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This place in the site is designed for the
college/school students and are likely to be helpful to them in mainly ways. In
this month we have decided to keep the glossary of mechanics.
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Here is your world of mechanics:
Glossary for Mechanics
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The following terms are defined for the Physics 1 - Mechanics program
- 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).
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- 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.
- 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
.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
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