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Topic: Parallel axes rule

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Second moment of area

Moment of inertia

List of moments of inertia

Centroid

Second moment of inertia

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	Parallel axes rule - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-08)
		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.
		Parallel axes rule for area moment of inertia.
	en.wikipedia.org /wiki/Parallel_axes_rule (206 words)

	MECHANICS - LoveToKnow Article on MECHANICS (Site not responding. Last check: 2007-10-08)
		These rules are sometimes dignified by the name of laws of nature, but they have ~relation to our present state of knowledge and to the degree of skill with which we have succeeded in giving more or less compact expression to it.
		Successive halfturns about intersecting axes a, b are equivalent to a rotation about the common perpendicular to a, b at their intersection, Of amount equal to twice the acute angle between them, in the direction from a to b.
		Successive half-turns about two skew axes a, b are equivalent to a twist about a screw whose axis is the common perpendicular to a, b, the translation being double the shortest distance, and the angle of rotation being twice the acute angle between a, b, in the direction from a to b.
	www.1911encyclopedia.org /M/ME/MECHANICS.htm (22021 words)

	Stretch rule - Wikipedia, the free encyclopedia
		In physics, the stretch rule states that the moment of inertia of a rigid object is unchanged when the object is stretched parallel to the axis of rotation, without changing the distribution of mass.
		That is, cylinders oriented parallel to the axis must be preserved.
		This rule can be applied with the parallel axes rule and the perpendicular axes rule to find moments of inertia for a variety of shapes.
	en.wikipedia.org /wiki/Stretch_rule (96 words)

	INSTRUMENTS - Online Information article about INSTRUMENTS
		pencil or parallel rays emerging from the eye-lens is to the diameter of the object-lens inversely as the magnifying power of the telescope.
		The focus of A for parallel rays is at F, that of B for parallel rays at f—between B and F. Parallel rays falling on A A converge at F, where an image r.
		Parallel rays falling on A A converge on the plane mirror B B, and are thence reflected at New right angles to the axis, forming an image in the focus of toalea.
	encyclopedia.jrank.org /I27_INV/INSTRUMENTS.html (6915 words)

	[No title]
		In fact, if in the case of composition of coaxial motions the axes are dispersed by negligibly small distances while preserving their parallelism, then the laws of algebraic composition of angles of rotation must be violated, because there is no dividing line between coaxial and non- coaxial motions.
		Algebraic composition of parallel vectors, orthogonal and axial coefficients, parallel forces and masses is governed by the same geometrical law, viz., that of relation of three points, or the lever principle.
		When two parallel angular velocities are composed, which are particular cases of orthogonal coefficients, the velocity vector of the centre of the sum angular velocity must be equal to zero.
	www.math.rsu.ru /zimin/3_2.html (1238 words)

	Newton's Mathematical Principles of Natural Philosophy
		RULE II Therefore to the same natural effects we must, as far as possible, assign the same causes.
		RULE IV In experimental philosophy we are to look, upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may cither be made more accurate, or liable to exceptions.
		This rule we must follow, that the argument of induction may not be evaded by hypotheses.
	www.marxists.org /reference/subject/philosophy/works/en/newton.htm (5030 words)

	Library Data
		The Vilani had coped with the problems of ruling a large empire by a rigid caste system with all citizens rooted permanently in their places, but this system could only last as long as there was no significant external threats.
		The -1776 date for the end of the Rule of Man is arbitrary and it notes the financial collapse of the central government which occurred when the Treasury at Hub/Ershur refused to honour a monetary issue of the branch treasury at Antares.
		The Rule of Terra's acts, although not its goals, have been disavowed by many other Solomani groups, including the Confederation government; in return, the Rule of Terra has attacked even Solomani populations, stating that "all who do not contribute to the Manifest Destiny of the Race are not worthy to be part of the Race".
	traveller.mu.org /library/library_data.html (20906 words)

	RayShade file formats (Site not responding. Last check: 2007-10-08)
		Exceptions to this rule are transparent primitives, for which rayshade uses the direction of the surface normal to determine if the incident ray is entering or exiting the object.
		The texture is implemented as roughly parallel alternating veins of marble, each of which is separated by 1/7 of a unit and runs perpendicular to the Z axis.
		If positive, the value of un gives the number of times the image should be repeated along the u axis, starting from the origin of the texture, and positive vn gives the number of times it should be repeated along the v axis.
	astronomy.swin.edu.au /~pbourke/geomformats/rayshade (10451 words)

	Function Diagrams
		One underused representation of functions, which I have found educationally rich, is the one with parallel x and y axes.
		One way to motivate many of the rules for operations with signed numbers is to generalize from patterns that work for positive numbers.
		Similar methods can be used to explore other patterns of this type, thus motivating the rules for signed number arithmetic, and providing students with a way to reconstruct them on their own.
	www.picciotto.org /math-ed/func-diag (1768 words)

	Tennis FAQ
		In accordance with Rule 21 the Umpire may either award the point to the player hindered or order the point to be replayed (See also Rule 25).
		Unless you have made a local ground rule designed to save chasing balls that are obviously going out, when you catch in the air a ball that is in play you have lost the point, regardless of whether you are inside or outside the court.
		A recent USTA Comment under Rule 12 provides that once the receiver has indicated that he is ready he cannot become unready and claim a let-- anymore than he could become unready during a point-- unless there is some outside interference.
	www.michianatennis.com /tennisrules.htm (16780 words)

	FR Doc 03-4788
		The purpose of this final rule is to make the necessary changes to the Commerce Control List to implement revisions to the Wassenaar List that were agreed upon in the February 2002 meeting (and finalized in May 2002) and to make necessary revisions to reporting requirements, definitions, and the General Technology and Software Notes.
		The changes that affected microprocessors were published in a separate rule on January 14, 2003 (68 FR 1796).
		A continuous throughput of 2 Gbit/s or more; Technical Note: For those instruments with a parallel bus architecture, the continuous throughput rate is the highest word rate multiplied by the number of bits in a word.
	a257.g.akamaitech.net /7/257/2422/14mar20010800/edocket.access.gpo.gov/2003/03-4788.htm (11121 words)

	Angular momentum
		The angular momentum of a rigid object rotating about one of its symmetry axes is the sum of the angular momenta of all its parts.
		The direction of the angular momentum of a rigid object rotating about one of its symmetry axes is the direction of the angular velocity (given by the right hand rule).
		The first term is of the moment of inertia of the object about a parallel axes through its center of mass.
	electron9.phys.utk.edu /phys135d/modules/m8/angular.htm (1699 words)

	Developments at the Edge (Site not responding. Last check: 2007-10-08)
		The requirements of the parallel projects (rows), can be explicitly recorded along with the dependency that each has on the different component releases.
		The "work to rule" strike is an extreme example of a kind of very low key workplace sabotage I've heard called "malicious compliance".
		Parallel activities can be of different types and ranging in scale.
	www.developedge.com (2914 words)

	VG: Critique: Mishosha
		In this sense, there is a parallel between Jane Schoolcraft's decision to choose a white partner, Henry Rowe, over a Native American, and the wife's decision to choose the man in the forest over her Indian husband.
		The idea of elders as a harmful force in "Mishosha" is paralleled on a national level.
		The boy's solution to these tensions parallel the methods used by the Native American people in their negotiations with settlers.
	voices.cla.umn.edu /vg/Critique/review_fiction/mishosha.html (1744 words)

	Teaching the Journal of American History
		While some "anti-imperialists" included criticisms of the treatment of Indians in their warnings against overseas colonial rule over additional "backward races," for most the conquest of the West represented the peaceful and natural outpouring of "civilization," the pushing back of the frontier of liberty.
		They had trekked north (rather than west) in search of liberty from British colonial rule; they had extirpated inferior races they had encountered and manfully challenged the imperial tyrannies that stood in their path.
		be ruled by a paternal government for their own good, not led to cherish a vain hope that the power they would only misuse will some day be placed in their hands." Even as he urged the Americans toward reform, Clifford cautioned them that their very Anglo-Saxonism was at stake.
	www.indiana.edu /~jah/teaching/2002_03/article.shtml (12668 words)

	Areas, Volumes, Centroids, & Moments of Inertia of Solids (Site not responding. Last check: 2007-10-08)
		In general, an object's moment of inertia depends on its shape and the distribution of mass within that shape: the greater the concentration of material away from the object's centroid, the larger the moment of inertia.
		The radius with reference to an axis is that distance form the axis at which the entire mass of a body may be considered as concentrating keeping the moment of inertia unchanged.
		To determine the Moment of Inertia about an axis which is parallel to a centroid axis and at a distance d.
	www.roymech.co.uk /Useful_Tables/Form/M_of_Inertia.html (275 words)

	Classics in the History of Psychology -- James (1890) Chapter 20
		An object appears smaller on the lateral portions of the retina than it does on the fovea, as may be easily verified by holding the [p.
		It is paralleled in the human race by the breath-holding stillness of the boy playing 'I spy,' to whom the seeker is near; and its obverse side is shown in our involuntary waving of arms, jumping up and down, and so forth, when we wish to attract someone's attention at a distance.
		We may be sure, therefore, that the general rule of our mind is to locate IN each other all sensations which are associated in simultaneous experience, and do not interfere with each other's perception.
	psychclassics.yorku.ca /James/Principles/prin20.htm (20676 words)

	Planet AgeofMythology - A Member of the GameSpy Network
		The Ottoman Empire was a multi-ethnic state that existed from 1299 to 1923 (624 years), one of the largest empires to rule the borders of the Mediterranean Sea.
		It was established by a tribe of Oghuz Turks in western Anatolia and ruled by the Osmanli dynasty.
		In diplomatic circles it was often referred to as the Sublime Porte or simply as the Porte, from the French translation of the Ottoman name Bâb-i-âlî "high gate", due to the greeting ceremony the sultan held for foreign ambassadors at the Palace Gate.
	www.planetageofmythology.com /aoe3/cultures (3158 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		If the type of rule in the second field is an a then the value in the third field indicates an exact variable value and, as with the logistic rule, the fourth field is inconsequential.
		The rule is defined by all variables avaiable to the model, that is, a range is defined for all variables even if they are not particularly useful in prediction.
		In a range rule a number of variables may be regarded as irrelevant, that is, all possible predictor variables need not be used in the rule.
	biodi.sdsc.edu /Doc/GARP/Manual/manual.html (15715 words)

	Visualization in Problem Solving Environments
		The selective coloring option assigns a color to each polygonal line on the rule that all points for which the selected constraint is violated are colored red, those points for which that constraint is active are colored yellow, and those points for which that constraint is satisfied are colored green.
		While implementing the parallel coordinates system in VizCraft, special consideration was given to two aspects: user interactivity for allowing interactive data exploration, and modularity, which is necessary for adapting the system in the future to the needs of different applications, not just those specific to HSCT design.
		The parallel coordinates module in VizCraft has been used to display multidimensional data sets for other application areas as well, provided the data file supplied to it is in the required format.
	www.ndltd.org /xml/etd/etd1/Thesis1.xml (16132 words)

	Newtonian(2) (Site not responding. Last check: 2007-10-08)
		Two of these are placed side-by-side in contact with a horizontal surface, and the third is placed upon the other two with its axis parallel to the axes of the other two.
		As long as the ladder remains in contact with the wall, the wall and the ladder form a circuit.
		When the ladder is moving, we can find the induced emf and therefore the induced current I using the flux rule.
	electron6.phys.utk.edu /phys594/archives/mechanics/newton/newtonian2.htm (970 words)

	Contrast properties of reflective liquid crystal light valves in projection displays (Site not responding. Last check: 2007-10-08)
		Imperfect coating response was distinguished from substrate birefringence in the measurements in Figures 1and 2 by crossing the PBS pass direction against parallel input and output sheet polarizers.
		However, single-pass compound-angle effects are reported [6] in rear-projection monitors that reduce box depth by using a reflective polarizer [7, 8] on the inside surface of the projection screen in order to make an extra fold in the imaging beam [6, 9].
		Even when surface tilts are restricted to the S or P axes of the central ray, compound-angle effects can cause first-order depolarization in off-center rays; this depolarization scales linearly with the difference in skew propagation angle between the off-center ray and the principal ray (linear in amplitude, quadratic in intensity).
	www.research.ibm.com /journal/rd/423/rosenbluth.html (7399 words)

	List of moments of inertia - Wikipedia, the free encyclopedia
		This is a trivial result from the parallel axes rule
		This is a consequence of the parallel axes rule and the fact that the distance between these two axes is always
		This page was last modified 00:23, 7 November 2005.
	en.wikipedia.org /wiki/List_of_moments_of_inertia (299 words)

	Rotational Motion FAQs (Site not responding. Last check: 2007-10-08)
		By convention the direction of the angular velocity is found by using the right-hand rule: Curl the fingers of your
		The direction of the torque is found from the right-hand rule.
		As you will see in the next lesson, these results may also be applied to the case of a moving axis provided that (a) the axis is an axis of symmetry passing through the center of mass of the object, and (b) that the axis moves parallel to itself.
	acad.udallas.edu /physics/GP1/rotationalmotion_faqs.htm (1363 words)

	XXIX-A
		The results show that five converging axes have been attracting entrepreneurship scholars over time: research on personal characteristics of the entrepreneur, on factors affecting new venture perfor-mance, on venture capitalist’s practices and their impact on entrepreneurship, on the influence of social networks, and research drawing from a resource-based perspective.
		This decision rule means, for instance, that a “meaningful” relationship will be said to exist between two references cited 15 times only if both texts are cited together a minimum of four times (i.e.
		Two other axes of convergence remain isolated: a first one links Porter’s (1980) model of industry structure and strategy to Abell’s (1980) text on strategic planning and the importance of “defining the business”; the second one is interestingly constituted of textbooks focusing on the entrepreneurship process (e.g.
	www.babson.edu /entrep/fer/Babson2001/XXIX/XXIXA/XXIXA/xxix-a.htm (4635 words)

	the Great Wall of China in Beijing (Site not responding. Last check: 2007-10-08)
		It is within these walls that 24 emperors of two dynasties, aided by their ministers, eunuch guards, concubines and servants, acted out the drama of ruling imperial China form the early Ming in 1420 the fall of the Qing in 1911.
		Later on in the year of 1473, under the ruling of emperor Chenghua, a building with five pagodas, based on the Bodhgaya model, was constructed here.
		Three parallel axes basically carry out the structure of the monastery with the most important structures on the central axis.
	www.chinaonyourmind.com /chinatravel/chinacity/beijing.html (13186 words)

	EV digest 3724
		It is the exception rather than the rule to find bikes prohibited from a sidewalk.
		Parallel, everybody, motor wise was getting a fair share of the power.
		Newer locos are in Parallel ALL the time, sillycon duz the speed control, nowadaze, as well as control wheelslip, the bain of RR stuff since the dawn of time.
	www.mail-archive.com /ev@listproc.sjsu.edu/msg04929.html (6026 words)

	How to Use 'freeCAD'?
		To fix the orientation fully define a another direction vector in XYZ components that the x axis or the xz plane must be parallel to.
		A rubber band line connects the 'i' and 'j' markers with an label 'rev' to denote the presence of a revolute joint between the 'i' and 'j' markers.
		A revoluteZ joint constraints the origins of 'i' and 'j' to be coincident and the z axes of 'i' and 'j' to be parallel.
	www.askoh.com /freecad/usage8 (1663 words)

	CATHOLIC ENCYCLOPEDIA: Universe
		The fixed stars were recognized to vibrate in double ellipses their major axes parallel to the ecliptic in periods of exactly one year.
		The double ellipses are the images of the terrestrial orbit projected on the celestial sphere by the parallactic displacement of the stars and by the finite velocity of light.
		Now, computation shows that they all have their common focus in the sun and that the earth is, as a rule, outside their orbits.
	www.newadvent.org /cathen/15183a.htm (4022 words)

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