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165 Cards in this Set

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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 (f-mg=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=Q-W (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 mass-spring 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)
Doppler-shifted 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=f1-f2
waves in increasing frequency
radio, micro, IR, vis, UV, X-rays, 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=(n-1)(1/R1-1/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=Vb-Va=-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=E-IR
(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 current-carrying 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 = hv-Wmin
(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^2-M(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
work-energy 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(Vb-Va)=q(kQ/rb-kQ/ra)
object falling with friction
Ff-mg=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)
power-intensity
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
Ba-Bb=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=f1-f2 (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...)
x-ray diffraction
scattering of light through specimens based on thickness and material of specimen