Coefficient of kinetic friction

Absolute zero

The lowest theoretical temperature a material can have, where the molecules that make up the material have no kinetic energy. Absolute zero is reached at 0 K or –273º C.

Acceleration

A vector quantity defined as the rate of change of the velocity vector with time.

Amplitude

In reference to oscillation, amplitude is the maximum displacement of the oscillator from its equilibrium position. Amplitude tells how far an oscillator is swinging back and forth. In periodic motion, amplitude is the maximum displacement in each cycle of a system in periodic motion. The precise definition of amplitude depends on the particular situation: in the case of a stretched string it would be measured in meters, whereas for sound waves it would be measured in units of pressure.

Angle of incidence

When a light ray strikes a surface, the angle of incidence is the angle between the incident ray and the normal.

Angle of reflection

The angle between a reflected ray and the normal.

Angle of refraction

The angle between a refracted ray and the line normal to the surface.

Angular acceleration

A vector quantity, , equal to the rate of change of the angular velocity vector with time. It is typically given in units of rad/s².

Angular velocity

A vector quantity, , that reflects the change of angular displacement with time, and is typically given in units of rad/s. To find the direction of the angular velocity vector, take your right hand and curl your fingers along the particle or body’s direction of rotation. Your thumb then points in the direction of the body’s angular velocity.

Atom

The building blocks of all matter, atoms are made up of a nucleus consisting of protons and neutrons, and a number of electrons that orbit the nucleus. An electrically neutral atom has as many protons as it has electrons.

Atomic number

A number, Z, associated with the number of protons in the nucleus of an atom. Every element can be defined in s of its atomic number, since every atom of a given element has the same number of protons.

Boiling point

The temperature at which a material will change phase from liquid to gas or gas to liquid.

Boyle’s Law

For a gas held at a constant temperature, pressure and volume are inversely proportional.

Center of mass

Given the trajectory of an object or system, the center of mass is the point that has the same acceleration as the object or system as a whole would have if its mass were concentrated at that point. In terms of force, the center of mass is the point at which a given net force acting on a system will produce the same acceleration as if the system’s mass were concentrated at that point.

Centripetal acceleration

The acceleration of a body experiencing uniform circular motion. This acceleration is always directed toward the center of the circle.

Centripetal force

The force necessary to maintain a body in uniform circular motion. This force is always directed radially toward the center of the circle.

Collision

When objects collide, each object feels a force for a short amount of time. This force imparts an impulse, or changes the momentum of each of the colliding objects. The momentum of a system is conserved in all kinds of collisions. Kinetic energy is conserved in elastic collisions, but not in inelastic collisions. In a perfectly inelastic collision, the colliding objects stick together after they collide.

Conduction

Heat transfer by molecular collisions.

Conservation of momentum

The principle stating that for any isolated system, linear momentum is constant with time.

Cross product

A form of vector multiplication, where two vectors are multiplied to produce a third vector. The cross product of two vectors, A and B, separated by an angle, , is , where is a unit vector perpendicular to both A and B. To deine which direction points, you must use the right-hand rule.

Displacement

A vector quantity, commonly denoted by the vector s, which reflects an object’s change in spatial position. The displacement vector points from the object’s starting position to the object’s current position in space. If an object is moved from point A to point B in space along path AB, the magnitude of the object’s displacement is the separation of points A and B. Note that the path an object takes to get from point A to point B does not figure when deining displacement.

Distance

A scalar quantity. If an object is moved from point A to point B in space along path AB, the distance that the object has traveled is the length of the path AB. Distance is to be contrasted with displacement, which is simply a measure of the distance between points A and B, and doesn’t take into account the path followed between A and B.

Efficiency

For a heat engine, the ratio of work done by the engine to heat intake. Efficiency is never 100%.

Elastic collision

A collision in which both kinetic energy and momentum are conserved.

Electric generator

A device that converts mechanical energy to electrical energy by rotating a coil in a magnetic field; sometimes called a “dynamo.”

Electromagnetic wave

A transverse traveling wave created by the oscillations of an electric field and a magnetic field. Electromagnetic waves travel at the speed of light, m/s. Examples include microwaves, X rays, and visible light.

Electron

A negatively charged particle that orbits the nucleus of the atom.

Energy

A conserved scalar quantity associated with the state or condition of an object or system of objects. We can roughly define energy as the capacity for an object or system to do work. There are many different types of energy, such as kinetic energy, potential energy, thermal energy, chemical energy, mechanical energy, and electrical energy.

Equilibrium

The state of a nonrotating object upon whom the net torque acting is zero.

Equilibrium position

The stable position of a system where the net force acting on the object is zero.

Faraday’s Law

A law, | | = , which states that the induced emf is the change in magnetic flux in a certain time.

First Law of Thermodynamics

Essentially a restatement of energy conservation, it states that the change in the internal energy of a system is equal to the heat added plus the work done on the system.

Force

A push or a pull that causes an object to accelerate.

Free-body diagram

Illustrates the forces acting on an object, drawn as vectors originating from the center of the object.

Frequency

The number of cycles executed by a system in one second. Frequency is the inverse of period, f = 1/T. Frequency is measured in hertz, Hz.

Frictional force

A force caused by the roughness of two materials in contact, deformations in the materials, and a molecular attraction between the materials. Frictional forces are always parallel to the plane of contact between two surfaces and opposite the direction that the object is being pushed or pulled.

Gravitational constant

The constant of proportionality in Newton’s Law of Gravitation. It reflects the proportion of the gravitational force and , the product of two particles’ masses divided by the square of the bodies’ separation. N · m²/kg².

Half-life

The amount of time it takes for one-half of a radioactive sample to decay.

Heat

A transfer of thermal energy. We don’t speak about systems “having” heat, but about their “transferring” heat, much in the way that dynamical systems don’t “have” work, but rather “do” work.

Hooke’s Law

For an oscillating spring, the restoring force exerted by the spring is directly proportional to the displacement. That is, the more the spring is displaced, the stronger the force that will pull toward the equilibrium position. This law is expressed mathematically as F = –kx, where F is the restoring force and x is the displacement. The constant of proportionality, –k, is the spring constant.

Ideal gas law

An equation, PV = nRT, that relates the pressure, volume, temperature, and quantity of an ideal gas. An ideal gas is one that obeys the approximations laid out in the kinetic theory of gases.

Impulse

A vector quantity defined as the product of the force acting on a body multiplied by the time interval over which the force is exerted.

Index of refraction

The index of refraction n = c/v of a substance characterizes the speed of light in that substance, v. It also characterizes, by way of Snell's Law, the angle at which light refracts in that substance.

Inelastic collision

A collision in which momentum is conserved but kinetic energy is not.

Inertia

The tendency of an object to remain at a constant velocity, or its resistance to being accelerated. Newton’s First Law is alternatively called the Law of Inertia because it describes this tendency.

Instantaneous velocity

The velocity at any given instant in time. To be contrasted with average velocity, which is a measure of the change in displacement over a given time interval.

Internal energy

The energy stored in a thermodynamic system.

Isolated system

A system that no external net force acts upon. Objects within the system may exert forces upon one another, but they cannot receive any impulse from outside forces. Momentum is conserved in isolated systems.

Isotope

Atoms of the same element may have different numbers of neutrons and therefore different masses. Atoms of the same element but with different numbers of neutrons are called isotopes of the same element.

Kepler’s First Law

The path of each planet around the sun is an ellipse with the sun at one focus.

Kepler’s Second Law

If a line is drawn from the sun to the planet, then the area swept out by this line in a given time interval is constant.

Kepler’s Third Law

Given the period, T, and semimajor axis, a, of a planet’s orbit, the ratio is the same for every planet.

Law of reflection

For a reflected light ray, . In other words, a ray of light reflects of a surface in the same plane as the incident ray and the normal, and at an angle to the normal that is equal to the angle between the incident ray and the normal.

Lenz’s Law

States that the current induced in a circuit by a change in magnetic flux is in the direction that will oppose that change in flux. Using the right-hand rule, point your thumb in the opposite direction of the change in magnetic flux. The direction your fingers curl into a fist indicates the direction of the current.

Magnetic flux

The dot product of the area and the magnetic field passing through it. Graphically, it is a measure of the number and length of magnetic field lines passing through that area. It is measured in Webers (Wb).

Magnification

The ratio of the size of the image produced by a mirror or lens to the size of the original object. This number is negative if the image is upside-down.

Magnitude

A property common to both vectors and scalars. In the graphical representation of a vector, the vector’s magnitude is equal to the length of the arrow.

Mass number

The mass number, A, is the sum of the number of protons and neutrons in a nucleus. It is very close to the weight of that nucleus in atomic mass units.

Mechanical energy

The sum of a system’s potential and kinetic energy. In many systems, including projectiles, pulleys, pendulums, and motion on frictionless surfaces, mechanical energy is conserved. One important type of problem in which mechanical energy is not conserved is the class of problems involving friction.

Mole

The number of hydrogen atoms in one gram of hydrogen, equal to . When counting the number of molecules in a gas, it is often convenient to count them in moles.

Moment of inertia

A rigid body’s resistance to being rotated. The moment of inertia for a single particle is MR², where M is the mass of the rigid body and R is the distance to the rotation axis. For rigid bodies, calculating the moment of inertia is more complicated, but it generally takes the form of a constant multiplied by MR².

Momentum

Linear momentum, p, commonly called “momentum” for short, is a vector quantity defined as the product of an object’s mass, m, and its velocity, v.

Neutron

A neutrally charged particle that, along with protons, constitutes the nucleus of an atom.

Neutron number

The number, N, of neutrons in an atomic nucleus.

Newton

A unit of force: 1 N is equivalent to a 1 kg · m/s².

Newton’s First Law

An object at rest remains at rest, unless acted upon by a net force. An object in motion remains in motion, unless acted upon by a net force.

Newton’s Second Law

F = ma. The net force, F, acting on an object causes the object to accelerate, a. The magnitude of the acceleration is directly proportional to the net force on the object and inversely proportional to the mass, m, of the object.

Newton’s Third Law

To every action, there is an equal and opposite reaction. If an object A exerts a force on another object B, B will exert on A a force equal in magnitude and opposite in direction to the force exerted by A.

Normal

The line perpendicular to a surface. There is only one normal for any given surface.

Normal force

The reaction force of the ground, a table, etc., when an object is placed upon it. The normal force is a direct consequence of Newton’s Third Law: when an object is placed on the ground, the ground pushes back with the same force that it is pushed upon. уаауа

As a result, the net force of an object on the ground is zero, and the object does not move.

Nucleus

The center of an atom, where the protons and neutrons reside. Electrons then orbit this nucleus.

Optics

The study of the properties of visible light, i.e., the portion of the electromagnetic spectrum with wavelengths between 360 and 780 nm (1 nm = m/s).

Pascals

The unit for measuring pressure. One Pascal is equal to one Newton per meter squared, 1 Pa = 1 N/m².

Pendulum

A pendulum consists of a bob connected to a rod or rope. At small angles, a pendulum’s motion approximates simple harmonic motion as it swings back and forth without friction.

Period

The time it takes a system to pass through one cycle of its repetitive motion. The period, T, is the inverse of the motion’s frequency, f = 1/T.

Photon

A small particle-like bundle of electromagnetic radiation.

Power

Defined as the rate at which work is done, or the rate at which energy is transformed. P is measured in joules per second (J/s), or watts (W).

Pressure

A measure of force per unit area. Pressure is measured in N/m² or Pa.

Proton

A positively charged particle that, along with the neutron, occupies the nucleus of the atom.

Pulley

A pulley is a simple machine that consists of a rope that slides around a disk or block.

Quark

The building blocks of all matter, quarks are the constituent parts of protons, neutrons, and mesons.

Radian

A unit for measuring angles; also called a “rad.” 2π rad = 360º.

Radioactivity

An object is called radioactive if it undergoes radioactive decay.

Reflect

A wave on a string that is tied to a pole at one end will reflect back toward its source, producing a wave that is the mirror-image of the original and which travels in the opposite direction.

Refraction

The bending of light as it passes from one medium to another. Light refracts toward the normal when going from a less dense medium into a denser medium and away from the normal when going from a denser medium into a less dense medium.

Right-hand rule

A means of defining the direction of the cross product vector. To define the direction of the vector , position your right hand so that your fingers point in the direction of A, and then curl them around so that they point in the direction of B. The direction of your thumb shows the direction of the cross product vector.

Rigid body

An object that retains its overall shape, meaning that the particles that make up the rigid body stay in the same position relative to one another.

Rotational kinetic energy

The energy of a particle rotating around an axis.

Rotational motion

Occurs when every point in the rigid body moves in a circular path around a line called the axis of rotation.

Sound

Waves carried by variations in air pressure. The speed of sound waves in air at room temperature and pressure is roughly 343 m/s.

Specific heat

The amount of heat of a material required to raise the temperature of either one kilogram or one gram of that material by one degree Celsius. Different units may be used depending on whether specific heat is measured in s of grams or kilograms, and joules or calories.

Speed

A scalar quantity that tells us how fast an object is moving. It measures the rate of change in distance over time. Speed is to be contrasted with velocity in that there is no direction associated with speed.

Spring

Objects that experience oscillatory or simple harmonic motion when distorted. Their motion is described by Hooke’s Law.

Spring constant

Indicates how “bouncy” or “stiff” a spring is. More specifically, the spring constant, k, is the constant of proportionality between the restoring force exerted by the spring, and the spring’s displacement from equilibrium. The greater the value of k, more resistant the spring is to being displaced.

Static friction

The force between two surfaces that are not moving relative to one another. The force of static friction is parallel to the plane of contact between the two objects and resists the force pushing or pulling on the object.

Superposition

The principle by which the displacements from different waves traveling in the same medium add up. Superposition is the basis for interference.

System

A body or set of bodies that we choose to analyze as a group.

Tail

In the graphical representation of vectors, the tail of the arrow is the blunt end (the end without a point).

Temperature

A measure of the average kinetic energy of the molecules in a system. Temperature is related to heat by the specific heat of a given substance.

Tension force

The force transmitted along a rope or cable.

Third Law of Thermodynamics

An object cannot be cooled to absolute zero.

Torque

The effect of force on rotational motion.

Uniform circular motion

The motion of a body in a circular path with constant speed.

Unit vector

A unit vector is a vector with length 1.

Vector

A vector quantity, or vector, is an object possessing, and fully described by, a magnitude and a direction. Graphically a vector is depicted as an arrow with its magnitude given by the length of the arrow and its direction given by where the arrow is pointing.

Velocity

A vector quantity defined as the rate of change of the displacement vector with time. It is to be contrasted with speed, which is a scalar quantity for which no direction is specified.

Wave

A system with many parts in periodic, or repetitive, motion. The oscillations in one part cause vibrations in nearby parts.

Wave speed

The speed at which a wave crest or trough propagates. Note that this is not the speed at which the actual medium (like the stretched string or the air particles) moves.

Wavelength

The distance between successive wave crests, or troughs. Wavelength is measured in meters and is related to frequency and wave speed by = v/f.

The unit of magnetic flux, equal to one T · m².

Weight

The gravitational force exerted on a given mass.

Weightlessness

The experience of being in free fall. If you are in a satellite, elevator, or other free-falling object, then you have a weight of zero Newtons relative to that object.

Work

Done when energy is transferred by a force. The work done by a force F in displacing an object by s is W = F · s.

Work function

The amount of energy that metal must absorb before it can release a photoelectron from the metal.

Work-energy theorem

States that the net work done on an object is equal to the object’s change in kinetic energy.