• multiply number, add exponents
• divide numbers, subtract exponents
• can only add/subtract numbers with same exponent

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

sinθ = 0 at 0° and 180°

cosθ = 0 at 90°

sin30 = 1/2

cos60 = 1/2

sinθ = 60°

cosθ = 30°

1. resolve vectors to be summed in x and y components
2. add x components
3. add y components
4. find magnitude using v = √v_x² + v_y²

v =  v₀ + at

v² = v₀² + 2aΔx

has vertical and horizontal components that are independent

attractive force felt by all matter

F = Gm₁m₂

r² 

G = 6.67 x 10^-11

force that causes rotation

Τ  = rFsinθ

max at 90°

min at 0°

counterclockwise motion creates positive torque

clockwise motion creates negative torque

force overcome to set an object in motion

0 ≤f_s≤ μ_sN

friction force during movement

f_k = μ_kN

radial component of acceleration

a = v²/r

gives rise to centripetal acceleration

F = mv²/r

Work = force * distance

W = fdcosθ

energy of position

mgh

E_i = Ef

ΔE = 0

product of force and the time it was applied

J = Ft = Δp

KE_before > KEafter

(lost to heat)

T_c = T_k - 273

T_f = 9/5T_c + 32

increasing temperature causes an increase in length

ΔL = αLΔT

 α = coefficient of linear expansion

q = mcΔT

q>0 heat is gained

q = mL

L = heat of fusion, heat of vaporization

P = F/A

pressure is created by gas molecules colliding with walls of container

positive work

increases volume

negative work

decreases volume

Q increases or W decreases

work is done on the system

Q decreases or W increases

work done by the system

Q = 0

ΔU = -W

W = 0

Δ = Q

ΔU = 0

Q = W

entropy

mass/volume

independent of size

ratio of density of object to water

change in pressure is transmitted to every portion of the fluid

F₁d₁ = F₂d₂

magnitude of electrostatic force

F = kq₁q₂/r²

vector defined by a group of electric charges

E = F/q₀

F = qE

positive - force is in direction of the field

 negative - force is opposite direction of the field

work needed to move a positive test charge from infinity to that point

V = W/q₀

Work depends on potential difference and not the path taken

Palm faces in direction of force

Fingers point in direction of field

Thumb points toward velocity

What happens when a charged particle moves perpendicular to a magnetic field?

Has constant circular motion where centripetal force = magnetic force

F = qvB = mv²/r

right thumb points in direction of current

fingers curl around wire to mimic circular direction of field

B = μ₀i

       2∏r

voltage drop across a resistor is proportional to current it carries

V = iR

length (R increases as L increases)

cross sectional area (R decreases as A increases)

temperature (R increases with temperature)

at any junction, sum of currents into the point equals sum of currents directed away from the point

sum of voltage sources is equal to sum of voltage drops around a closed curcuit loop

increases resistance

total current decreases

decreases resistance

total current increases

two plate system connected to a voltage device that stores charge

C = Q/V

C = ε₀A/d

 (capacitance depends on geometry of plate)

usually insulating material

when added to a capacitor, decreases voltage so increases capacitance

R_s = R₁ + R₂ .... R_n

1/C_s = 1/C₁ + 1/C₂ .... 1/C_n

1/R_p = 1/R₁ + 1/R₂ .... 1/R_n

C_p = C₁ + C₂ ... C_n

1. always directed back towards equilibrium

2. magnitude is proportional to displacement from the equilibrium position

F = -kx

U=0 and K=max at equilibrium point

U=max and K=0 at maximum displacment

reciprocals

v =  fλ

k=2∏/λ

power/area

p=IA

β = 10 log I/I₀

I_{0 =} 10^-12 (hearing threshold)

Source that emits sound and that detects sound move relative to one another so perceived frequency changes

f' = f(v‡v_detect)

       (v‡v_source)

v = speed of sound in medium

converging

positive focal length

diverging mirror

negative focal length

refracted angle is 90°

if angle is greater than the critical angle, total internal reflection occurs

E = hv

c = λv

energy of emitted electron is the energy of the incident light minus work function of hte metal

KE = hv - W

W = hv₀

lower to higher energy

yields color

higher to lower energy

yields fluorescence

Holds nucleus together

comes from mass defect

BE = Δmc²

Z_daughter = Z_parent -2

A_daughter = A_parent - 4

A stays the same

Z+1

(ß- is electron)

A stays the same

Z-1

(ß⁺ = positron)

n = n₀e^-λt

n₀ = number of undecayed nuclei at t=0