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165 Cards in this Set
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 Back
torque

torque=(force)(lever arm)sinø=Ia
I=moment of inertia, a=angular acceleration CCW is positive, CW is negative 

terminal velocity

when frictional force balances weight of object (fmg=ma=0), usually mg>f


mechanical advantage of pulley

MA=Force out/Force in


efficiency of pulley

Efficiency=Work out/Workin=(Fd out)/(Fd in)


Young's modulus

Y=(F/A)/(∆L/L)


bulk modulus

B=(∆P)/(∆V/V)


shear modulus

S=(F/A)/(x/h)
A=area of face moving through distance x with original height h 

pressure (taking hydrostatic pressure into account)

P = P atm+dgh


Pascal's principle

an external pressure applied to a confined fluid will be transmitted equally to all points within the fluid


Archimedes' principle

buoyant force=weight of displaced fluid=dVg


surface tension

y=F/d
ratio of surface force to the length d along which the force acts 

viscosity

resistance exerted by a fluid in motion in newtons seconds per square meter


continuity equation

Q=Av=A1v1=A2v2
(q is fluid flow) 

Bernoulli's equation

E(total)=P+(1/2)dv^2+dgh=constant


critical velocity (above give turbulant flow)

vc=nRe/pd
(n=viscosity, Re=constant, p=density, d=diameter of tube) 

laminar flow

fluid flows in continuous layers stacked one on another and moving with same velocity


turbulent flow

fluid particles fluctuate between these laminar ordered layers as the velocity of fluid increases (random, chaotic motion gives vortices)


linear expansion of solids

∆L=aLo∆T
(a=constant, Lo=original length, ∆T=change in temp.) 

volumetric expansion of liquids

∆V=ßVo∆T
(ß=constant, Vo=original volume, ∆T=change in temp.) 

Charles's law

V1/T1=V2/T2


Boyle's law

P1V1=P2V2


conduction

heat energy transfer in solids, heat energy transferred by collisions between rapidly moving molecules of hot region to slower molecules of cold region)


convection

heat energy transfer in liquids and gases, transfer of heat energy due to physical motion or flow of heated suubstance carrying heat to cooler regions


radiation

heat energy transfer in space (and vacuum) by EM waves emitted by rapidly vibrating, electrically charged particles


1st Law of Thermodynamics

∆U=QW (change in internal energy)
W is positive when work is done by the system, Q is positive when heat is added to the system (and negative for opposite) 

entropy change in equilibrium

∆S=∆Q/T


position of oscillating object

x=Acos(wt+ø)
(A=amplitude in meters, w is angular frequency, t is time, ø is phase angle from reference) 

frequency

f=1/T


angular velocity

w=2πf=2π/T


period

T=2π/w


Hooke's law

F=kx
a=(k/m)x 

period/frequency/angular velocity of massspring system

T=2πsqrt(m/k)
f=(1/2π)sqrt(k/m) w=sqrt(k/m) 

period of a pendulum

T=2πsqrt(L/g)


restoring force of a pendulum

F=mgsinø
(ø=angle between negative tension vector and weight vector) 

Dopplershifted frequency

f2=f1(v±vo)/(v±vs)
(top is positive if observer is moving toward source, bottom is negative if source if moving toward observer) 

sound level

ß=10log(I/Io)
(I is sound intensity) 

wavelength/frequency of stretched string

has nodes at both ends
harmonics: l=2L, L, (2/3)L f=nv/2L (n=1,2,3...) 

pipe with both ends open

has antinodes at both ends
harmonics: l=2L, L, (2/3)L f=nv/2L (n=1,2,3...) 

pipe with both ends closed

has nodes at both ends
harmonics: 1=2L, L, (2/3)L f=nv/2L (n=1,2,3...) 

pipe with one end open

has a node and antinode
harmonics: 1=4L, 2L, L f=nv/4L (n=1,2,3...) 

beats

fbeat=f1f2


waves in increasing frequency

radio, micro, IR, vis, UV, Xrays, gamma rays


critical angle

sinø=n2/n1
(total internal reflection occurs as the angle is equal or greater than the critical angle to the normal) 

incident light on a prism

violet light bends more than red light for separation (lower wavelength is bent the most)


2 slit bright fringes

dsinø=ml where m=0,1,2...


2 slit dark fringes

dsinø=(m+1/2)l where m=0,1,2...


magnification

m=di/do=hi/ho


spherical mirror rays (concave)

parallel to mirror normal: reflect back through focal length
through focal length: parallel to normal through radius of curvature: that's all 

spherical mirror rays (convex)

parallel to normal: draw fake line toward focal point and reflection on other real side
through focal length: reflects back to real side radius of curvature to object: that's all 

thin lenses

same ray tracing as mirrors


lens maker's equation

1/f=(n1)(1/R11/R2)


potential related to work

V=W/q
(electrical potential becomes stored as a result of work W done against an electric field to move a positive test charge q from infinity to that point) 

electric potential difference

∆V=VbVa=Wab/q


electric potential from a charged particle

V=kq/r
(for more than one charge, add the V's together at each point) 

electric field from a charge

E=kq/r^2 N/C (V/m)


electric dipole potential

V=kqdcosø/r^2
(q is the charge on the two ± charges, r is the distance to the middle of the line between the charges, d is the distance between the charges, ø is the angle made to the line between the charges with the line making the radius r) 

voltage by electromotive force

V=EIR
(E is the voltage or potential difference in the battery without current flowing, IR is subtracted because of an internal resistance when current flows) 

current in series, parallel

series: Inet=I1=I2=I3=In
parallel: Inet=I1+I2+...+In 

voltage in series, parallel

series: Vnet=V1+V2+V3+...+Vn
parallel: Vnet=V1=V2=Vn 

electric potential energy W in a capacitor

W=(1/2)qV=(1/2)CV^2=(1/2)q^2/C
(V is potential difference across plates, q is charge on each plate) 

capacitance, area, distance

C is proportional to area/distance


dielectric and capacitance

C'=KC
(K is dielectric constant) 

Kirchhoff, loop rule

potential drops around a circuit must be equal to zero, if resistor is traversed in direction of current, then ∆V=IR (opposite current is +), if batter is traversed in direction of voltage then ∆V=+V (V in opposite direction)


difference between AC and DC

DC have continuous, constant voltage and AC has sinusoidal voltaage causing periodic changes in direction of current flow (AC is associated with a frequency)


voltage in AC at any given time

V=Vosinwt=Vosin(2πft)
(Vo is max voltage) 

root mean square voltage

V(AC)=Vrms=Vmax/sqrt(2)


root mean square current

I(AC)=Irms=Imax/sqrt(2)


AC relation between current and voltage

Vrms=IrmsR


inductance

impedes voltage and caused by reversed emf induced by changing magnetic fields as voltage rises and falls
Vrms=IrmsX(L) X(L)=inductive reactance, represents ability of inductor to resist flow of AC current X(L)=2πfL=wL L=inductance loop of circuitry is an inductor 

pure capacitance

for AC circuit with capacitor:
Vrms=IrmsX(C) X(C) is capacitive reactance X(C)=1/(2πfC) 

resistance, inductance, and capacitance in combination

Z=sqrt(R^2+(X(L)X(C))^2)
Vrms=IrmsZ 

phase angle in AC

angle between voltage and current
tanø=(X(L)X(C))/R 

power dissipated in AC circuit (average power)

Pavg=(Irms)(Vrms)(cosø)


magnetic field of long straight wire

B=µI/(2πr), r is distance to wire axis


magnetic field at center of circular coil

B=µNI/(2r), r is radius, N is number of number of loops of coil


magnetic force on a charged particle in motion

F=qvBsinø
(ø between B field and velocity, right hand rule: thumb=v, fingers=B, palm=F) 

magnetic force on a currentcarrying wire

F=ILBsinø
(L=length of wire, ø=angle b/w current and B field, right hand rule: thumb=I, fingers=B, palm=F) 

photoelectric effect

KEmax = hvWmin
(maximum kinetic energy of electron being released from atom by light greater than its work function, the minimum amount of work required for electron liberation) 

energy level of an electron

E=(13.6 eV)(Z^2/n^2), as n increases the energy differences become smaller
(Z=atomic number, n=shell) 

radioactive decay

N(t)=No e^(lt)
l (lamba)=ln(2)/T(1/2) 

alpha decay

caused by repulsive electric forces between protons


beta decay

nuclei with too many neutrons emit beta particle (B is an electron (Z up 1, A unchanged), B+ is a positron (Z down 1, A unchanged)


rest mass of nucleus and mass defect

less than the sum of the rest masses of the protons and neutron, negative energy (gives off energy) required to bind individual nucleus particles


nuclear binding energy

NBE=Zm(p)c^2+Nm(n)c^2M(nuc)c^2
(mass defect is M(nuc)c^2) 

nuclear fission and fusion

fision usually occurs when A>230 and fusion when A<20


pressure units

1 Pa = 1 N/m^2
1 atm = 1.01 x 10^5 Pa = 1.01 bar = 760 mmHg = 760 torr 

5 motion equations

1. Vf=Vo+at
2. x=.5at^2+Vot+Xo 3. Vf^2=Vo^2+2as 4. Vavg=(Vf+Vo)/2 5. s=Vavg x time 

Newton's 3 laws

1. inertia (remain at rest or constant V unless force)
2. F=ma 3. Fa=Fb 

uniform motion

when object speed remains constant (in centripetal, only radial acceleration)


nonuniform motion

speed of object changes, so there is some tangential and some centripetal circular accerlation


work

Fdcosø


total mechanical energy

E=KE+PE


workenergy theorem

W=∆KE


conservative forces

work done to move particle in round trip is zero, work to move particle between 2 points is the same regardless of path (any force with associated PE, ∆E=∆KE+∆PE=0)


nonconservative force work

W'=∆KE+∆PE=∆E


conservation of angular momentum

L=mvr where as r increases v decreases so that L remains constant


conduction

direct transfer of energy from molecule to molecule by collisions (metals are best, gases are worst)


convection

transfer of heat by physical motion of heated material (fluids), heated parts rise and colder parts sink


special cases of first law of thermodynamics

adiabatic (∆U=W), constant volume (∆U=Q), closed cycle (Q=W)


entropy of system in reversible isothermal process

∆S=Q/T


conservations in hydraulic lever

∆P=F1/A1=F2/A2
Volume=A1d1=A2d2 Work=F1d1=F2d2 

float or sink?

if fluid displaced by object has a greater weight than object then the object will float, it will sink if fluid weight is less than object weight until the two are balanced


streamlines

velocity is tangent to line and lines may not cross


liquid/gas viscosity

in fluids, liquid has greater viscosity than gas


electric field and force

E=F/q, F=Eq


heat equations

q=mL and q=mc∆T


E field lines

point away from positive charge and into negative charge, E at any point is tangent to the line, total E is equal to the vector sum at any point from a number of charges


potential from a number of point charges

add up the V=kq/r from each charge (scalar sum)


equipotential line

every point along line has equal potential, no work done in moving charge along these lines


work to move charge to new potential

Wab=q(VbVa)=q(kQ/rbkQ/ra)


object falling with friction

Ffmg=ma (terminal velocity when Ff=mg)


electric potential energy

EPE=W=qV=kqQ/r (work needed to move charge from infinity to that point)


dipole moment

p=qd, points from negative to positive charge


electric field along perpendicular bisector of electric dipole

E=(1/4πEo)(p/r^3), points in opposite direction of p


dipole in electric field

generally random orientation without field, zero translational force in field because the force on each charge is equal in magnitude and opposite in direction, there is nonzero torque to align dipole moment with E field (torque=pEsinø) with ø the angle between dipole and E


torque on dipole in E field

torque=pEsinø (ø is angle between dipole and E)


circular motion of charged particle

F=qvB=mv^2/r, r=mv/qB


diamagnetic

individual atoms have no net magnetic field, repelled from strong bar magnet, weakly antimagnetic


paramagnetic

individual atoms have a net magnetic field but they are aligned randomly so whole material has no magnetic field, some degree of alignment occurs and be attracted towards pole of strong bar magnet (weakly magnetic)


ferromagnetic

individual atoms have net magnetic field bu randomly aligned as in paramagnetic, temp below a critical value causes a high amount of alignment and atomic B field occurs (above critical value the material is paramagnetic, otherwise strongly magnetic and if the critical temperature is greater than room temp then you have a bar magnet)


insulators

have electric charge bound to constituent atoms to retard electron flow (nonmetals)


power dissipated by resistor

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


total resistance for n equal resistors in parallel

Rtotal=R/n
(R is resistance of each) 

capacitance

C=Q/V=EoA/d


electric field between capacitor plates

E=V/d (toward negative plate away from positive plate)


function of dialectric

lowers voltage across charged up capacitor and makes room for more charge to increase capacitance (charge remains the same before and after)


AC current equation

I=Imaxsin(2πft)=Imaxsin(wt)


linear restoring force of simple harmonic motion (spring)

F=kx and a=(w^2)x


energy in SHM

E=K+U=constant
K=.5mv^2 U=.5kx^2 (spring) =mgh (pend.) (at equilibrium position KE is max and PE is zero, at max displacement PE is max and KE is zero) 

transverse wave

particle oscillates perpendicular to direction of wave motion


longitudinal wave

particle oscillates in direction of motion


traveling wave

string fixed at one end, incident wave is reflected and inverted back


standing wave

ends are either nodes or antinodes as in strings and pipes, there is no energy propagation


resonance

when forced oscillation occurs at natural frequency, energy is inputted and amplitude increases


sound

longitudinal wave, moved by mechanical disturbance propagated through deformable medium (sound is fasted in solid then liquid then gas)


powerintensity

Power=Intensity x Area
(intensity is avg. rate per unit area at which energy is transported across a perpendicular surface by the wave) 

ratio of sound levels

BaBb=10log(Ia/Ib)


sound production

1. vibration of solid object that sets adjacent air molecules in motion
2. acoustic sound (vibrating motion of air) 3. pitch determined by length of pipe on tension in string 

beat frequency

fbeat=f1f2 (wavelengths add)


plane mirrors

virtual images, law of reflection (angles equal)


focal length sign conventions

converging lenses/mirrors have positive focal lengths, diverging lenses/mirrors have negative focal lengths


lens power

P=1/f(meters) in diopters


lenses in contact (f, P, M)

1/ftot=1/f1+1/f2+...
P=P1+P2+... M=m1 x m2 x m3 x ... 

index of refraction function

increasing n causes decrease in lamba, decrease in velocity and no change in frequency (n=lamba in vacuum/new lamba)


dispersion

separation of wavelengths as different wavelenghts of light have different speeds when frequency remains constant (causes violet light to bend more as it moves slower)


blackbody spectrum

lamba(peak)=2.9x10^3mK/T
E=sigmaT^4 (energy emitted per unit area per second) (blackbodies at higher temp have lower peak lamba) 

ionization energy and work function

KE (ionization) = hf (photon)  w (work function of a threshold photon energy for ionization)


current produced from light beam

current created by shooting light at metal with high enough energy, higher intensity causes greater current (directly proportional) (frequency of light must be greater than threshold frequency)


fluorescence

substances emit visible light when excited by other radiation (usually UV), the electron returns to its state in 2 or more steps and at each step a longer wavelength is emitted


electron capture

unstable radionuclei can capture K or L shell electron as it combines with a proton to form a neutron (Z decreases by 1, A stays the same)


iron peak

binding energy per nucleon peaks at iron (most stable nucleus)


decay equation

N=Noe^(lt) and l=(ln2)/T(1/2)


general gravitational potential energy (not local, mgh)

PE=GmM/r


wave amplitude and intensity

amplitude is directly related to the intensity of the wave


sound attenuation

conversion of sound wave energy into heat


sound pitch

the frequency of the sound, higher pitches have higher frequencies


acoustic resonance

the tendency of an acoustic system to absorb energy if frequency of oscillations matches natural frequency


ultrasound

20 kilohertz or greater (humans can't hear)


electrostatic induction

an electrically charged object can charge an uncharged object even without direct contact between the two


solenoid

coil is wrapped around central object where current flows through the coil to generate a magnetic field of center object (B=uNI constant in interior, N is loops of coil per meter)


toroid

magnetic circular solid core with wire wrapped around with current flowing, magnetic field in center of circle is B=uNI/2πr (N loops)


thin film interference

light waves can be reflected on top of film or at the bottom and can interfere constructively if the n of the film is greater than the underlying substance and destructively if the n is less than the underlying (phase shifts 180 and interferes with first reflected wave)


diffraction grating

lines situated close together can diffract light into constituent wavelengths (dispersion)


single slit diffraction

largest bright fringe iin center, dark fringes found by sinø=ml/d (l=lambda, d=slit width, m=1,2,3...)


xray diffraction

scattering of light through specimens based on thickness and material of specimen
