# Glossary


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Glossary Entries

Word(s)

Definition

beat frequency frequency of beats produced by sound waves that differ in frequency       OpenStax
beats constructive and destructive interference of two or more frequencies of sound       OpenStax
bow wake v-shaped disturbance created when the wave source moves faster than the wave propagation speed       OpenStax
Doppler effect alteration in the observed frequency of a sound due to motion of either the source or the observer       OpenStax
Doppler shift actual change in frequency due to relative motion of source and observer       OpenStax
fundamental the lowest-frequency resonance       OpenStax
harmonics the term used to refer collectively to the fundamental and its overtones       OpenStax
hearing perception of sound       OpenStax
loudness perception of sound intensity       OpenStax
notes basic unit of music with specific names, combined to generate tunes       OpenStax
overtones all resonant frequencies higher than the fundamental       OpenStax
phon numerical unit of loudness       OpenStax
pitch perception of the frequency of a sound       OpenStax
shock wave wave front that is produced when a sound source moves faster than the speed of sound       OpenStax
sonic boom loud noise that occurs as a shock wave as it sweeps along the ground       OpenStax
sound traveling pressure wave that may be periodic; the wave can be modeled as a pressure wave or as an oscillation of molecules       OpenStax
sound intensity level unitless quantity telling you the level of the sound relative to a fixed standard       OpenStax
sound pressure level ratio of the pressure amplitude to a reference pressure       OpenStax
timbre number and relative intensity of multiple sound frequencies       OpenStax
transducer device that converts energy of a signal into measurable energy form, for example, a microphone converts sound waves into an electrical signal       OpenStax
antinode location of maximum amplitude in standing waves       OpenStax
constructive interference when two waves arrive at the same point exactly in phase; that is, the crests of the two waves are precisely aligned, as are the troughs       OpenStax
destructive interference when two identical waves arrive at the same point exactly out of phase; that is, precisely aligned crest to trough       OpenStax
fixed boundary condition when the medium at a boundary is fixed in place so it cannot move       OpenStax
free boundary condition exists when the medium at the boundary is free to move       OpenStax
fundamental frequency lowest frequency that will produce a standing wave       OpenStax
intensity (I) power per unit area       OpenStax
interference overlap of two or more waves at the same point and time       OpenStax
linear wave equation equation describing waves that result from a linear restoring force of the medium; any function that is a solution to the wave equation describes a wave moving in the positive x-direction or the negative x-direction with a constant wave speed v       OpenStax
longitudinal wave wave in which the disturbance is parallel to the direction of propagation       OpenStax
mechanical wave wave that is governed by Newton’s laws and requires a medium       OpenStax
node point where the string does not move; more generally, nodes are where the wave disturbance is zero in a standing wave       OpenStax
normal mode possible standing wave pattern for a standing wave on a string       OpenStax
overtone frequency that produces standing waves and is higher than the fundamental frequency       OpenStax
pulse single disturbance that moves through a medium, transferring energy but not mass       OpenStax
standing wave wave that can bounce back and forth through a particular region, effectively becoming stationary       OpenStax
superposition phenomenon that occurs when two or more waves arrive at the same point       OpenStax
transverse wave wave in which the disturbance is perpendicular to the direction of propagation       OpenStax
wave disturbance that moves from its source and carries energy       OpenStax
wave function mathematical model of the position of particles of the medium       OpenStax
wave number $$\frac{2 \pi}{\lambda}$$       OpenStax
wave speed magnitude of the wave velocity       OpenStax
wave velocity velocity at which the disturbance moves; also called the propagation velocity       OpenStax
wavelength distance between adjacent identical parts of a wave       OpenStax
amplitude (A) maximum displacement from the equilibrium position of an object oscillating around the equilibrium position       OpenStax
critically damped condition in which the damping of an oscillator causes it to return as quickly as possible to its equilibrium position without oscillating back and forth about this position       OpenStax
elastic potential energy potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring       OpenStax
equilibrium position position where the spring is neither stretched nor compressed       OpenStax
force constant (k) characteristic of a spring which is defined as the ratio of the force applied to the spring to the displacement caused by the force       OpenStax
frequency (f) number of events per unit of time       OpenStax
natural angular frequency angular frequency of a system oscillating in SHM       OpenStax
oscillation single fluctuation of a quantity, or repeated and regular fluctuations of a quantity, between two extreme values around an equilibrium or average value       OpenStax
overdamped condition in which damping of an oscillator causes it to return to equilibrium without oscillating; oscillator moves more slowly toward equilibrium than in the critically damped system       OpenStax
period (T) time taken to complete one oscillation       OpenStax
periodic motion motion that repeats itself at regular time intervals       OpenStax
phase shift angle, in radians, that is used in a cosine or sine function to shift the function left or right, used to match up the function with the initial conditions of data       OpenStax
physical pendulum any extended object that swings like a pendulum       OpenStax
resonance large amplitude oscillations in a system produced by a small amplitude driving force, which has a frequency equal to the natural frequency       OpenStax
restoring force force acting in opposition to the force caused by a deformation       OpenStax
simple harmonic motion (SHM) oscillatory motion in a system where the restoring force is proportional to the displacement, which acts in the direction opposite to the displacement       OpenStax
simple harmonic oscillator a device that oscillates in SHM where the restoring force is proportional to the displacement and acts in the direction opposite to the displacement       OpenStax
simple pendulum point mass, called a pendulum bob, attached to a near massless string       OpenStax
stable equilibrium point point where the net force on a system is zero, but a small displacement of the mass will cause a restoring force that points toward the equilibrium point       OpenStax
torsional pendulum any suspended object that oscillates by twisting its suspension       OpenStax
underdamped condition in which damping of an oscillator causes the amplitude of oscillations of a damped harmonic oscillator to decrease over time, eventually approaching zero       OpenStax
absolute pressure sum of gauge pressure and atmospheric pressure       OpenStax
Achimedes' principle buoyant force on an object equals the weight of the fluid it displaces       OpenStax
Bernoulli's equation equation resulting from applying conservation of energy to an incompressible frictionless fluid: $$p + \frac{1}{2} \rho v^{2} +\rho gh = constant,$$throughout the fluid       OpenStax
Bernoulli's principle Bernoulli's equation applied at constant depth:$$p_{1} + \frac{1}{2} \rho v_{1}^{2} = p_{2} + \frac{1}{2} \rho v_{2}^{2}$$       OpenStax
buoyant force net upward force on any object in any fluid due to the pressure difference at different depths       OpenStax
density mass per unit volume of a substance or object       OpenStax
flow rate abbreviated Q, it is the volume V that flows past a particular point during a time t, or Q = $$\frac{dV}{dt}$$       OpenStax
fluids liquids and gases; a fluid is a state of matter that yields to shearing forces       OpenStax
gauge pressure pressure relative to atmospheric pressure       OpenStax
hydraulic jack simple machine that uses cylinders of different diameters to distribute force       OpenStax
hydrostatic equilibrium state at which water is not flowing, or is static       OpenStax
ideal fluid fluid with negligible viscosity       OpenStax
laminar flow type of fluid flow in which layers do not mix       OpenStax
Pascal's principle change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container       OpenStax
Poiseuille's law rate of laminar flow of an incompressible fluid in a tube: $$Q = \frac{(p_{2} - p_{1}) \pi r^{4}}{8 \eta l} \ldotp$$       OpenStax
Poiseuille’s law for resistance resistance to laminar flow of an incompressible fluid in a tube: $$R = \frac{8 \eta l}{\pi r^{4}}$$       OpenStax
pressure force per unit area exerted perpendicular to the area over which the force acts       OpenStax
Reynolds number dimensionless parameter that can reveal whether a particular flow is laminar or turbulent       OpenStax
specific gravity ratio of the density of an object to a fluid (usually water)       OpenStax
turbulence fluid flow in which layers mix together via eddies and swirls       OpenStax
turbulent flow type of fluid flow in which layers mix together via eddies and swirls       OpenStax
viscosity measure of the internal friction in a fluid       OpenStax
action-at-a-distance force type of force exerted without physical contact       OpenStax
aphelion farthest point from the Sun of an orbiting body; the corresponding term for the Moon’s farthest point from Earth is the apogee       OpenStax
apparent weight reading of the weight of an object on a scale that does not account for acceleration       OpenStax
black hole mass that becomes so dense, that it collapses in on itself, creating a singularity at the center surround by an event horizon       OpenStax
escape velocity initial velocity an object needs to escape the gravitational pull of another; it is more accurately defined as the velocity of an object with zero total mechanical energy       OpenStax
event horizon location of the Schwarzschild radius and is the location near a black hole from within which no object, even light, can escape       OpenStax
gravitational field vector field that surrounds the mass creating the field; the field is represented by field lines, in which the direction of the field is tangent to the lines, and the magnitude (or field strength) is inversely proportional to the spacing of the lines; other masses respond to this field       OpenStax
gravitationally bound two object are gravitationally bound if their orbits are closed; gravitationally bound systems have a negative total mechanical energy       OpenStax
Kepler’s first law law stating that every planet moves along an ellipse, with the Sun located at a focus of the ellipse       OpenStax
Kepler’s second law law stating that a planet sweeps out equal areas in equal times, meaning it has a constant areal velocity       OpenStax
Kepler’s third law law stating that the square of the period is proportional to the cube of the semi-major axis of the orbit       OpenStax
neap tide low tide created when the Moon and the Sun form a right triangle with Earth       OpenStax
neutron star most compact object known—outside of a black hole itself       OpenStax
Newton’s law of gravitation every mass attracts every other mass with a force proportional to the product of their masses, inversely proportional to the square of the distance between them, and with direction along the line connecting the center of mass of each       OpenStax
non-Euclidean geometry geometry of curved space, describing the relationships among angles and lines on the surface of a sphere, hyperboloid, etc.       OpenStax
orbital period time required for a satellite to complete one orbit       OpenStax
orbital speed speed of a satellite in a circular orbit; it can be also be used for the instantaneous speed for noncircular orbits in which the speed is not constant       OpenStax
perihelion point of closest approach to the Sun of an orbiting body; the corresponding term for the Moon’s closest approach to Earth is the perigee       OpenStax
principle of equivalence part of the general theory of relativity, it states that there no difference between free fall and being weightless, or a uniform gravitational field and uniform acceleration       OpenStax
Schwarzschild radius critical radius (RS) such that if a mass were compressed to the extent that its radius becomes less than the Schwarzschild radius, then the mass will collapse to a singularity, and anything that passes inside that radius cannot escape       OpenStax
space-time concept of space-time is that time is essentially another coordinate that is treated the same way as any individual spatial coordinate; in the equations that represent both special and general relativity, time appears in the same context as do the spatial coordinates       OpenStax
spring tide high tide created when the Moon, the Sun, and Earth are along one line       OpenStax
theory of general relativity Einstein’s theory for gravitation and accelerated reference frames; in this theory, gravitation is the result of mass and energy distorting the space-time around it; it is also often referred to as Einstein’s theory of gravity       OpenStax
tidal force difference between the gravitational force at the center of a body and that at any other location on the body; the tidal force stretches the body       OpenStax
universal gravitational constant constant representing the strength of the gravitational force, that is believed to be the same throughout the universe       OpenStax
breaking stress (ultimate stress) value of stress at the fracture point       OpenStax
bulk modulus elastic modulus for the bulk stress       OpenStax
bulk strain (or volume strain) strain under the bulk stress, given as fractional change in volume       OpenStax
bulk stress (or volume stress) stress caused by compressive forces, in all directions       OpenStax
center of gravity point where the weight vector is attached       OpenStax
compressibility reciprocal of the bulk modulus       OpenStax
compressive strain strain that occurs when forces are contracting an object, causing its shortening       OpenStax
compressive stress stress caused by compressive forces, only in one direction       OpenStax
elastic object that comes back to its original size and shape when the load is no longer present       OpenStax
elastic limit stress value beyond which material no longer behaves elastically and becomes permanently deformed       OpenStax
elastic modulus proportionality constant in linear relation between stress and strain, in SI pascals       OpenStax
equilibrium body is in equilibrium when its linear and angular accelerations are both zero relative to an inertial frame of reference       OpenStax
first equilibrium condition expresses translational equilibrium; all external forces acting on the body balance out and their vector sum is zero       OpenStax
gravitational torque torque on the body caused by its weight; it occurs when the center of gravity of the body is not located on the axis of rotation       OpenStax
linearity limit (proportionality limit) largest stress value beyond which stress is no longer proportional to strain       OpenStax
normal pressure pressure of one atmosphere, serves as a reference level for pressure       OpenStax
pascal (Pa) SI unit of stress, SI unit of pressure       OpenStax
plastic behavior material deforms irreversibly, does not go back to its original shape and size when load is removed and stress vanishes       OpenStax
pressure force pressing in normal direction on a surface per the surface area, the bulk stress in fluids       OpenStax
second equilibrium condition expresses rotational equilibrium; all torques due to external forces acting on the body balance out and their vector sum is zero       OpenStax
shear modulus elastic modulus for shear stress       OpenStax
shear strain strain caused by shear stress       OpenStax
shear stress stress caused by shearing forces       OpenStax
static equilibrium body is in static equilibrium when it is at rest in our selected inertial frame of reference       OpenStax
strain dimensionless quantity that gives the amount of deformation of an object or medium under stress       OpenStax
stress quantity that contains information about the magnitude of force causing deformation, defined as force per unit area       OpenStax
stress-strain diagram graph showing the relationship between stress and strain, characteristic of a material       OpenStax
tensile strain strain under tensile stress, given as fractional change in length, which occurs when forces are stretching an object, causing its elongation       OpenStax
tensile stress stress caused by tensile forces, only in one direction, which occurs when forces are stretching an object, causing its elongation       OpenStax
Young’s modulus elastic modulus for tensile or compressive stress       OpenStax
angular momentum rotational analog of linear momentum, found by taking the product of moment of inertia and angular velocity       OpenStax
law of conservation of angular momentum angular momentum is conserved, that is, the initial angular momentum is equal to the final angular momentum when no external torque is applied to the system       OpenStax
precession circular motion of the pole of the axis of a spinning object around another axis due to a torque       OpenStax
rolling motion combination of rotational and translational motion with or without slipping       OpenStax
angular acceleration time rate of change of angular velocity       OpenStax
angular position angle a body has rotated through in a fixed coordinate system       OpenStax
angular velocity time rate of change of angular position       OpenStax
instantaneous angular acceleration derivative of angular velocity with respect to time       OpenStax
instantaneous angular velocity derivative of angular position with respect to time       OpenStax
kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time       OpenStax
lever arm perpendicular distance from the line that the force vector lies on to a given axis       OpenStax
linear mass density the mass per unit length λ of a one dimensional object       OpenStax
moment of inertia rotational mass of rigid bodies that relates to how easy or hard it will be to change the angular velocity of the rotating rigid body       OpenStax
Newton’s second law for rotation sum of the torques on a rotating system equals its moment of inertia times its angular acceleration       OpenStax
parallel axis axis of rotation that is parallel to an axis about which the moment of inertia of an object is known       OpenStax
parallel-axis theorem if the moment of inertia is known for a given axis, it can be found for any axis parallel to it       OpenStax
rotational dynamics analysis of rotational motion using the net torque and moment of inertia to find the angular acceleration       OpenStax
rotational kinetic energy kinetic energy due to the rotation of an object; this is part of its total kinetic energy       OpenStax
rotational work work done on a rigid body due to the sum of the torques integrated over the angle through with the body rotates       OpenStax
surface mass density mass per unit area $$\sigma$$ of a two dimensional object       OpenStax
torque cross product of a force and a lever arm to a given axis       OpenStax
total linear acceleration vector sum of the centripetal acceleration vector and the tangential acceleration vector       OpenStax
work-energy theorem for rotation the total rotational work done on a rigid body is equal to the change in rotational kinetic energy of the body       OpenStax
center of mass weighted average position of the mass       OpenStax
closed system system for which the mass is constant and the net external force on the system is zero       OpenStax
elastic collision that conserves kinetic energy       OpenStax
explosion single object breaks up into multiple objects; kinetic energy is not conserved in explosions       OpenStax
external force force applied to an extended object that changes the momentum of the extended object as a whole       OpenStax
impulse effect of applying a force on a system for a time interval; this time interval is usually small, but does not have to be       OpenStax
impulse-momentum theorem change of momentum of a system is equal to the impulse applied to the system       OpenStax
inelastic collision that does not conserve kinetic energy       OpenStax
internal force force that the simple particles that make up an extended object exert on each other. Internal forces can be attractive or repulsive       OpenStax
Law of Conservation of Momentum total momentum of a closed system cannot change       OpenStax
linear mass density $$\lambda$$, expressed as the number of kilograms of material per meter       OpenStax
momentum measure of the quantity of motion that an object has; it takes into account both how fast the object is moving, and its mass; specifically, it is the product of mass and velocity; it is a vector quantity       OpenStax
perfectly inelastic collision after which all objects are motionless, the final kinetic energy is zero, and the loss of kinetic energy is a maximum       OpenStax
rocket equation derived by the Soviet physicist Konstantin Tsiolkovsky in 1897, it gives us the change of velocity that the rocket obtains from burning a mass of fuel that decreases the total rocket mass from mi down to m       OpenStax
system object or collection of objects whose motion is currently under investigation; however, your system is defined at the start of the problem, you must keep that definition for the entire problem       OpenStax
conservative force force that does work independent of path       OpenStax
conserved quantity one that cannot be created or destroyed, but may be transformed between different forms of itself       OpenStax
energy conservation total energy of an isolated system is constant       OpenStax
equilibrium point position where the assumed conservative, net force on a particle, given by the slope of its potential energy curve, is zero       OpenStax
exact differential is the total differential of a function and requires the use of partial derivatives if the function involves more than one dimension       OpenStax
mechanical energy sum of the kinetic and potential energies       OpenStax
non-conservative force force that does work that depends on path       OpenStax
non-renewable energy source that is not renewable, but is depleted by human consumption       OpenStax
potential energy function of position, energy possessed by an object relative to the system considered       OpenStax
potential energy diagram graph of a particle’s potential energy as a function of position       OpenStax
potential energy difference negative of the work done acting between two points in space       OpenStax
renewable energy source that is replenished by natural processes, over human time scales       OpenStax
turning point position where the velocity of a particle, in one-dimensional motion, changes sign       OpenStax
average power work done in a time interval divided by the time interval       OpenStax
kinetic energy energy of motion, one-half an object’s mass times the square of its speed       OpenStax
net work work done by all the forces acting on an object       OpenStax
power (or instantaneous power) rate of doing work       OpenStax
work done when a force acts on something that undergoes a displacement from one position to another       OpenStax
work done by a force integral, from the initial position to the final position, of the dot product of the force and the infinitesimal displacement along the path over which the force acts       OpenStax
work-energy theorem net work done on a particle is equal to the change in its kinetic energy       OpenStax
banked curve curve in a road that is sloping in a manner that helps a vehicle negotiate the curve       OpenStax
centripetal force any net force causing uniform circular motion       OpenStax
Coriolis force inertial force causing the apparent deflection of moving objects when viewed in a rotating frame of reference       OpenStax
drag force force that always opposes the motion of an object in a fluid; unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid       OpenStax
friction force that opposes relative motion or attempts at motion between systems in contact       OpenStax
ideal banking sloping of a curve in a road, where the angle of the slope allows the vehicle to negotiate the curve at a certain speed without the aid of friction between the tires and the road; the net external force on the vehicle equals the horizontal centripetal force in the absence of friction       OpenStax
inertial force force that has no physical origin       OpenStax
kinetic friction force that opposes the motion of two systems that are in contact and moving relative to each other       OpenStax
noninertial frame of reference accelerated frame of reference       OpenStax
static friction force that opposes the motion of two systems that are in contact and are not moving relative to each other       OpenStax
terminal velocity constant velocity achieved by a falling object, which occurs when the weight of the object is balanced by the upward drag force       OpenStax
dynamics study of how forces affect the motion of objects and systems       OpenStax
external force force acting on an object or system that originates outside of the object or system       OpenStax
force push or pull on an object with a specific magnitude and direction; can be represented by vectors or expressed as a multiple of a standard force       OpenStax
free fall situation in which the only force acting on an object is gravity       OpenStax
free-body diagram sketch showing all external forces acting on an object or system; the system is represented by a single isolated point, and the forces are represented by vectors extending outward from that point       OpenStax
Hooke's law in a spring, a restoring force proportional to and in the opposite direction of the imposed displacement       OpenStax
inertia ability of an object to resist changes in its motion       OpenStax
inertial reference frame reference frame moving at constant velocity relative to an inertial frame is also inertial; a reference frame accelerating relative to an inertial frame is not inertial       OpenStax
law of inertia see Newton’s first law of motion       OpenStax
net external force vector sum of all external forces acting on an object or system; causes a mass to accelerate       OpenStax
newton SI unit of force; 1 N is the force needed to accelerate an object with a mass of 1 kg at a rate of 1 m/s2       OpenStax
Newton’s first law of motion body at rest remains at rest or, if in motion, remains in motion at constant velocity unless acted on by a net external force; also known as the law of inertia       OpenStax
Newton’s second law of motion acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system and is inversely proportional to its mass       OpenStax
Newton’s third law of motion whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts       OpenStax
normal force force supporting the weight of an object, or a load, that is perpendicular to the surface of contact between the load and its support; the surface applies this force to an object to support the weight of the object       OpenStax
tension pulling force that acts along a stretched flexible connector, such as a rope or cable       OpenStax
thrust reaction force that pushes a body forward in response to a backward force       OpenStax
weight force $$\vec{w}$$ due to gravity acting on an object of mass m       OpenStax
acceleration due to gravity acceleration of an object as a result of gravity       OpenStax
average acceleration the rate of change in velocity; the change in velocity over time       OpenStax
average speed the total distance traveled divided by elapsed time       OpenStax
average velocity the displacement divided by the time over which displacement occurs       OpenStax
displacement the change in position of an object       OpenStax
distance traveled the total length of the path traveled between two positions       OpenStax
elapsed time the difference between the ending time and the beginning time       OpenStax
free fall the state of movement that results from gravitational force only       OpenStax
instantaneous acceleration acceleration at a specific point in time       OpenStax
instantaneous speed the absolute value of the instantaneous velocity       OpenStax
instantaneous velocity the velocity at a specific instant or time point       OpenStax
kinematics the description of motion through properties such as position, time, velocity, and acceleration       OpenStax
position the location of an object at a particular time       OpenStax
total displacement the sum of individual displacements over a given time period       OpenStax
two-body pursuit problem a kinematics problem in which the unknowns are calculated by solving the kinematic equations simultaneously for two moving objects       OpenStax
acceleration vector instantaneous acceleration found by taking the derivative of the velocity function with respect to time in unit vector notation       OpenStax
angular frequency $$\omega$$, rate of change of an angle with which an object that is moving on a circular path       OpenStax
centripetal acceleration component of acceleration of an object moving in a circle that is directed radially inward toward the center of the circle       OpenStax
displacement vector vector from the initial position to a final position on a trajectory of a particle       OpenStax
position vector vector from the origin of a chosen coordinate system to the position of a particle in two- or threedimensional space       OpenStax
projectile motion motion of an object subject only to the acceleration of gravity       OpenStax
range maximum horizontal distance a projectile travels       OpenStax
reference frame coordinate system in which the position, velocity, and acceleration of an object at rest or moving is measured       OpenStax
relative velocity velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame       OpenStax
tangential accleration magnitude of which is the time rate of change of speed. Its direction is tangent to the circle.       OpenStax
time of flight elapsed time a projectile is in the air       OpenStax
total accleration vector sum of centripetal and tangential accelerations       OpenStax
trajectory path of a projectile through the air       OpenStax
velocity vector vector that gives the instantaneous speed and direction of a particle; tangent to the trajectory       OpenStax
accuracy the degree to which a measured value agrees with an accepted reference value for that measurement       OpenStax
base quantity physical quantity chosen by convention and practical considerations such that all other physical quantities can be expressed as algebraic combinations of them       OpenStax
base unit standard for expressing the measurement of a base quantity within a particular system of units; defined by a particular procedure used to measure the corresponding base quantity       OpenStax
conversion factor a ratio that expresses how many of one unit are equal to another unit       OpenStax
derived quantity physical quantity defined using algebraic combinations of base quantities       OpenStax
derived units units that can be calculated using algebraic combinations of the fundamental units       OpenStax
dimension expression of the dependence of a physical quantity on the base quantities as a product of powers of symbols representing the base quantities; in general, the dimension of a quantity has the form $$L^{a} M^{b} T^{c} I^{d} \Theta^{e} N^{f} J^{g}$$ for some powers a, b, c, d, e, f, and g       OpenStax
dimensionally consistent equation in which every term has the same dimensions and the arguments of any mathematical functions appearing in the equation are dimensionless       OpenStax
dimensionless quantity with a dimension of $$L^{0} M^{0} T^{0} I^{0} \Theta^{e} N^{0} J^{0}$$= 1; also called quantity of dimension 1 or a pure number       OpenStax
discrepancy the difference between the measured value and a given standard or expected value       OpenStax
English units system of measurement used in the United States; includes units of measure such as feet, gallons, and pounds       OpenStax
estimation using prior experience and sound physical reasoning to arrive at a rough idea of a quantity’s value; sometimes called an “order-of-magnitude approximation,” a “guesstimate,” a “back-of-the-envelope calculation”, or a “Fermi calculation”       OpenStax
kilogram SI unit for mass, abbreviated kg       OpenStax
law description, using concise language or a mathematical formula, of a generalized pattern in nature supported by scientific evidence and repeated experiments       OpenStax
meter SI unit for length, abbreviated m       OpenStax
method of adding percents the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation       OpenStax
metric system system in which values can be calculated in factors of 10       OpenStax
model representation of something often too difficult (or impossible) to display directly       OpenStax
order of magnitude the size of a quantity as it relates to a power of 10       OpenStax
percent uncertainty the ratio of the uncertainty of a measurement to the measured value, expressed as a percentage       OpenStax
physical quantity characteristic or property of an object that can be measured or calculated from other measurements       OpenStax
physics science concerned with describing the interactions of energy, matter, space, and time; especially interested in what fundamental mechanisms underlie every phenomenon       OpenStax
precision the degree to which repeated measurements agree with each other       OpenStax
second the SI unit for time, abbreviated s       OpenStax
SI units the international system of units that scientists in most countries have agreed to use; includes units such as meters, liters, and grams       OpenStax
significant figures used to express the precision of a measuring tool used to measure a value       OpenStax
theory testable explanation for patterns in nature supported by scientific evidence and verified multiple times by various groups of researchers       OpenStax
uncertainty a quantitative measure of how much measured values deviate from one another       OpenStax
units standards used for expressing and comparing measurements       OpenStax
anticommutative property change in the order of operation introduces the minus sign       OpenStax
antiparallel vectors two vectors with directions that differ by 180°       OpenStax
associative terms can be grouped in any fashion       OpenStax
commutative operations can be performed in any order       OpenStax
component form of a vector a vector written as the vector sum of its components in terms of unit vectors       OpenStax
corkscrew right-hand rule a rule used to determine the direction of the vector product       OpenStax
cross product the result of the vector multiplication of vectors is a vector called a cross product; also called a vector product       OpenStax
difference of two vectors vector sum of the first vector with the vector antiparallel to the second       OpenStax
direction angle in a plane, an angle between the positive direction of the x-axis and the vector, measured counterclockwise from the axis to the vector       OpenStax
displacement change in position       OpenStax
distributive multiplication can be distributed over terms in summation       OpenStax
dot product the result of the scalar multiplication of two vectors is a scalar called a dot product; also called a scalar product       OpenStax
equal vectors two vectors are equal if and only if all their corresponding components are equal; alternately, two parallel vectors of equal magnitudes       OpenStax
magnitude length of a vector       OpenStax
null vector a vector with all its components equal to zero       OpenStax
orthogonal vectors two vectors with directions that differ by exactly 90°, synonymous with perpendicular vectors       OpenStax
parallel vectors two vectors with exactly the same direction angles       OpenStax
parallelogram rule geometric construction of the vector sum in a plane       OpenStax
polar coordinate system an orthogonal coordinate system where location in a plane is given by polar coordinates       OpenStax
polar coordinates a radial coordinate and an angle       OpenStax
radical coordinate distance to the origin in a polar coordinate system       OpenStax
resultant vector vector sum of two (or more) vectors       OpenStax
scalar a number, synonymous with a scalar quantity in physics       OpenStax
scalar component a number that multiplies a unit vector in a vector component of a vector       OpenStax
scalar equation equation in which the left-hand and right-hand sides are numbers       OpenStax
scalar product the result of the scalar multiplication of two vectors is a scalar called a scalar product; also called a dot product       OpenStax
scalar quantity quantity that can be specified completely by a single number with an appropriate physical unit       OpenStax
tail-to-head geometric construction geometric construction for drawing the resultant vector of many vectors       OpenStax
unit vector vector of a unit magnitude that specifies direction; has no physical unit       OpenStax
unit vectors of the axes unit vectors that define orthogonal directions in a plane or in space       OpenStax
vector mathematical object with magnitude and direction       OpenStax
vector components orthogonal components of a vector; a vector is the vector sum of its vector components       OpenStax
vector equation equation in which the left-hand and right-hand sides are vectors       OpenStax
vector product the result of the vector multiplication of vectors is a vector called a vector product; also called a cross product       OpenStax
vector quantity physical quantity described by a mathematical vector—that is, by specifying both its magnitude and its direction; synonymous with a vector in physics       OpenStax
vector sum resultant of the combination of two (or more) vectors       OpenStax