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Topic: Perpendicular axes rule

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Parallel axis theorem

List of moments of inertia

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	Tensors, Contravariant and Covariant
		For example, polar coordinates are not rectilinear, i.e., the axes are not straight lines, but they are orthogonal, because as we vary the angle we are always moving perpendicular to the local radial axis.
		This is not ordinarily done, but it is possible. Recall that the contravariant components are measured parallel to the coordinate axes, and the covariant components are measured normal to all the other axes.
		The transformation rule for such representations is more complicated than either (6) or (8), but each component can be resolved into sub-components that are either purely contravariant or purely covariant, so these two extreme cases suffice to express all transformation characteristics of tensors.
	www.mathpages.com /rr/s5-02/5-02.htm (2511 words)

	CRYSTAL,
		The thirty-two classes are grouped into six crystal systems, based on the length and position of the crystal axes, imaginary lines passing through the center of the crystal, intersecting the faces, and bearing definite relations to the symmetry of the crystal.
		This system comprises crystals with three axes, all perpendicular to one another; two are of equal length.
		This system comprises crystals with three axes of unequal lengths, two of which are oblique (that is, not perpendicular) to one another, but both of which are perpendicular to the third.
	www.history.com /encyclopedia.do?articleId=206845 (1785 words)

	Crystal (mineral) - Search View - MSN Encarta
		The thirty-two classes are grouped into six crystal systems, based on the length and position of the crystal axes, imaginary lines passing through the center of the crystal, intersecting the faces, and bearing definite relations to the symmetry of the crystal.
		This system comprises crystals with three axes, all perpendicular to one another; two are of equal length.
		This system comprises crystals with three axes of unequal lengths, two of which are oblique (that is, not perpendicular) to one another, but both of which are perpendicular to the third.
	encarta.msn.com /text_761570052__1/Crystal_(mineral).html (1595 words)

	Perpendicular axes rule
		In mechanics the perpendicular axes theorem can be used to determine the moment of inertia of a rigid object, which lies entirely within a plane, about an axis at right angles to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane.
		The axes must all pass through a single point on the plane.
		This rule can be applied with thee stretch rule and parallel axes rule to find moments of inertia for a variety of shapes.
	www.algebra.com /algebra/about/history/Perpendicular-axes-rule.wikipedia (158 words)

	Axial Ratios, Parameters, Miller Indices
		The lengths of the crystallographic axes are controlled by the dimensions of the unit cell upon which the crystal is based.
		The angles between the crystallographic axes are controlled by the shape of the unit cell.
		Axial ratios are defined as the relative lengths of the crystallographic axes.
	www.tulane.edu /~sanelson/eens211/axial_ratios_paramaters_miller_indices.htm (1584 words)

	Dagorhir Manual of Arms
		Rules are kept as simple as possible, to keep battles exciting and fast-paced, and to keep the system easy to learn.
		These rules are as plain, straightforward, and detailed as possible, but not every angle of every situation has been covered.
		Hafts on axes, morning stars, maces and the like must be safely padded except for a reasonable area for a handhold.
	www.dagorhir.com /dagorhir/Rules.htm (3433 words)

	American Platform Tennis Association - Rules
		This ruling applies whether the member of the receiving team is hit while standing on or off the court.
		Rule 2) after it has hit the deck within the boundaries of the court, the ball remains in play and may be returned, so long as it has not hit the deck a second time within the court or the playing area.
		Rule 20, if the player who is attempting to strike the ball is willfully hindered by his opponent, the player is entitled to the point by reason of interference, whether such interference is verbal or physical.
	www.platformtennis.org /rules/index.shtml (4801 words)

	file_nav_name Encyclopedia Index
		In physics, the parallel axes rule can be used to determine the moment of inertia of a rigid object about any axis, g...
		Jumping the shark is a metaphor used by US TV critics and fans since the 1990s to denote the moment when a TV s...
		In physics, the perpendicular axes rule can be used to determine the moment of inertia of a rigid object, which lies e...
	www.brainyencyclopedia.com /topics/moment.html (3297 words)

	CRYSTAL HABIT
		The faces are not parallel and in fact converge around a crystallographic axes forming a multi-sided tent (compare the dome and sphenoid) with a point unless capped by a pedion or pinacoid.
		The diagonal of "deformation" becomes the prominent axes of symmetry and is trigonal with a three fold rotation about the axes.
		The trapezohedron is a general term for two crystal forms differentiated by the symmetry of the prominent axes.
	mineral.galleries.com /minerals/property/crystal.htm (2460 words)

	Parallel axes rule (Site not responding. Last check: )
		In physics, the parallel axes rule can be used to determine the moment of inertia of a rigid object about any axis, given the moment of inertia of the object about the parallel axis through the object's center of mass and the perpendicular distance between the axes.
		This rule can be applied with the stretch rule and perpendicular axes rule to find moments of inertia for a variety of shapes.
		The parallel axes rule also applies to the second moment of area (area moment of inertia);
	www.abcworld.net /Parallel_axes_rule.html (172 words)

	Glossary (Site not responding. Last check: )
		The process of producing an "output" from a given "input", by applying the "rule" of the given function.
		A function is piecewise-defined, if its rule is given by more than one other formula for different sets of input.
		A transformation of the x-y plane that moves each point to the opposite side of a fixed line, called its axis, along the line perpendicular to the axis so that the resulting point is the same distance from the axis as the original point.
	campus.northpark.edu /math/PreCalculus/glossary.html (1423 words)

	Rotation
		This is an important interpretation as it highlights that it is the tangential component (perpendicular to radial direction) of force, which is capable to produce change in the rotation.
		Perpendicular distance is obtained by drawing a perpendicular on the extended line of application of force as shown in the figure below.
		The vector equation of torque reveals that torque is perpendicular to the plane formed by position and force vectors and is also perpendicular to each of them individually.
	cnx.org /content/m14277/latest (3146 words)

	SparkNotes: Vector Multiplication: The Cross Product
		The only vectors that won't change at all under a rotation of the u-v plane are those vectors that are perpendicular to the plane.
		Fortunately, as is the case with the dot product, there is a simple geometric formula for computing the cross product of two vectors, if their respective lengths and the angle between them is known.
		Notice that when the two vectors are perpendicular to each other, θ =90 degrees, so sinθ =1 and we recover the familiar formula for the area of a square.
	www.sparknotes.com /physics/vectors/vectormultiplication/section2.rhtml (1276 words)

	571.218
		Helmet positioning index means the distance in inches, as specified by the manufacturer, from the lowest point of the brow opening at the lateral midpoint of the helmet to the basic plane of a reference headform, when the helmet is firmly and properly positioned on the reference headform.
		The origin of the coordinate axes also is located at the center of the mounting ball on the supporting assembly (See Figures 6, 7, and 8).
		The x—y—z axes of the test headform assembly on a monorail drop test equipment are oriented as follows: From the origin, the x—axis is horizontal with its positive direction going toward and passing through the vertical centerline of the monorail.
	www.fmcsa.dot.gov /rules-regulations/administration/fmcsr/fmcsrruletext.asp?rule_toc=777§ion=571.218§ion_toc=2113 (2781 words)

	Molecular Expressions: Science, Optics, and You: Light and Color - Optical Birefringence
		Anisotropic crystals, on the other hand, have crystallographically distinct axes and interact with light in a manner that is dependent upon the orientation of the crystalline lattice with respect to the incident light.
		These axes are perpendicular to each other and result in a totally dark field when viewed through the eyepieces without insertion of a birefringent crystal.
		As a rule, the greater the thickness or difference in refractive indices, the greater the degree of retardation.
	micro.magnet.fsu.edu /optics/lightandcolor/birefringence.html (2366 words)

	ITF Tennis - Technical - The Ball
		The Committee also recommends that Rule 3 be amended to include a statement advising that the ITF shall rule on the question of whether a ball complies with the regulations.
		The Committee considers it necessary to amend Rule 3 to clarify the long standing confusion resulting from the current disparity between Rule 3 and Appendix 1 of the Rules of Tennis with regards to the figures given for the size of a tennis ball.
		The Rules of Tennis Committee and the Technical Commission have recommended that Rule 3 – The Ball and Appendix 1 paragraphs iv and vii be amended, and a new Case 1 be inserted, to ratify the introduction of two new types of tennis ball.
	www.itftennis.com /technical/rules/history/index.asp (8020 words)

	Lecture Notes Chapter 1
		There is an infinite number of ways to choose a coordinate system, although the choice of the coordinate axes is usually influenced by the symmetry of the problem.
		is a vector whose magnitude is equal to the area of an infinitesimal surface element and whose direction is perpendicular to the surface, pointing outwards.
		It is a vector whose magnitude is equal to the area of the surface element and whose direction is perpendicular to the surface.
	teacher.nsrl.rochester.edu /PHY217/LectureNotes/Chapter1/LectureNotesChapter1.html (4668 words)

	THE CHARM OF GEOMETRY (Site not responding. Last check: )
		Prove that perpendicular lines from A’, B’, and C’ on the opposite sides of the triangle BC, CA and AB are concurrent.
		The radical axe of two circles is the geometric place of all points with equal powers to two circles.
		Perspective rules developed after this new mathematical perspective, and now the projective geometry is a fundamental instrument in understanding the universe.
	www.austega.com /florin/CharmOfGeometry.htm (12419 words)

	NumberNut.com: Glossary: A
		A line segment (or its length) drawn from the vertex of the cone perpendicular to the plane containing the base.
		A line segment (or its length) drawn from any point on one base perpendicular to the plane containing the other base.
		A line segment (or its length) drawn from a vertex perpendicular to the line containing the opposite side.
	www.numbernut.com /glossary (1144 words)

	GD&T Glossary of Symbols and Terms
		Perpendicularity Control - A geometric tolerance that limits the amount a surface, axis, or centerplane is permitted to vary from being perpendicular to the datum.
		Rule #1 - Where only a tolerance of size is specified, the limits of size of an individual feature prescribe the extent to which variations in its form--as well as in its size--are allowed.
		Rule #2 - RFS applies, with respect to the individual tolerance, datum reference, or both, where no modifying symbol is specified.
	etinews.com /gdt_glossary.html (2858 words)

	Federal Motor Vehicle Safety Standards; Door Locks and Door Retention Components and Side Impact Protection
		We have analyzed this rule in accordance with the principles and criteria set forth in Executive Order 13132 and have determined that this rule does not have sufficient Federal implications to warrant consultation with State and local officials or the preparation of a Federalism summary impact statement.
		This proposed rule would not preempt the states from adopting laws or regulations on the same subject, except that it would preempt a state regulation that is in actual conflict with the federal regulation or makes compliance with the Federal regulation impossible or interferes with the implementation of the federal statute.
		Before promulgating a NHTSA rule for which a written statement is needed, section 205 of the UMRA generally requires us to identify and consider a reasonable number of regulatory alternatives and adopt the least costly, most cost‑effective or least burdensome alternative that achieves the objectives of the rule.
	www.nhtsa.dot.gov /cars/rules/rulings/DoorLocks/DoorLocks_NPRM.html (15478 words)

	February 3 and 5
		rule 3 - The negative of a vector is the original vector flipped 180º.
		rule 4 - Two vectors, A and B are added by placing the tail of one on the head of the other (in either order) with the sum being the vector drawn from the tail of the first to the head of the second.
		x-y axes are perpendicular to each other with x the horizontal axis and y the vertical axis.
	www.phys.ufl.edu /~peterson/phy1033C/Feb_3and5.htm (1337 words)

	Parametric Equations
		Identifying the appropriate perpendicular directions in a kinematics problem is one of the first steps in solving it.
		There is no rule behind naming axes, but it is tradition to call the principle horizontal direction +x.
		All the laws of physics are always true without modification no matter where you place the origin, how you orient the axes (as long as they're perpendicular, of course), or what you name them.
	hypertextbook.com /physics/mechanics/parametric (2621 words)

	Triplet Below Singlet -- Hund’s Rule for Molecules
		There is a rule that the triplet excited state always has a lower energy than the corresponding singlet excited state in dye molecules.
		It wasn’t immediately obvious to me that the corresponding rule would be valid in one dimension (instead of three), or valid for excited states (as opposed to ground states), let alone valid for molecules (as opposed to single atoms).
		Equation 2 satisfies the fermionic exchange rule quoted at the beginning of section 3, as you can verify by exchanging 1 ↔ 2 everywhere on the RHS, and observing that the sign of the wavefunction is flipped.
	www.av8n.com /physics/triplet-singlet.htm (2171 words)

	illiMaze4D Description
		Up (and down) symbols will now more generally indicate the direction that is wall-free, perpendicular to the slice, and which is designated by his local orientation of front and left together with the right-hand rule.
		For each coordinate axis, the perpendicular interior levels are indexed from 0 to N. The user's location is an integer array {i,j,k,h}, which means that the user's actual coordinates in the maze are {i+.5, j+.5, k+.5, h+.5}, (so the user is in the center of some unit hypercube of the 4D lattice).
		During a rotation between slices perpendicular to, say, the z- and x-axes, the axes of rotation are parallel to the the (remaining) y- and w-axes, and pass through the user's coordinates.
	www.math.uiuc.edu /~pelsmaje/illiMaze4D (1115 words)

	The Biaxial Indicatrix
		Perpendicular to the major and minor axes is the intermediate axis.
		The direction perpendicular to each circular section is the optic axis.
		If the optic axes are perpendicular to each other, the mineral is on the dividing line between positive and negative.
	www.uwgb.edu /dutchs/petrolgy/IndicatrixB.HTM (460 words)

	Parallels of Gravitational Waves to Electromagnetism
		This particular rule tells you how to figure out which way the magnetic field is going, and, thus, what it looks like (the two being one and the same, really).
		The effects of the wave are still detectable in the perpendicular plane to the direction of the wave---the fork in the sheet of jello is still the direction in which the wave travels and the jello sheet is still the plane of oscillation.
		However, instead of being 90° apart (perpendicular), they are 45° apart---which is related to the type of particle that carries the wave, but that's for further down.
	www.gothosenterprises.com /gravitational_waves/parallels.html (1692 words)

	six crystal system (Site not responding. Last check: )
		To classify crystal structure, we may use the three axes and the three interaxial angles to make 5 crystal systems.
		The three axes equally divide the circle, so the angle between any two axes is 120°.
		The c-axis is perpendicular to the ab plane.
	muskingum.edu /~ericlaw/pd_courses/geol301/Crystallography/crystalSystems/crystalSystem.html (153 words)

	How to Specify Beam Orientation
		and axis 3 is formed by the right-hand rule (an engineering concept used to determine the direction of a vector normal to other vectors).
		With the element axes known, the cross-sectional properties A, J1, I2, I3, S2, S3, Sa2 and Sa3 can be entered appropriately in the "Element Definition" dialog as shown in Figure 2.
		The orientation of the element axes determines how cross-sectional properties, such as the moments of inertia about the axes, must be entered.
	www.algor.com /service_support/hints_tips/beam_orientation.asp (687 words)

	Cartesian coordinate system Summary
		The intersection of these axes is called the origin, and the four sections into which the axis divide a given plane are called quadrants.
		To define the coordinates, two perpendicular directed lines (the x-axis or abscissa and the y-axis or ordinate), are specified, as well as the unit length, which is marked off on the two axes (see Figure 1).
		The standard way of orienting the axes, with the positive x-axis pointing right and the positive y-axis pointing up (and the x-axis being the "first" and the y-axis the "second" axis) is considred the positive or standard orientation.
	www.bookrags.com /Cartesian_coordinate_system (3956 words)

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