Physics and Math Flashcards
vectors
physical qualities with a magnitude and direction.
examples: displacement, velocity, acceleration and force.
scalars
quantities without direction.
vector addition
tip-to-tail-method or can be broken into component parts and use pythagorean theorem.
vector subtraction
change the direction of the subtracted vector, and do tip-to-tail-addition
vector multiplication
by scalar: changes the magnitude and may reverse the direction
dot product
results in a Scalar quantity.
cross product
results in a new vector. direction of the new vector can be found using the right hand rule.
free body diagrams
representation of the forces acting on an object.
translational equilibrium
occurs in the absence of any net forces acting on an object
rotational equilibrium
occurs in absence of any net torques acting on an object. center mass is the most commonly used pivot point.
displacement
vector representation of a change in position. path independent
Velocity
vector representation of a change in DISPLACEMENT with respect to time
instantaneous velocity
change displacement over time as time approaches 0.
instantaneous speed
magnitude of instantaneous velocity vector
force
any push or pull that has the result in an acceleration
gravity
attractive force between two objects as a result of their masses
Friction
force that opposes motion as a function of electrostatic interactions at the surfaces between two objects.
static friction
stationary objects
kinetic friction
sliding objects
mass
measure of inertia of an object – its amount of material
weight
force experienced by a given mass due to the gravitational attraction to the Earth.
acceleration
vector representation of the change in velocity over time.
torque
twisting force that causes rotation
POS = counterclockwise NEG = clockwise
Newton’s First law
an object will remain at rest or move with a constant velocity if there is no net force on the object.
F=ma=0 if the at rest or constant velocity
Newton’s second law
any acceleration is the result of the net force > 0
F=ma
Newton’s third law
two objects interacting with one another experience equal and opposite forces as a result of their interaction
Fab= -Fba
linear motion
includes free fall and motion where velocity and acceleration vectors are parallel and antiparallel
projectile
contains both and x and y component. assuming negligible air resistance, only force acting the object is gravity. X velocity is constant throughout
inclined planes
force components:
parallel to ramp use sin theta. “sin is sliding down the slide”
perpendicular to the ramp use costheta.
circular motion
best thought of as having radial and tangential dimensions.
centripetal force vector points radially inward, the instantaneous velocity vector points tangentially.
structural proteins
property of a system that enables it to do something or make something happen, including the capacity to do work.
kinetic energy
energy associated with the movement of objects. it depends on the mass and speed squared.
potential energy
energy stored within a system.
gravitational potential energy
related to the mass of an object and its height above
a zero point.
elastic potential energy
related to the spring constant and the degree of stretch or compression of a spring squared.
chemical potential energy
energy stored in the bonds of compounds
conservative forces
path independent and do not dissipate the mechanical energy system.
examples: gravity and electrostatic forces
nonconservative forces
path dependent and cause dissipation of mechanical energy from a system
examples: friction, air resistance, and vicious drag
work
process where energy is transferred from one system to another vis dot product of force and displacement
power
rate at which work is done or energy is transferred.
si unit is watts
Work energy theorem
when net work is done on or by a system, the system’s kinetic energy will change by the same amount.
mechanical advantage
factor by which a simple machine multiplies the input force to accomplish work.
input force is reduced and the distance through which the reduced input force must be applied is increased by the same factor.
MA of an inlined plane
MA = length of incline/height of incline
simple machines
inclined plane, wedge, wheel and axle, lever, pulley and screw
efficiency
ratio of the machine’s work output to the work input when nonconservative forces are taken into account
mechanical advantage = Fout/Fin
Thermal Equilibrium
systems have the same KE and same temperature. no heat transfer.
Temperature
average kinetic energy of particle that make up a substance.
thermal expansion
describes how a substance changes in length or volume as a function of change in temperature,
isolated system
do not exchange matter or energy with surroundings.
closed system
exchange energy but not matter with surroundings.
open system
exchange both energy and matter with surroundings.
state functions
pathway independent and are not themselves defined by the process.
include: pressure, density, temp, volume, enthalpy, internal energy, Gibbs free energy, and entropy.
process function
describe the pathway from one equilibrium state to another. Include: work and heat
0th Law of Thermodynamics
thermal equilibrium, temperature, and thermal expansion.
1st Law of Thermodynamics
statement of conservation of energy. total energy of the universe can never decrease or increase.
(delta)U = Q -W
(delta)U = change in system's internal energy. Q = energy transferred into system as heat. W = work done by the system.
Heat
process by which energy transfer between two objects at different temperatures that occurs until the two objects come into thermal equilibrium (reach the same temperature).
specific heat
amount of energy necessary to raise one gram of substance by 1 degree Celsius or 1 kelvin.
heat of transformation
energy required for a phase change of a substance. (temperature does not change during the transformation)
Processes with constant variable
isobaric
isothermal
adiabatic
isovolumetric
isobaric
pressure is constant
(delta)P=0
Isothermal
temperature is constant, (delta) U = 0
adiabatic
No heat is changed, Q=0
isovolumetric (isochoric)
volume is constant, (delta)V = 0. so work = 0
2nd Law of Thermodynamics
in a closed system, up to and including the universe, energy will spontaneously and irreversibly go from being localized to spread out.
entropy
measure of how much energy has spread out or how spread out energy has become.
Logarithm rules
1) Log of 1 is always 0.
2) The log of the base number is always 1.
3) So long as the base numbers are the same, the log of two factors equals the sum of the log of the individual factors.
4) Likewise, the log of a fraction equals the difference between the log of the dividend and the log of the divisor.
Heat
the transfer of energy based on a temperature difference between two objects.
Temperature
a measure of the average energy due to motion of particles in an object (i.e., a cold object has slow-moving particles while a hot object has fast-moving particles)
Heat capacity
heat required to raise the temperature of an object by a certain unit of temperature
joules
unit of energy
kelvins
unit of tempertature
specific heat
the amount of heat required to raise one gram of an object by one degree Kelvin (or Celsius).
phase changes
Ice is the solid form of water, and the process of converting ice to water requires heat. Similarly, the process of converting water to water vapor (the gaseous form of water) requires heat.
often represented by phase change diagrams
thin lens equation
relates to different lengths associated with geometric optics: 1) focal length 2) object distance 3) image distance
focal length (f)
distance between the focal point and center of lens or mirror
object length
distance between the object and center of lens or mirror
image distance
distance between image and center of mirror
Positive focal lengths
characteristic of concave mirrors and converging lenses
negative focal lengths
characteristic of convex mirrors and diverging lenses.
Positive object distances
occur when the object is in front of the mirror or lens, and negative object distances occur when the object is behind.
positive image distance
mage is in front of the mirror or behind a lens.Such an image is referred to as a real image and is always inverted.
negative image distance
the image is behind the mirror or in front of a lens.Such an image is a virtual image and is always upright.
phase change equation
q=mL
q=heat gained or lost from the substance
m=mass of the substance
L=latent heat or heat of transformation of substance
heat of transformation
intrinsic property of a substance.
defines the energy needed to generate a phase change.
heat of fusion
heat of transformation constant for a solid to liquid transformation
heat of vaporization
heat of transformation constant for a liquid to gas transformation.
heat of transfer
can occur in three ways:
1) conduction
2) convection
3) radiation
conduction
direct transfer of heat through contact and without movement of the objects
convection
transfer of heat through the motion of a liquid or gas over another object
radiation
indirect transfer of heat through electromagnetic waves that does not require the two objects to be in contact
thermal expansion
temperature changes in solid objects can change their length.
Solid objects tend to increase in length when they are heated up
railroad example and wiggle room.
coefficient of linear expansion
constant intrinsic to a specific material.
four laws of thermodynamics
1) zeroth law of thermodynamics
2) first law of thermodynamics
3) second law of thermodynamics
4) third law of thermodynamics states
State functions
properties that do not depend on the path taken to reach a value and depend only on the current state of the system.
Examples of state functions are mass, pressure, temperature, volume, Gibbs free energy, enthalpy, entropy, among others.
Path functions
depend on the path taken to reach a certain value.
Examples of path functions include heat and work.
Types of systems
1) open systems
2) closed systems
3) isolated systems
open systems
can exchange both matter and energy with the environment.
closed systems
can exchange energy, but not matter, with the environment.
isolated systems
can exchange neither energy nor matter with the environment.
four thermodynamic processes
isothermal, adiabatic, isovolumetric, and isobaric.
Isothermal processes
constant temperature, and as we discussed earlier, and therefore ∆U = 0.
adiabatic processes
heat is not exchanged and Q = 0.
isovolumetric processes
volume cannot change, work cannot be done, and therefore W = 0.
isobaric processes
pressure is constant, but this does not affect our ∆U = Q – W equation.
kinematics
science of how objects move.
Displacement
a change in position, written as Δx.
Velocity
a change in position over a change in time, written v=Δx/Δt.
Acceleration
a change in velocity over a change in time, written a = Δv/Δt.
Vector
a quantity that has both magnitude and direction
Projectile motion
the two-dimensional motion of something under the influence of gravity.
Acceleration due to gravity
the vertical acceleration felt by objects on earth. Equals -9.8 m/s2.
Circular motion
the motion of an object that is moving in a circle.
Angular displacement
the change in angle of an object’s location, written Δθ.
Angular velocity
rate of change of angular displacement, written ω=Δθ/Δt
Angular acceleration
change of angular velocity over a change in time, written α=Δω/Δt.
Period
the amount of time it takes for an object in circular motion to complete one orbit
Frequency
the number of orbits completed in one second by an object in circular motion
Centripetal acceleration
linear acceleration that points towards the center of the circle
Tangential velocity
linear velocity of the object moving in a circle
Inclined planes
slope that changes the direction of the acceleration due to gravity
Torque
force applied to an object that pivots around a point; causes angular acceleration.
Force
push or pull that makes something accelerate if unopposed and is measured in Newtons
Vector
quantity that has both magnitude and direction.
Gravitational force
the force between any two masses
Weight
word that describes how hard gravity pulls down on something and equals the gravitational force on the object
Mass
amount of matter in something and is measured in kilograms.
Friction
force that opposes sliding motion.
Normal force
force that a surface applies to an object on top of it and is always perpendicular to the surface
Coefficient of static friction
when multiplied by the normal force, gives the maximum resistance friction will give before an object begins to move.
Coefficient of kinetic friction
when multiplied by the normal force, gives the constant friction force that opposes the movement
Newton’s first law
objects in motion will stay in motion, and objects at rest will stay at rest, unless forces act on them
Newton’s second law
acceleration of an object is proportional to the net force on it and inversely proportional to its mass
Newton’s third law
for every action, there is an equal and opposite reaction
Net force
final sum of all the initial forces
Displacement
change in an object’s position
velocity
change in an object’s position over a change in time
acceleration
change in an object’s velocity over a change in time
Conservative force
force that doesn’t dissipate energy, and work done by it is path-independent
Non-conservative force
force that does dissipate energy, and work done by it is path-dependent
Energy
amount of activity in something now or is predisposed to have in the future
Translational kinetic energy
energy in an object that is moving, or has a velocity
Rotational kinetic energy
energy in an object that is rotating
Potential energy
energy of an object that has the potential to be in motion.
Gravitational potential energy
potential energy of an object due to gravity
Elastic potential energy
potential energy of a stretched or compressed spring
Electric potential energy
potential energy of a charge in an electric field
Thermal energy
energy from an object’s temperature, such as microscopic kinetic energy
Conservation of energy
energy isn’t created or destroyed, and in a closed system, you only gain or lose energy from the work put into the system
work
transfer of energy caused by a force
Work-kinetic energy theorem
work put into an object equals its change in kinetic energy
Power
amount of energy transferred per unit time, or work divided by time
Mechanical advantage
how beneficial it is to use a certain simple machine
Fluid
substance that will flow under any shear stress; includes liquids, gases, and plasmas
Shear stress
external force that acts coplanar to the material’s cross-section
Density
object’s mass per unit volume
Specific gravity
ratio of a fluid’s density to that of water
Buoyancy
force on a floating object that opposes gravity
Archimedes’ principle
buoyant force on a suspended object is equal to the weight of the fluid it displaces
Hydrostatic pressure
pressure resulting from all stresses on an object at rest in a fluid
Gauge pressure
pressure difference between the surface of a fluid and a submerged point
Absolute pressure
gauge pressure plus the atmospheric pressure
Atmospheric pressure
pressure due to Earth’s atmosphere; 1 atm = 101,000 Pa = 760 mmHg
Pascal’s law
pressure applied to a liquid is distributed evenly across the liquid
Work
energy transferred by a force applied over a distance
Viscosity
measure of the resistance a fluid has against stresses; a measure of the “internal friction” or “thickness” of a fluid
Poiseuille flow
flow of a viscous fluid in a pipe whose front takes on a parabolic shape
Incompressibility
approximation often used for fluids; implies a constant volume flow rate
Laminar flow
smooth flow caused by low-velocity moving fluids
Turbulent flow
chaotic flow characterized by eddies caused by high-velocity moving fluids
Surface tension
result of strong surface bonds that may allow liquids to form droplets or hold light objects
Dynamic pressure
pressure from moving fluids, or the kinetic energy per unit volume
Bernoulli’s equation
form of energy conservation that conserves the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume
Venturi effect
describes a fluid’s increase in velocity and decrease in pressure when it enters a constriction
Pitot tube
device that measures flow velocity by monitoring pressure on a fluid in a tube
Electrostatics
study of electromagnetic phenomena of stationary charges
Charge
physical property of matter that causes it to feel a force in an electric field
Elementary charge
proton or electron; the smallest possible units of charge; 1.6 x 10^(-19) C
Charge conservation
charge is neither created nor destroyed; it only moves around
Coulomb’s law
the force between two charges
Electric field
region in which a charge will feel a force
Field lines
collection of straight arrows used to represent electric fields
Induced charge
charge distribution resulting from placing a conductor in an electric field
Conductor
a material that allows charge to move freely
Electric potential
amount of work needed to move a charge a certain distance inside of an electric field
Electric potential energy
potential energy of a charge inside of an electric potential
Equipotential lines
contour lines of the electric potential
Circuit
closed path that allows current to flow from one place to another
Voltage
a difference in potential between two points in a circuit
Electromotive force
action of converting non-electric energy into electric energy
Internal resistance
material constraints of the battery that make it hard to produce voltage
Induced voltage
voltage caused by a change in magnetic flux through a loop of wire over a change in time
Electrical current
rate of flow of charge past a given point
Resistance
how hard it is for current to flow through a material
Resistivity
property of a material that determines the resistance of a piece of that material
In series
when circuit components are directly connected by a wire and share a current
In parallel
when circuit components are on alternate branches of wire and share a voltage
Equivalent resistance
single resistance equivalent to the combination of all resistances in the circuit
Equivalent capacitance
a single capacitance equivalent to the combination of all capacitances in the circuit
Ohm’s law
law that says current is directly proportional to voltage and inversely proportional to resistance
Capacitors
devices used to store charge
RC circuit
a circuit with a capacitor
Capacitance
the ability of a capacitor to store charge
Dielectrics
materials that are placed in between the plates of a capacitor
Ammeter
device that measures the current of a wire
Voltmeter
device that measures the voltage across a certain section of wire
Conductivity
a measure of how easy it is for current to flow through a material
Metallic conductivity
conductivity resulting from the presence of unbound valence electrons in metals
Electrolyte solution
conducting solutions made of polarized molecules that have been dissolved in water
Magnetism
concerns moving charges
Magnetic field
a region of space where a moving charge feels a force
Lorentz force
force on a charge moving in a magnetic field
Right-hand rule
shortcut used to find the direction of vector cross products
Biot-Savart law
gives the magnetic field created by a current
Solenoid
current-carrying coil of wire
light
electromagnetic wave of any wavelength
visible light
light you can see, at wavelengths of about 400-700 nm
electromagnetic wave
wave that is made of perpendicularly oscillating electric and magnetic fields
speed of light
speed at which light travels in a vacuum; equal to 3 x 10^8 m/s
photon
massless particle that represents a discrete unit (or a “quantum”) of light
wave-particle duality
light exhibits properties of both particles and waves
opacity
measure of light’s ability to penetrate a given object, or the ability of an object to transmit light
transparent
describes an object that allows all light to pass through it
translucent
describes an object that allows some light to pass through it
Opaque
describes an object that allows no light to pass through it
Reflection
when light bounces off of a surface
Specular reflection
when light reflects off a smooth surface at a definite angle (equal to the angle of incidence)
Angle of incidence
the angle at which a ray of light hits a surface
Angle of reflection
the angle at which a ray of light is reflected off a surface
Diffuse reflection
occurs when light bounces off a rough surface at a random angle
Index of refraction
the extent to which a material bends light that it transmits
Snell’s law
determines the angle of refraction at a boundary between two materials
Total internal reflection
when the angle of incidence is small enough for all light to be reflected
critical angle
smallest possible angle (from vertical) at which total internal reflection occurs
Dispersion
organized separation of different frequency light due to frequency-dependent indices of refraction
Mirror
an object that perfectly reflects light
Plane mirror
a flat mirror that produces specular reflection and preserves the position of reflected images
concave mirror
a mirror that focuses, or makes converge, incident light
focal point
the point at which a uniform field of light is focused by a concave mirror
convex mirror
a mirror that scatters, or makes diverge, incident light
Spherical Mirror
a mirror that has circular curvature
Center of Curvature
point equidistant from all points on the spherical mirror
real image
image formed by the focus points of converging light. Always inverted
virtual image
image formed by inferred focus points of diverging light rays. Not inverted
Magnification
how much an optical device changes the apparent size of an object
Focal length
distance between the center of a curved mirror and its focus point
Lens aberration
the imprecision of focal lengths of realistic lenses
Photon energy
discretized unit of light energy absorbed by objects
Constructive interference
when waves are in phase and combine to make a larger wave
Destructive interference
when waves are out of phase and cancel out
Coherent
describes light sources that maintain the same phase relationship
Monochromatic
Describes light that is only one color or frequency
X-ray diffraction
a technique for determining the atomic or molecular structure of a material
Polarized light
light whose electric fields all oscillate in the same plane
Selective absorption
a technique that uses a polarizer to filter out light that isn’t polarized in a certain direction
Polarizing angles
angles at which all reflected light is polarized
Double refraction
when a polarization-dependent index of refraction splits incident up into differently polarized beams of light
Optically active molecules
molecules that rotate incident light
Doppler effect
describes a change in frequency of a wave that is the result of a relative motion between a wave source and its observer
Blue shift
when a source traveling towards you makes the frequency seem to be higher than it really is
Red shift
when a source traveling away from you makes the frequency seem to be lower than it really is
periodic motion
any motion that repeats itself
amplitude
maximum displacement from rest (or displacement=0); always given in units of a displacement
equilibrium position
point in space at which an object’s displacement is equal to zero
frequency
simple harmonic motion quantifies how many cycles occur in one second
Period of oscillation
the time it takes to complete one full cycle of harmonic motion
angular frequency
how many radians are passed through in one second
Transverse waves
waves with displacement perpendicular to the axis of motion; examples include waves in water and electromagnetic waves
Longitudinal waves
waves with displacement parallel to the direction of motion; examples include sound waves
intensity
power per unit area (W/m2) expended by the sound, measured in decibels
attenuation
gradual dampening of sound intensity as it propagates through a material
resonance
phenomenon that occurs when waves oscillate in a space that is equal in length to some multiple of the wave’s wavelength
atom
smallest unit of matter that can comprise a chemical element
proton
positively charged particle in the nucleus
neutron
neutrally charged particle in the nucleus
electron
negatively charged particle that orbits the nucleus
nucleon
particle in the nucleus (a proton or a neutron)
Plum pudding model
early model of the atom in which all constituent particles were distributed throughout the atom
gold foil experiment
proved the existence of a positively charged nucleus, disproving the plum pudding model
bohr model
model of the atom in which electrons orbit the nucleus in elliptical orbits; outdated but still provides reasonable approximation for the hydrogen atom
energy quantization
when there are discrete, not continuous, possible energy levels
dissociation
when an electron gains too much energy and escapes the atom
ionization energy
energy required to make the highest energy electron dissociate
atomic number
number of protons in an atom; defines the element
atomic mass
number of nucleons in an atom
isotope
variations of the same element that have different atomic masses
atomic weight
average atomic mass of all the natural isotopes of an element
strong nuclear force
force that binds protons and neutrons in the nucleus
binding energy
energy required to separate the nucleons of an atom
mass defect
difference in predicted and experimental mass due to e=mc^2
experimental mass
measured mass of an atom
predicted mass
mass calculated from adding the individual weights of nucleons
fission
process that splits a nucleus into two smaller nuclei
fusion
process that fuses multiple nuclei into a single nucleus
alpha decay
radioactive decay in which a nucleus emits an alpha particle at a low speed
alpha particle
particle made of two protons and two neutrons, basically a helium nucleus
beta decay
radioactive decay in which a nucleus emits a beta particle at a high speed
beta particle
a fast-moving electron
gamma decay
radioactive decay in which a nucleus emits a gamma photon
exponential decay
a decay that starts off fast but slows with time
half-life
time it takes for half the original sample to decay
decay constant
constant that allows you to write the half-life equation as a power of e
