The following terms are defined for the Physics 1 - Mechanics course

A

Absolute Value

The absolute value of a number is -1 times the number if it is negative or +1 times the number if it is positive.

Acceleration

The rate of change of velocity with respect to time. Acceleration is a vector quantity. Acceleration is related to the force on an object and its mass by Newton's second law, stating that acceleration equals force divided by mass. A=F/m

Angular Frequency

The frequency of a periodic system, multiplied by 2p. The units are in radians per unit time but since radians are unitless, it comes out to be t^-1, the same as angular velocity of circular motion. Angular frequency is symbolized by the Greek letter omega (w).

B

C

Conservative System

A dynamical system in which no energy is either lost or gained by the system. These are systems where friction is negligible.

Cosine

In a right triangle, the ratio of the adjacent side to the hypotenuse. See the background page on trigonometric functions .

Cycle

The set of all the states visited by a periodic system during one period . In other words one cycle of anything that is repetitive is everything it does during one repetition.

D

Density

The mass per unit volume of an object. It would be measured in kilograms per cubic meter in the SI system of units.

Displacement

The difference between an initial position and a final one. Displacement is a vector quantity.

Dynamical System

A system that changes with the passage of time. Basically that is any system with moving parts.

Dynamics

The study of motion and the forces which cause it.

E

Effective Mass

The mass in a dynamical system that must be included when we treat the moving parts of the system as though they were a particle , using the free body analysis in applying Newton's laws of motion .

Elastic Scattering

An interaction where two particles collide and the total kinetic energy of the two particles remains constant. The direction and speed of both particles will in general be different after the collision.

Energy

Energy is defined as the ability of an object to do work on its surroundings. It may be in the form of kinetic energy or of potential energy .

Exponentiation

Raising a number to a power. The symbol ^ is used in this program to indicate this operation. The expression b^e means multiply b (the base) by itself e (the exponent) times.

F

Free Body

An object that is unconstrained so that it may respond to forces in accordance with Newton's laws of motion .

Frequency

The number of cycles per unit time that a periodic system completes. The fequency (f) is related to the period (T) by f=1/T.

Force

Quite simply a force is a push or a pull. Force is a vector quantity.

G

Gaussian

The bell shaped curve that is used to describe the distribution of quantities around some normal value, named in honor of Mr. Gauss we believe. This function is expressed as Y=A*exp(-(b-X)^2) , where "A" is the amplitude or height of the curve and "b" is the location of the peak of the curve on the X axis. The exp() symbol represents the number "e" (approximately equal to 2.7182818284), raised to the power of the stuff in its parentheses. For example exp(0)=1, exp(1)=e, exp(2)=e^2, exp(-1)=1/e, exp(-2)=1/(e^2), and so on. As you can see when X=b, Y=A in the Gaussian function. As X departs from b in either direction, the value of the exp() approaches zero, forcing Y to approach zero as well. See the Non-Linear Rate of Change display in the Rate of Change lesson for an illustration

H

I

Impulse Force

A force applied for a time which is short compared to the observation time, as for example the force between a bat and ball where the observation is over the entire flight of the ball from leaving the pitcher's hand to landing in the bleachers.

J

K

Kinetic Energy

The energy an object has as a result of its motion. Numerically the kinetic energy is equal to 1/2*m*v^2 where m is the mass of the object and v is the magnitude of its velocity .

Kinematics

The study of objects in motion without explicit consideration for the forces which produced the motion.

L

M

Magnitude

The size of a thing, without regard for its sign (+ or -) or direction. Similar to the absolute value of a number but applies to vectors as well.

Mass

The property of an object which determines its resistance to changes in velocity . In the presence of a gravitational field, as near the surface of a planet, the mass of an object is proportional to its weight, the force exerted on the object by the planet.

Mechanics

The study of objects in motion. Mechanics is normally limited to a small number of large slow objects, as opposed to statistical mechanics which deals with large numbers of objects, relativistic mechanics which deals with objects moving near the speed of light and quantum mechanics which deals with objects more or less the size of atoms. Mechanics encompasses the topics of kinematics and dynamics .

N

Normal

Another word for perpendicular. Normal in this sense is usually used in refering to a vector's orientation relative to some surface. For example a vertical vector is normal to a horizontal surface.

O

Object

A thing. The term "object" is the most general form of thingness. There are physical objects like baseballs and uranium atoms, and mathematical objects like numbers and vectors . It will be clear from the context what sort of object we are talking about.

Origin

The point in a reference frame from which measurements are made. It is the location of the zero value for each axis in the frame.

P

Particle

An object whose size is negligible in the context of our observation of it. For example the Earth might be considered a particle if we were studying its orbit around the Sun, but not if we want to know anything about its rotation about its axis. The nucleus of an atom might be a particle in an experiment on elastic scattering , but not in considering nuclear fission.

Period

The interval of time between the occurrence of identical states in a periodic system.

Periodic System

A dynamical system which at some point in its motion returns to the same state. If a system ever revisits the identical state it will continue to come back to it again and again in equal intervals of time. That is why we call such a system periodic.

Phase Angle

The offset from the origin of a periodic function like the sine or cosine. For example in the function x=A*sin(w*t + f), f is the phase angle. The units on f are radians.

PI

The ratio of the circumference of a circle to its diameter is named by the Greek letter pi. We use it in the upper case to help distinguish it from regular text. The numerical value of PI is approximately 3.1415926.

Position

The location of an object relative to some point we have chosen to be the reference point. Position is a vector quantity.

Potential Energy

The potential energy of an object is the energy that object has as a result of its position relative to other objects. The numerical value of potential energy depends on the nature of the interaction of the object with its surroundings and the choice of a position to be the zero energy point.

Property

A characteristic that is inherently associated with the object which is said to have that property. For example the mass of an object is one of its properties. So also might be color, density and many other characteristics. Properties are classified as extensive or intensive. Extensive properties increase in proportion to the size of the object, as mass does for example. Intensive properties are independent of the size of the object. The density for examples remains the same if I cut an object in half and throw half of it away. Things like an object's position or velocity are not considered to be properties of the object. They are not a characteristic of the object only but are also dependent on the reference frame in which the object is located.

Q

Quadratic

A function involving the second and lower power, and none higher, of the independent variable. A quadratic function may contain x^2 explicitly or it may contain terms like x*(1-x), where the second power of x is implied. In general a quadratic may be written as y=a*x^2+b*x+c . For an illustration of a quadratic function, see the Quadratic Derivative display in the Rate of Change lesson.

Quantity

A numerical value either scalar or vector , which describes some attribute of an object like its position or its velocity . We sometimes speak of physical quantities to signify that we are talking about an object's properties or attributes as opposed to a purely mathematical quantity.

R

Radian

An angular unit of measure. A radian is an angle subtended by an arc whose length equals one radius. Since the circumference of a circle is 2* PI *radius and a radian spans an arc of one radius, there are 2*PI radians in a complete circle. So 1 radian equals 360/(2*PI) degrees. This is illustrated below.

Radius or Curvature

The radius of the largest circle containing the point at which the radius of curvature is to be determined and fitting within the curve. See the illustration below.

Reference Frame

A mathematical object which is used to allow comparison of the positions in space of physical objects like particles, or the comparison of one particle's positions at different times. For examples see the Measurement in Mechanics lesson. The reference frame may be made up of any set of coordinates which uniquely specify a point in space.

S

Scalar

A scalar quantity is one having only magnitude , not direction information. This is as opposed to a vector quantity which has both magnitude and direction.

Systéme International (International System)

The most commonly accepted system of units in scientific work. The fundamental units in this system are the meter, kilogram and second.

Significant Figures

The number of digits in a numerical value that are reliably known. If the numbers being used in a calculation are measured values, there will always be a limit on the accuracy of the measurement. The results of any calculations based on those numbers should not be reported with more significant figures than the least acurate of the measured values. For example if the length of a rectangle is measured to within 0.1 cm to be 25.3 cm and its width to within 0.1 cm to be 6.6 cm, multiplying shows the area to be 166.98 cm^2. The result however should be reported only to 2 significant figures since the width is only known to that accuracy, giving an area of 170 cm^2.

Sine

In a right triangle, the ratio of the opposite side to the hypotenuse. See the background page on trigonometric functions .

State

Dynamical systems evolve over the course of time. The state of the system at any instant may be identified by the values of certain variables at that instant. For example specifying the angle from the vertical and the velocity of a frictionless pendulum allows us to predict its position and velocity at any future time. Therefore the state of the pendulum at any instant is its position and velocity. In this example the position and velocity are known as state variables.

State Variable

An observable quantity which is must be specified in order to determine how a Dynamical systems changes over the course of time. In conservative systems if all the state variables are known at any instant, the state of the system is determined for all future time.

T

Tangent

A straight line which touches a curve in one and only one point. The slope of a tangent is the slope of the curve at that point. Slope is the change in the vertical coordinate divided by the corresponding change in the horizontal coordinate. See the Rate of Change lesson for more on slopes.

Also, in a right triangle, the ratio of the opposite side to the adjacent. See the background page on trigonometric functions .

Trajectory

The path an object takes through space. Frequently associated with a projectile like a bullet or a missle.

U

V

Vector

A quantity having both magnitude and direction. The direction may be expressed as an angle from a single axis in two dimensions. In three dimensions, the direction must be a pair of angles measured from different axes.

Velocity

The speed of an object in a given direction. Velocity is a vector quantity.

W

Wavelength

The distance covered by a travelling wave in one period . It is the distance between points of the same phase angle in a travelling wave. For example the distance between peaks, or the distance between valleys of a wave train. The wavelength is frequently symbolized by the Greek letter lambda l .

Work

Work is defined as the application of force over some displacement . Numerically the work done is the product of the force and the distance moved in the direction of that force. This may be calculated as force times displacement times the cosine of the angle between force and displacement. The angle gets involved because things do not always move in the direction in which you push them.

X

Y

Z