Physics
Antiferromagnetism
- magnetism in which adjacent ions that act as tiny magnets spontaneously
align
themselves at relatively low temperatures into
opposite (antiparallel) arrangements so that overall the
solid does not exhibit magnetism; occurs with
manganese oxide
Auger
Effect - outer shell electron replaces removed inner electron, releasing
energy as X-ray or ejecting
another electron
Cherenkov
Radiation - light produced by charged particles when they pass through an
optically transparent
medium at speeds greater than the speed of light in
that medium; named for 1958 Soviet Nobel winner
Compton
Effect - increase in wavelength of X-rays that have been elastically scattered
by electrons;
principal way in which radiant energy is absorbed in
matter; named for 1927 American Nobel
winner
Diamagnetism
- magnetism characteristic of materials that line up at right angles to a
nonuniform magnetic
field and that partially expel from their interior
the magnetic field in which they are placed
Doppler
Effect - the apparent difference between the frequency at which sound or light
waves leave a
source and that at which they reach an observer,
caused by the relative motion of the observer and the
wave source; red shift if receding, blue shift if
approaching
Dynamo
Effect - production of the Earth's main magnetic field by an electric field in
the core
Edison
Effect - thermionic emission; discharge of electrons from heated materials;
used as electron source
in electron tubes
Faraday
Effect - rotation of the plane of polarization of a light beam by a magnetic
field
Ferroelectricity
- spontaneous electric polarization occurs in crystals with perovskite
structure, such as
barium titanate
Ferromagnetism
- electrically uncharged materials strongly attract others
Hall
Effect - development of a transverse electric field in a solid material when
it carries an electric current
and is placed in a magnetic field that is
perpendicular to the current
Hysteresis
Effect - magnetization of ferromagnetic substances lags behind the magnetizing
field
Hawking
Radiation - when a particle pair is created near a black hole, one falls into
the hole and the other
escapes as radiation
Josephson
Effect - flow of electric current between two pieces of superconducting
material separated by a
thin layer of insulating material
Joule-Thompson
Effect - cooling of a gas as it undergoes adiabatic expansion
Lamb
Shift - separation of energy in nearly coincident electron levels of hydrogen;
named for 1955
American Nobel winner
Lorentz-Fitzgerald
Contraction - space contraction; the shortening of an object along the
direction of its
motion relative to an observer
Meissner
Effect - the expulsion of a magnetic field from the interior of a material
that is in the process of
becoming a superconductor
Mikheyev-Smirnov-Wolfenstein
Effect - neutrinos with mass oscillate among flavor states
Mossbauer
Effect - also called recoil-free gamma-ray resonance absorption; nuclear
process permitting the
resonance absorption of gamma rays; radioactive atoms
are imbedded in a crystal lattice, allowing
very precise measurements; named for 1961 German
Nobel winner
Paramagnetism
- magnetism characteristic of materials weakly attracted by a strong magnet
Paschen-Back
Effect - Zeeman spectral patterns are lost at magnetic separations for natural
doublets,
triplets, etc.
Peltier
Effect - the cooling of one junction and the heating of the other when
electric current is maintained
in a circuit of material consisting of two dissimilar
conductors
Photoelectric
Effect - charged particles are released from a material when it absorbs
radiant energy
Quantum
Tunneling - barrier penetration; particle travels through a barrier despite
the fact that the
particle's presence in the barrier is forbidden by
classical physics
Raleigh
Scattering - dispersion of electromagnetic radiation by particles that have a
radius less than one-
tenth the wavelength of the radiation; angle of
sunlight varies inversely as fourth power of
wavelength so blue is scattered most and sky appears
blue
Raman
Effect - change in wavelength of light that occurs when a light beam is
deflected by molecules;
named for 1930 Indian Nobel winner
Seebeck
Effect - production of an electromagnetic force and consequently an electric
current in a loop of
material consisting of at least two dissimilar
conductors when two junctions are maintained at
different temperatures; applicable in thermocouples
Stark
Effect - splitting of spectral lines in an electric field; named for 1919
German Nobel winner
Tachyons
- particles that travel faster than the speed of light
Tyndall
Effect - scattering of light by a colloid
Voigt
Effect - a constant magnetic field applied to a transparent gaseous medium
produces a birefringence
such that the vapor has different indices of
refraction in different directions
Zeeman
Effect - splitting of spectral lines in a magnetic field; named for 1902 Dutch
Nobel winner
Equations
of Motion:
v = v0 + at
x = x0 = v0t + at2/2
v2 = v02 + 2a(x - x0)
x - x0 = ((v0 + v)/2)t
v = dx/dt
a = dv/dt
Projectile
Motion in 2D
x = (v0cos(a0)t
y = (v0sin(a0))t
- gt2/2
vx = v0cos(a0)
vy = v0sin(a0)
- gt
Radial
acceleration = v2/R ; period
= 2pR/v
Relative
velocity: vP/A = vP/B + vB/A
Newton's
First Law states that when the vector sum of all forces acting on a body is
zero, the body is in
equilibrium; in inertial frames of reference, a body
in motion will stay in motion and a body at rest will stay
at rest.
Newton's
Second Law states that F = ma.
Unit
of force is Newton = 1 kg*m/s2
Weight
is the gravitational force exerted on an object.
Newton's
Third Law states that two bodies exert forces on each other that are equal in
magnitude and
opposite in direction; action equals reaction.
Free-body
diagrams are used to show forces acting on a body.
The
coefficient of kinetic friction is directly proportional to the normal force
(perpendicular to interaction surface).
The
acceleration toward the center in uniform circular motion has magnitude v2/R.
The
fundamental forces are gravitational, electromagnetic, strong, and weak.
Work
= F*s*cos(f)
= dot product of F and s vectors
Kinetic
energy is the amount of work required to accelerate a particle from rest to
speed v = mv2/2
Unit
of work is the Joule = 1 N*m = 1 kg*m2/s2
Work
energy theorem: Wtotal = K2 - K1
Power
is the time rate of doing work; P = dW/dt
Unit
of power is the watt = 1 J/s = 1 kg*m2/s3
Potential
energy -DU
= mgy1 - mgy2
Elastic
work by compressed spring: W = kx12/2 - kx22/2
K1
+ U1 +Wother = K2 + U2
For
a conservative force, the work-kinetic energy relation is completely
reversible and can be represented by a
potential-energy
function; F(x) = -dU/dx
Momentum:
p = mv
SF
= dp/dt
Impulse:
J = SF Dt
= p2 - p1
Momentum
equals the impulse that accelerated a particle from rest to its present speed.
Total
momentum: P = pA + pB + ...
Each
component of total momentum is conserved if the net external force is zero.
In
an elastic collision, the initial and final total kinetic energies are equal
and the initial and final relative velocities
have
the same magnitude.
In
an inelastic collision the final total kinetic energy is less than the initial
total kinetic energy (if same final velocity,
it
is completely inelastic).
Center
of mass: xcenter = (Smx)/Sm ;
ycenter = (Smx)/Sm
Total
momentum equals total mass times velocity of center of mass.
Fexternal
= Macenter of mass
Angular
velocity: w
= dq/dt
Angular
acceleration: a
= dw/dt
Equations
of motion of rigid body about a fixed axis with constant angular acceleration
q
= q0
+ w0t
+ at2/2
q
- q0
= (w0
+ w)t/2
w
= w0
+ at
w2
= w02
+ 2a(q
- q0)
v
= rw
atangential
= ra
aradial
(centripetal) = v2/r = w2r
Moment
of inertia: I = Smr2
Kinetic
energy: K = Iw2/2
Parallel
axis theorem: Iparallel axis = Icm + Md2
Moments
of inertia
Slender rod, axis through center: ML2/12
Slender rod, axis through one end: ML2/3
Plate, axis through center: M(a2+b2)/12
Plate, axis along edge b: Ma2/3
Hollow cylinder: M(R12 + R22)/2
Solid cylinder: MR2/2
Thin-walled hollow cylinder: MR2
Solid sphere: 2MR2/5
Thin-walled hollow sphere: 2MR2/3
Torque:
t = Fl
(l is lever arm) ; counterclockwise
positive; torque equals cross
product of r and F
St = Ia
Translational
and rotational kinetic energy: K = Mvcm2/2 + Icmw2/2
If
the rigid body rolls without slipping, vcm = Rw
Work:
W = tDq
Work-energy
theorem for rotation of rigid body: W = Iw22/2
- Iw12/2
Power:
P = tw
Angular
momentum: L = Iw
= cross product of r and p, with p = mv
St = dL/dt
If
net torque of external forces is zero, the total angular momentum is zero.
For
a rigid body in equilibrium, the vector sum of forces is zero and the sum of
torques about any point is
zero.
The
weight can be assumed to be concentrated at the center of gravity, which is
the center of mass.
Hooke's
Law states that in elastic deformations, stress is proportional to strain;
elastic modulus =
stress/strain.
Tensile
stress is tensile force per unit area, and tensile strain is fractional change
in length.
Young's
modulus is the ratio of tensile stress to tensile strain; Y = (Ft/A)/(Dl/l0)
Compressive
stress and strain are defined the same way as tensile stress and strain.
Pressure
in fluid is force per unit area.
Unit
of pressure and stress is pascal = N/m2
Bulk
modulus is the negative of the ration of pressure change (bulk stress) to
fractional volume change;
B = -Dp/(DV/Vo)
Compressibility
is the reciprocal of the bulk modulus.
Shear
stress is force per unit area for a force applied parallel to a surface.
The
shear modulus is the ratio of shear stress to the shear strain angle; S =
(F/A)/f
The
proportional limit is the maximum stress for which stress and strain are
proportional; Hooke's law is
invalid beyond this.
The
elastic limit is the stress beyond which irreversible deformation occurs, and
the breaking (or ultimate)
strength is the stress at which the material breaks.
Newton's
law of gravitation: F = Gm1m2/r2
Acceleration
due to gravity near Earth's surface is GmE/RE2
Gravitational
potential energy: U = - integral of F = -Gm1m2/r
Speed
of satellite: v = sqrt(Gm/r)
Period
of satellite: T = 2pr/v
Johannes
Kepler's Laws
Each planet moves in an elliptical orbit with the sun at one focus.
A line from the sun to a given planet sweeps out equal areas in equal
times.
The periods of the planets are proportional to the 3/2 powers of the
major axis lengths of their
orbits.
Weight
is 0.3% less at equator.
If
a nonrotating spherical mass distribution has radius less than the
Schwarzschild radius, 2GM/c2 , the
gravitational interaction prevents anything including
light from escaping; this is a black hole.
Periodic
motion occurs whenever a body has a stable equilibrium position and a
restoring force or torque.
Frequency
is inverse of period.
Angular
frequency: w
= 2pf
In
simple harmonic motion (SHM), the net force is a restoring force that is
directly proportional to the
displacement; F
= -kx ; a = F/m
The
projection on the horizontal axis of a rotating vector (using the circle of
reference construction) called
the phasor represents the actual motion of a body in
SHM.
w
= sqrt(k/m)
x
= A*cos(wt
+ f) (amplitude
A and phase angle f)
E
= kA2/2 = constant
Angular
simple harmonic motion: w
= sqrt(K/I)
(torsion constant K)
Pendulum:
w = sqrt(g/L)
Physical
pendulum: w
= sqrt(mgd/I)
Damping
force: F = -bv
Damped
oscillation: critically damped if b = 2sqrt(km); w'
= sqrt(k/m - b2/(4m2))
Forced
oscillation occurs when a sinusoidally varying driving force is added to a
damped harmonic
oscillator.
Density:
p = m/V
Specific
gravity is ratio of density of a material to density of water.
Pascal's
law states that pressure applied to the surface of an enclosed fluid is
transmitted undiminished to
every portion of the fluid.
Gauge
pressure is the difference between absolute pressure and atmospheric pressure.
Pressure
at depth h of incompressible liquid is pressure at surface plus p*g*h.
Archimedes'
principle states that a fluid exerts an upward buoyant force on an immersed
body equal to the
weight of the fluid the body displaces.
Surface
tension is the force per unit length across a line on the surface.
An
ideal fluid is incompressible and has no viscosity.
A
flow line is the path of a fluid particle and a streamline is a curve tangent
at each point to the velocity
vector at that point.
A
flow tube is a tube bounded at its sides by flow lines.
In
laminar flow, layers of fluid slide smoothly past each other.
In
turbulent flow there is great disorder and a constantly changing flow pattern.
Equation
of continuity: A1v1 = A2v2
Volume
flow rate: Av = dV/dt
Bernoulli's
equation relates pressure, flow speed, and elevation for steady flow in an
ideal fluid;
p1 + pgy1 + pv12/2 = p2
+ pgy2 + pv22/2
The
viscosity of a fluid characterizes its resistance to shear strain; in a
Newtonian fluid the viscous force is
proportional to strain rate.
Poiseuille's
equation for total volume rate in a cylindrical pipe; dV/dt = p/8 * (R4/n)((p1-p2)/L)
Stokes'
law for a sphere moving through a fluid: F = 6pnrv
TF
= 9/5 TC + 32 ; TC
= 5/9 (TF - 32) = Tk - 273.15
The
triple point of water is at 273.16 K
DL
= aL0DT
DV
= 3aV0DT
for solids
Tensile
stress: F/A = -YaDT
Quantity
of heat required to raise the temperature of a material is mass times specific
heat capacity times
change in temperature.
Mass
= number of moles times molecular mass
The
Rule of Dulong and Petit states that the molar heat capacities of many solid
elements are
approximately 25 J/(mol*K).
Quantity
of heat required to change a material to a different state is mass times heat
of
fusion/vaporization/sublimation.
Conduction
is transfer of energy without bulk motion, convection involves mass motion,
and radiation is
energy transfer through electromagnetic radiation.
Heat
current for conduction: H = dQ/dt
= kA(TH - TC)/L
(thermal conductivity k)
Heat
current for radiation: H = AesT4 (emissivity e, Stefan-Boltzmann constant s)
Net
heat current: H = Aes(T4
- Ts4)
Ideal-gas
equation of state: pV = nRT
Isotherms
on pV diagram show pressure as a function for volume at constant temperature.
Average
translational kinetic energy of gas particles:
K = 3/2 nRT
Root
mean square speed of molecules in ideal gas: vrms = sqrt(3RT/M)
Mean
free path: l
= vt = V/(4pr2Nsqrt(2))
Molar
heat capacity for ideal: monatomic gas 3R/2, diatomic gas 5R/2, monatomic
solid 3R
Speeds
of molecules in an ideal gas are distributed according to the Maxwell-Boltzmann
distribution.
On
a phase diagram, the vaporization curve ends at the critical point, above
which there is no distinction
between the gas and liquid phases.
W
= p(V2 - V1)
Heat
and work in a thermodynamic process are not state functions.
First
Law: DU = Q - W
Internal
energy is a state function.
In
an adiabatic process, no heat is transferred in or out of the system;
isochoric is constant volume, isobaric
constant pressure, isothermal constant temperature.
The
internal temperature of an ideal gas depends only on its temperature; for all
else, it also depends on
pressure.
Molar
heat capacity at constant pressure equals molar heat capacity at constant
volume plus R.
p1V1Cp/Cv
= p2V2Cp/Cv
A
heat engine takes heat QH from a source, converts part of it to
work W, and discards the rest at lower
temperature
QC .
Thermal
efficiency: e = W/QH = 1 + QC/QH
Thermal
efficiency of Otto cycle gasoline engine: e = 1 - 1/rCp/Cv-1
Coefficient
of performance: K = | QC/W |
The
Second Law states that no cyclic process can convert heat completely into work
(engine statement) or
transfer
heat from a colder place to a hotter place with no work input (refrigerator
statement).
Thermal
efficiency of the Carnot cycle of reversible processes between two heat
reservoirs: e = 1 - TC/TH
All Carnot engines between the same two temperatures have the same efficiency.
A
backwards Carnot engine is a Carnot refrigerator.
Kelvin
scale is based on Carnot cycle efficiency.
Entropy:
DS = DQ/DT ; the entropy of an isolated system can
never decrease
S
= k*ln(w) (Boltzmann
constant k = R/NA , number
of possible microscopic states w)
A
wave is any disturbance from an equilibrium condition that propagates from one
region to another; a mechanical
wave
travels within a medium material.
v
= lf
y
= A*sin(2*p*(t/T
- x/l)) = A*sin(wt
- kx) with k = 2p/l and w
= vk
Wave
equation: second partial of y with respect to x equals second partial of y
with respect to t, over v2
Speed
of transverse wave on a string: v = sqrt(F/m)
Speed
of longitudinal wave in a fluid: v = sqrt(B/p) (bulk modulus B, density p)
Speed
of longitudinal wave in a solid rod: v = sqrt(Y/p) (Young's modulus Y)
Speed
of sound in ideal gas: v = sqrt((Cp/Cv)RT/M)
Average
power of sinusoidal wave on stretched string: P = w2A2
sqrt(mF)/2
called intensity for longitudinal
The
principle of superposition states that the total wave displacement at any
point where two or more
waves overlap is the sum of the displacements of the
individual waves.
When
a wave is reflected from a fixed or free end of a stretched string, the
incident and reflected waves
combine to form standing wave with nodes l/2 apart and antinodes between.
y
= (A*sin(k*x)*cos(w*t)
(angular frequency w = 2pf, wave number k = 2p/l)
If
both ends of a string are fixed, standing waves occur only when the string
length is an integer multiple of
l/2;
f = nv/(2L)
Each
frequency and its associated vibration pattern is called a normal mode.
The
lowest frequency is the fundamental frequency
f = sqrt(F/m)/(2L)
A
closed end of a pipe or tube is a displacement node and a pressure antinode.
Open
pipe: f = nv/(2L) for integral n;
Stopped pipe: f = nv/(4L) for odd n
Interference
(in-phase constructive or out-of-phase destructive) interference is the
overlap of waves.
Forced
oscillation is the vibration at the same frequency as an applied periodically
varying force, which
causes resonance if near a normal-mode frequency.
Pressure
amplitude of sound: p = BkA (bulk
modulus B)
Loudness
depends on amplitude and frequency, pitch on frequency, and tone quality
(timbre) on harmonic
content and the attack and decay characteristics.
Intensity
is the time average rate at which energy is transported by the wave per unit
area.;
I = p2/(2rv)
(pressure amplitude p)
Sound
intensity level (in decibels): b
= (10 dB)log (I/I0)
I0 = 10-12 W/m2
Beats
are two tones with slightly different frequencies sounded together;
f = f1 - f2
Doppler
effect: fL = (v + vL)/(v + vS) fS
Shock
wave: sin(a)
= v/vS (vS
> v, the speed of sound)
Charge
is conserved; likes repel and opposites attract.
Coulomb's
Law: F = kq1q2/r2
k
= 1/(4pe0)
= 8.99*109 Nm2/C2
; e0
is
permittivity of free space = 8.85*10-12 C2/(N*m2)
Electric
field is the force per unit charge exerted on a test charge at any point;
E = kq/r2 = F/q
Unit
of electric field is N/C or V/m
The
principle of superposition of forces or fields states that the total force or
field on a charge is the vector
sum of the forces or fields exerted by the individual
charges.
The
tangent to a field line is the direction of E.
Electric
dipole: magnitude p = q*d, torque
t = p*E*sin(f) (cross product of dipole moment and electric
field)
Potential
energy of an electric field: U =
-p*E (dipole moment
p)
Electric
flux is the flow of electric field through a surface; flux F
= integral of E*dA
Gauss's
Law states that the total electric flux through a closed surface equals 4pk times the enclosed
charge; F = 4pkQenc
Excess
charge on a conductor at rest resides entirely on the surface.
Line
charge: E = 2kl/r
Sheet
charge E = 2pks
Outside
solid insulating sphere: E = kQ/r2
Inside
solid insulating sphere: E =
kQr/R3
Potential
energy: U = kq1q2/r
Potential
is potential energy per unit charge; V
= kq/r
V2
- V1 = integral of E times dl
1
eV = 1.602*10-19 J
An
equipotential surface is a surface on which the potential has the same value
at every point.; field lines
cross equipotentials perpendicular.
Ex
= -dV/dx
A
capacitor is any pair of conductors separated by an insulating material;
capacitance C = Q/V
Parallel
plate capacitor: C = A/(4pkd)
Unit
of capacitance is the farad = 1 C/V
Capacitors
in series: 1/C = 1/C1
+ 1/C2 + . . .
Capacitors
in parallel: C = C1 + C2 + . . .
Energy
of capacitor: U = QV/2 = CV2/2
= Q2/(2C)
Capacitance
increases by a factor of K, the dielectric constant, when the space between
the conductors is
filled with a dielectric material;
C = KC0 ; permittivity
is Ke0
In
dielectric breakdown, under electric field greater than dielectric strength,
dielectrics become conductors.
Current
is the amount of charge flowing through a specified area per unit time.
Unit
of current is ampere = C/s
I
= n*|q|*vd*A = J*A (concentration
n, drift velocity vd, current density J )
Resistivity:
r = E/J
Unit
of resistivity is ohm-meter.
Resistivity
increases with temperature and is small in conductors.
Ohm's
Law: V = I*R
R
= rL/A
Unit
of electromotive force is volt.
V
= e - I*r
Power:
P = V*I = I2*R
Resistors
in series: R = R1 + R2
+ . . .
Resistors
in parallel: 1/R = 1/R1
+ 1/R2 + . . .
Kirchhoff's
junction rule states that the sum of the currents into any junction must be
zero.
Kirchhoff's
loop rule states that the sum of potential differences around any loop must be
zero.
Deflection
is proportional to current in a d'Arsonval galvonometer.
A
galvanometer with a shunt resistor is an ammeter and should have low
resistance.
A
galvanometer with a resistor in series is a voltmeter and should have high
resistance.
Capacitor
charged by battery with resistor in series:
q = C*e*(1
- e-t/RC), I = (e/R)*e-t/RC
The
time constant t
= RC is time for charge to get within 1/e of its final value.
Capacitor
discharge: q = C*e*(e-t/RC),
I = (e/R)*(1
- e-t/RC)