Shop Essentials (Applied Mathematics)

Applied and Engineering Sciences 110

This class provides an overview of the key concepts of physics and works through practical mathematic application.

  • Difficulty Beginner

  • Format Online

  • Number of Lessons 18

  • Language English


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Course Outline
  • Objectives
  • Mechanics
  • Mechanics Applications
  • Light
  • Light Applications
  • Sound
  • Sound Applications
  • Heat Exchange
  • Heat Exchange Applications
  • Dynamics
  • Dynamics Applications
  • Electrical Circuits
  • Circuit Applications
  • Electromagnetism
  • Electromagnetism Applications
  • Material Strength
  • Material Strength Applications
  • Summary
  • Identify Newton’s Laws.
  • Solve basic statics problems.
  • Describe the behavior of light.
  • Describe applications of light.
  • Describe the characteristics of sound.
  • Calculate relative sound intensity.
  • Distinguish between means of heat exchange.
  • Describe heat exchange applications.
  • Describe dynamics.
  • Calculate acceleration through the application of dynamics principles.
  • Solve basic electrical circuit problems.
  • Calculate equivalent resistance.
  • Explain the principles of electromagnetism.
  • Identify common electric motor components.
  • Identify types of material stress.
  • Calculate allowable material stress.
Vocabulary Term

angle of incidence

An angle measured between an incoming light ray and a line drawn perpendicular to the surface of an object. The angle of incidence is equal to the angle of reflection if the line is normal to the surface.

angle of reflection

The angle formed by a reflected light ray and a line drawn perpendicular to the surface at the point of reflection. The angle of reflection is equal to the angle of incidence if the line is normal to the surface.

angular motion

Any motion that occurs along a curved path. Angular motion with a constant angular rate of rotation is considered uniform.


The rotating portion of a DC generator or motor. Voltage is induced in the armature.

classical mechanics

The branch of physics concerned with the motion of objects. Mechanics deals with different forces that cause or prevent motion.

coefficient of expansion

The change in density that occurs as a material changes in temperature. A metal typically increases in volume and decreases in density as it is heated.

coefficient of friction

The relationship between the force required to move an object along a surface to the force that presses those two surfaces together. Objects with a greater coefficient of friction require greater force to produce motion.


Multiple loops of conducting wire used to create a magnetic field when current is passed through it. Coils are used in electromagnets and electric motors.

compression strength

A material's ability to resist forces that attempt to compress or squeeze the material together. Floor materials that will support constant, heavy loads must have high compression strength.

compression stress

A force that attempts to flatten or "squeeze" a material. Compression strength is a material's ability to resist compression stress.


A form of heat transfer. Conduction allows heat to pass from a solid object to an object or area when they come into contact with each other and have differences in temperature.


The transfer of heat as a warm fluid passes over the surface of a cooler material. The water cooling of heat treated steel is an example of convection.


The branch of the science of mechanics that deals with objects that are not in equilibrium. Kinetics and kinematics are two major branches of dynamics.

electromagnetic radiation

The transfer of energy through electromagnetic waves that induce a temperature change when absorbed by an object. The sun transfers heat through electromagnetic radiation.

electromagnetic spectrum

The full range of electric, magnetic, and visible radiation, from gamma rays having a wavelength of 0.001 angstrom to long waves having a wavelength of more than 1 million km.

electromotive force

Electrical pressure, abbreviated emf. It is the force that pushes electrons through a conductor, measured in volts.

energy methods

A means to solve kinetics problems by an application of the conservation laws. Energy methods often are a simpler way to solve problems than through an application of Newtonian methods.

factor of safety

A multiplier designed to ensure that an object is not stressed to the point of failure. A factor of safety of two means using a material that is twice as strong as necessary.

Faraday’s Law

A law that states an electric field is induced in any system in which a magnetic field is changing with time. Faraday's Law is the basis for magnetic induction.


A state of matter that has the ability to flow. Fluids can be liquids or gases.

focal point

The point at which rays or waves meet after reflection or refraction, or the point from which diverging rays or waves appear to proceed. A lens is used to create a focal point.


The push or pull that gives energy to an object. A force changes an object's motion or state of rest.

free-body diagram

A drawing used to identify the relevant forces and moments that affect an object. Free-body diagrams isolate the object from any other objects in contact with it.


The number of sound wave oscillations or vibrations in a unit of time. Measured in hertz (Hz), high frequencies involve more wave cycles than low frequencies in the same amount of time.


A force that resists motion between two components that are in contact with each other. Friction can be either static or dynamic.

heat capacity

The amount of energy that is needed to change a material's temperature. Heat capacity is commonly expressed in terms of specific heat.


A measure of the energy that a sound wave transmits. Intensity is equal to power divided by exposed surface area.


The science of motion without regard for the forces that cause that motion. Kinematics is a branch of dynamics.

kinetic energy

Energy existing due to an object's motion. Kinetic energy can be converted into heat through friction.


The study of the forces that cause motion. Kinetics is a branch of dynamics.

Kirchhoff’s Laws

A set of rules used to explain the equalities that exist within electrical circuits. Kirchhoff's Law's are based on the theory of conservation of charge.

Kirchhoff’s Loop Rule

The universal truth stating that the sum of all changes in voltage around any closed loop must equal zero. The Loop Rule is related to the first law of thermodynamics.

Kirchhoff’s Point Rule

The universal truth stating that at any junction in a circuit, current in is equal to current out. Mathematically speaking, the current adds to zero.


A curved, transparent material used to concentrate or disperse light rays. A lens can be used to create a focal point.

logarithmic ratio

The exponent by which a fixed base number has to be raised to produce that number. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities.


Meters per second squared. m/s2 is the international unit of acceleration.

magnetic flux

A measure of the strength of the field formed around a magnet. Flux is expressed in webers (Wb).

magnetic induction

The use of magnets to cause voltage in a conductor. Magnetic induction occurs whenever a conductor passes through magnetic lines of flux.


The measurement of the amount of an applied force. Magnitude is a vector quantity.


A substance that has mass and exists as a solid, liquid, or a gas. Matter can change states based on temperature and pressure.


A force that attempts to produce motion around a given point or fulcrum. Moment is the combination of weight and distance from the fulcrum.


A line that is perpendicular to the tangent plane of a surface at the point of contact with that surface.

Ohm’s Law

The universal truth stating that it takes one volt to push one amp through one ohm. Ohm's Law is used to understand the relationship of variables in electrical circuits.

optical comparator

A sophisticated measuring instrument that projects an image of a part onto a screen to compare the shape, size, and location of its features.

parallel circuit

A route for the flow of electricity that has multiple paths. In a parallel circuit, the addition of new paths reduces overall resistance.


The perceived fundamental frequency of a sound. Pitches are compared to each other in relative "highness" and "lowness."


Having two oppositely charged poles, one positive and one negative. Polarity determines the direction in which current tends to flow.

pole piece

Devices mounted on the inside of a generator or DC motor armature. When connected to field windings, the pole pieces form the electromagnets that create lines of flux.

potential energy

Power that is stored or suppressed or that exists because of its position and the effects of gravity. Machines that have large components that raise and lower, such as a press, contain potential energy that becomes kinetic energy when it is released.

product over sum method

An equation for determining the total resistance for a parallel circuit. The product over sum method divides a pair of resistors, and then divides the result by another resistor, over and over again until only one pair is left.


A decrease in the density and pressure in a medium, caused by a sound wave. Rarefaction is the opposite of compression.

ray theory

The branch of physics that explains the physical behavior of light rays. Reflection and refraction are two phenomena explained by ray theory.

reciprocal formula

An equation for determining the total resistance for a parallel circuit. The reciprocal formula finds the total resistance of a parallel circuit by calculating the reciprocal of the sum of the reciprocals of the individual branches.

rectilinear motion

Any motion that occurs in a straight line. Rectilinear motion is a product of velocity and displacement over time.


The portion of a light wave that is redirected away from an object that it contacts. In most cases, some of the light is absorbed by the object.


The bending of light as it passes from one medium to the next. Every material has its own unique index of refraction.

relative intensity

A logarithmic ratio of actual sound intensity to the threshold of human hearing. Relative intensity gives the power of sound a point of reference, and is measured in decibels.

resistors of equal value method

An equation for determining the total resistance for a DC parallel circuit with resistors that have the same value. The resistors of equal value method finds the total resistance by dividing the value of one individual resistor by the number of branches.


The rotating part of a motor. The term rotor is often associated with AC motors, where the armature is not necessarily the rotating piece.

series circuit

A route for the flow of electricity that has only one path. In a series circuit, current must pass through every resistor.

shear stress

A force that attempts to cause the internal structure of a material to slide against itself. Shear strength is a material's ability to resist shear stress.

Snell’s Law

The law stating that for a light ray passing between two media the ratio of the sines of the angle of incidence and the angle of refraction is a constant. Light is refracted based upon the different indices of refraction of the two media.


An output device that converts electrical energy into linear mechanical force. Solenoids are often used to actuate valves.


The physical phenomenon that stimulates our sense of hearing. Sound is an acoustic wave that results when a vibrating source disturbs the air.

specific heat

The amount of heat that is required to raise the temperature of a specific amount of material by one degree. Every material has its own unique specific heat value.


The branch of the science of mechanics that deals with objects that are in equilibrium. A static object is either completely still or moving at a consistent rate.


The stationary part of a motor. In AC motors, the armature is often stationary.


The ratio of change in a dimension that takes place with a material under stress. Strain can be represented graphically as a stress-strain curve.


A force that attempts to deform an object. Common forms of stress include compression, shear, and tensile.


A vector that is tangent to an arc of rotation at a specific point. All angular motion has a tangential velocity.

tensile strength

A material's ability to resist forces that attempt to pull it apart or stretch it. Materials under tension beyond their yield strength often experience "necking" before breaking.

tensile stress

A force that attempts to pull apart or stretch a material. Tensile strength is a material's ability to withstand tensile stress.

thermal conductivity

The ability of a material to conduct heat. Materials with low thermal conductivity make good insulators.

thermal expansion

The tendency of a material to increase in size as it increases in temperature. Every material has its own unique rate at which it expands when subjected to increases in temperature.


The branch of physics that studies energy in transitional states. Any process involving energy, heat, and work can be explained through the first two laws of thermodynamics.

torsion stress

A type of stress that attempts to twist a material against itself. Torsion stress is a form of shear stress.


The absence of matter. The pressure inside a vacuum is lower than the pressure outside the vacuum.

vector quantity

An amount or measurement that is related to a direction. Velocity, acceleration, and weight are vector quantities.

visible light

The portion of the electromagnetic spectrum that is visible to humans. Light is a form of radiation.

voltage drop

The amount of voltage needed to push a given amount of current through a given amount of resistance.


Watts per meter squared. W/m2 is the international unit of measure for intensity.


A unit used to express flux density. One weber (Wb) is equal to 100 million lines of flux.