objects that oppose relative motions

kinetic force
 if object on surface moving
 f_{k}=µ_{k}F_{N}
 µk=coefficient of kinetic friction

static force
 if object on surface @ rest
 f_{s}=µ_{s}F_{N}

tension force
 F_{t}
 pulls by massless "string"

electromagnetic
 F_{e}
 attractive or repulsive
 btwn charges

Newton's Third Law
 "law of action and reaction"
 a=F_{net}/m

mechanical energy
 kinetic (motion)
 potential (spring)
 energy is neither created nor destroyed
 E=KE+PE
 KE_{i} + PE_{i} = KE_{f }+ PE_{f}

Kinetic energy
 KE = 1/2mv^{2}
 KE is scalar
 measured in joules [J]

Work
 ΔKE=KE_{final}  KE_{initial} [J]
 W_{g}=ΔPE_{g}
 work done against gravity = mgΔh


gravitational force
PE_{g}=mgΔh

mechanical energy in terms of gravity
 mgh_{i} + 1/2mv_{i}^{2} = mgh_{f} + 1/2mv_{f}^{2}>
 V_{f}^{2} = V_{i}^{2}  2g(h_{f} h_{i})
 use in roller coaster examples

Power
 P = work / time [J/s]
 P_{avg} = F * V_{avg}

conservation of linear momentum
 P = mv [kg * m/s]
 P_{f} = P_{i}
 collision of two objects:
 P_{1i} + P_{2i} = P_{1f} + P_{2f}
 P_{T} = m_{1}v_{1} = m_{2}v_{2}

Impulse
 change in linear momentum
 =ΔP = Δ(mv)
 F_{net} = ma = m(Δv/t)
 ΔI = F_{net} * Δt

elastic collision
 momentum and KE is conserved
 P_{f} = P_{i}
 KE_{f} = KE_{i}
 for 2 body system:
 1/2mv_{i1}^{2} + 1/2mv_{i2}^{2} = 1/2m_{i}v_{f1}^{2} + 1/2m_{2}v_{f2}^{2}

inelastic collisions
 see distorting and heating
 completely inelastic = stick together:
 V_{1f} = V_{2f} = V_{sysf}
 V_{f} = m_{1}v_{1i} + m_{2}v_{2i} / m_{1} + m_{2}

newton's law of universal gravitation
 F = (Gm_{1}m_{2}) / r^{2}
 G = 6.67 X10^{11}
 near the earth F = (GM_{E}) / r_{E}^{2}

Field lines
 field is strong when lines are closer together
 trajectories of a test charge
 field describes the property of space around one object

Bohr model of an atom
 nucleus = protons and neutrons
 electrons orbit nucleus
 fundamental unit of charge  e = 1.6 X10^{19}
 neutron = 0

Coulumb's law
 lFel = (k lq_{1}l lq_{2}l) / r^{2}
 k = 8.99 X10^{9} [N * m^{2}/c^{2}]

charge by induction (electroscope)
neg. rod close to top = pos. atoms and the negatively charged particles repel

charging by contact (pith ball)
neg. rod touches ball, share electrons, bring it back and they repel

electric field
 E = F / q [N/C]
 positive  go out
 negative  go in
 E = (k lql) / r^{2}

Electric potential
 field lines are perpendicular to PE lines
 PE_{e} = kq_{1}q_{2} / r
 V = kq / 2 [volts]

Charges in configuration
 parallel plate capacitor: uniform electric field inside
 F = = ΔPE/Δx = qΔV/Δx = qE >E =ΔV/Δx

electric currrent
I = Δq / Δt

direction of current in a circuit
the direction in which the positive charges flow

work done in a battery
W = ΔPE = qΔV = ΔqE > P = IV

Resistance
 R = ρ (L/A)
 ρ  resistivity of material
 L  length of wire
 A  cross sectional area = ∏r^{2}


power in an electric current
 P = W/Δt =ΔqE/Δt = IE
 P = IV = I^{2}R = V^{2}/R

Series circuit
 I = I_{1} = I_{2} = I_{3}
 V = V_{1} + V_{2} + V_{3}
 R_{eq} = R_{1 }+ R_{2} + R_{3}

parallel circuit
 I = I_{1} + I_{2} + I_{3}
 V = V_{1} = V_{2} = V_{3}
 1/R_{eq} = 1/R_{1} + 1/R_{2} + 1/R_{3}

power in a series circuit
 P_{1} = I_{1}V_{1}
 P_{2} = I_{2}V_{2}
 P_{T} = P_{1} + P_{2}
 P_{T} = I_{T}V_{T}

power in a parallel circuit
 P_{T} = I_{T}V_{T}
 P_{1} = I_{1}V_{1}
 P_{2} = I_{2}V_{2}
 P_{T} = P_{1} + P_{2}
 power = E/t

dipole
 two charges
 flow from a postive charge to a negative charge


magnitude of a magnet
 F = qVB
 q = charge
 V = velocity
 B = magnetic field
 right hand rule:
 palm = B
 fingers = V
 thumb = force
 ( x= in, ∙ = out )

current in wire
 force on a current carrying wire F = ILB sinƟ
 magnetic field created B=µ_{i}I/2∏d
 right hanf rule:
 thumb direction of current
 fingers wrap in direction of field (B)

Solenoid
 thumb direction of field
 fingers current
 B = µ_{i}IN/L
 mag B = Nµ_{i}I/2R

induction
changing current and B_{field} in the primary induces a changing B_{field} and current in the secondary

power in the circuits
 power is the same in both circuits
 V_{p}/V_{s} = I_{s}/I_{p}
 V_{p}/V_{s} = N_{p}/N_{s}
 I_{s}/I_{p} = N_{p}/N_{s}

transverse wave
oscillates perpendicular to direction intensity of the light ray/wave

electromagnetic waves
 for light c =λf
 speed of any wave  V = λf

doppler effect
 source moving towards observer:
 f_{obs} > f_{source} , λ_{obs} < λ_{source} = blue shift
 source moving away from observer:
 f_{obs} < f_{source} , λ_{obs} > λ_{source} = red shift

law of reflection
angle of reflection is = to the angle of incidence

reflectio in plane mirror
 image is upright
 image is same size
 image is virtual
 h_{i} = mh_{o}
 m = d_{i}/d_{o}

reflection in concave
 d_{o}>c>f
 form a real image
 inverted
 smaller
 c>d_{o}>f
 real image
 inverted
 larger
 c>f>d_{o}
 virtual
 upright
 larger

reflection in convex
 virtual image
 upright
 smaller

refraction of light
 V = c/n
 less dense to more dense>closer to normal

snell's law
 n_{1}sinƟ_{1} = n_{2}sinƟ_{2}

critical angle
 n_{1}>n_{2}, if Ɵ "too big" >total internal reflection
 critical angle = sin^{1}(n_{2}/n_{1} * sin 90)

converging lenses
 either a real or a virtual image
 double convex or plano convex

diverging lenses
 only virtual images
 double concave
 plano concave

refraction in convex lenses
 d_{o }> f
 real
 inverted image
 f>d_{o}
 virtual
 upright image

refraction in concave lenses
 d_{o} > f
 upright
 virtual image
 f>d_{o}
 upright
 virtual image

thin lens equations
 1/f = 1/d_{o} + 1/d_{i}
 m = d_{i}/d_{o}

diopter
 = 1/f
 two lenses:
 d_{effective} = d_{1} + d_{2}
 f_{eff} = 1/d_{eff}

