Physics 2 Final

Period

time it takes for an oscillation to repeat itself, T=1/f

Frequency

number of complete oscillations per second, f = 1/T

Angular frequency oscillating spring

w = sqrt(k/m)

Frequency oscillating spring

f = w/2pi

Period oscillating spring

T = 2pi(sqrt(m/k))

Potential energy spring

U = 1/2kx^2

Max potential energy spring

U = 1/2kA^2

Angular frequency simple pendulum

w = sqrt(g/L)

Frequency simple pendulum

f = w/2pi = 1/2pi((sqrt(g/L))

Period simple pendulum

T = 2pi/w = 2pi((sqrt(L/g))

Which spring oscillates faster? Same mass but one has higher k

Spring with higher k

Total energy in spring

1/2kx^2 + 1/2mv^2 = 1/2kA^2

Velocity of spring when x = A

v = 0, K = 0

Angular speed circular motion

w = Δθ/ΔT

Linear speed circular motion

v = rw

Centripetal acceleration

a = v^2/r = rw^2

Angular position circular motion

θ = wt + ɸinitial

X position circular motion

x = Acosθ = Acos(wt + ɸ)

X component of velocity

v = -vsinθ = -wAsin(wt + ɸ)

X component of acceleration

a = -w^2Acos(wt + ɸ) = -w^2x

X component of acceleration for spring

a = -(k/m)x

Transverse wave

medium oscillates perpendicular/transverse to direction wave travels (ex. wave on a string)

Longitudinal wave

medium oscillates along direction of propagation of wave (ex. compression of spring, sound wave)

Surface wave

combination of transverse and longitudinal waves (ex. waves on water)

Wave speed

wavelength x frequency = w/k where k = wave number

When wave speed changes

only when the physical properties of the medium change, such as its density, temperature, tension, or depth

Wave number

k = 2pi/wavelength

Angular frequency of wave

w = 2pi x frequency

Constructive interference

phase difference = 0 or 2pi

Destructive interference

phase difference = pi

Antinodes

points of max amplitude, harmonic number

Nodes

points of zero amplitude

Beat frequency

|f2 - f1| = number of loud-soft cycles/second

Insulator

charges can’t move within material, electrons remain in place (ex. glass, plastics)

Conductor

charges can move freely within material (ex. metals)

Electric force

F = (kq1q2)/r^2

Electric field

E = F/q = (kQ)/r^2, property of space, defined using positive test charge, vector

Electric field direction

points away from positive charge, towards negative charge

Density of electric field lines

related to strength of field/magnitude of charge

Electric field magnitude

same when lines are same density

Displacement in same direction as field

ΔUelectric is negative, electric field does positive work on charge

Displacement in opposite direction as field

ΔUelectric is positive, electric field does negative work on charge

Particle released from rest

travels tangent to direction of field lines - field lines indicate the direction of acceleration, not the velocity, of the particle

Electric potential energy

U = (kq1q2)/r

Electric potential energy of system of opposite charges

negative because they are already attracted to each other

Change in potential energy

ΔU = -qEd = qΔV

Electric potential

V = (kQ)/r = U/q = Ed = Q/C

Electric potential decreases

along direction of electric field lines

Voltage

property of space, high voltage = high energy per charge, voltage is not energy

Positive charges move

toward lower electric potential/voltage to increase KE

Negative charges move

toward higher electric potential (towards +), decreases PE

Equipotential lines

perpendicular to electric field, spacing indicates strength of electric field, electric field lines point to regions of lesser voltage

v max simple harmonic motion

wA where w = sqrt(k/m) - directly proportional to amplitude, smaller for object with larger mass

Potential energy of positive charge

high (positive) when electric potential is large

Potential energy of negative charge

low (negative) when electric potential is large

Electric potential near positive charge

large and positive

Electric potential near negative charge

large and negative

Plastic rod is rubbed with fur

plastic rod becomes negatively charged and fur becomes positively charged

Glass rod rubbed with silk

glass rod becomes positively charged and silk becomes negatively charged

Work

W = qΔV (-qΔV for work done by electric field)

Work done by electric field/force

positive when displacement is in same direction as force/field

Wave equation

y = Asin(kx - wt), k = wave number = 2π/λ

Energy in capacitator

U = 1/2QV= 1/2CV² = Q²/2C, Q = CV

Capacitance

C = eA/d = Q/V

Proton/electron moving through potential difference

qΔV = 1/2mv^2​

Amount of charge a capacitor can store depends on

voltage applied and capacitor’s physical characteristics, like size

Voltage in uniform electric field

V = Ed, where d is distance btwn 2 points

Capacitance

C = Q/V, C = e0(A/d)

At constant Q or V

increasing distance decreases capacitance

Total capacitance in series

1/Cs = 1/C1 + 1/C2 + 1/C3…

Total capacitance in parallel

Cs = C1 + C2 + C3…

Energy stored in capacitor

Ecap = ½(QV) = ½CV^2 = Q^2/2C

Current

rate at which charge flows, I = ΔQ/Δt (A)

Direction of current

direction positive charge moves

Current equation (w/ drift velocity)

I = nqAvd, where A = cross-sectional area of wire, n = free-charge density of wire material, q = charge of each carrier, vd = drift velocity

Ohm’s law

V = IR

Resistance given cylinder length and area

R = pL/A, where p = resistivity of material, L = length, A = cross-sectional area of wire

Higher temperature

higher resistivity in metals (bc metal atoms vibrate more), lower resistivity in semiconductors/insulators (bc more charge carriers)

Electrical power

rate that energy is supplied by a source or dissipated by a device

Power equations

P = IV = V^2/R = I^2R

Total resistance in series

Rs = R1 + R2 + R3…

Total resistance in parallel

1/Rs = 1/R1 + 1/R2 + 1/R3…

Resistors in series - current

each resistor in a series circuit has the same amount of current flowing through it

Resistors in series - voltage/power

voltage drop/power dissipation across each individual resistor in series is different, combined total adds up to power source input

Resistors in parallel - current

current flowing through each resistor in a parallel circuit is different, depending on the resistance

Resistors in parallel - voltage/power

each resistor in a parallel circuit has the same full voltage of the source applied to it.

EMF

potential difference of a source when no current is flowing

Voltage output of a device - terminal voltage V

V = emf - Ir, where r = internal resistance of a voltage source

Multiple voltage sources in series

internal resistances add, emfs add algebraically

Kirchhoff’s junction rule

the sum of all currents entering a junction must equal the sum of all currents leaving the junction

Kirchhoff’s loop rule

the algebraic sum of changes in potential around any closed circuit path (loop) must be zero

Voltmeter

placed in parallel with voltage source to receive full voltage, must have large resistance to limit its effect on circuit

Ammeter

placed in series to get full current flowing through a branch, must have small resistance to limit its effect on circuit

RC circuit

has both a resistor and capacitor

Time constant RC circuit

τ = RC

Magnetic force exerted by field on moving charge q

F = qvBsinθ, where θ is the angle between the directions of v and B

RHR1 - direction of force on moving charge

thumb toward v, fingers toward B, palm points toward F

Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius

r = mv/qB, where v is the component of the velocity perpendicular to B for a charged particle with mass m and charge q

Magnetic force on a current-carrying conductor

F = ILBsinθ, where I = current, L = length of a straight conductor in a uniform magnetic field B, θ = angle between I and B

RHR2

thumb toward I, fingers toward B, palm points toward F