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Topic: Radius of gyration

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	Radius of gyration - Wikipedia, the free encyclopedia
		The radius of gyration (possibly multiplied by a constant factor) is a useful estimate of the size of a molecule.
		In structural engineering, the two-dimensional radius of gyration is used to describe the distribution of cross-sectional area in a beam around its centroidal axis.
		The gyration radius is useful in estimating the stiffness of a beam.
	en.wikipedia.org /wiki/Radius_of_gyration (427 words)

	Kin 241b
		The radius of gyration is used to calculate the rotational inertia of a body whereas the radius of rotation is used to calculate the linear velocity of a rotating point.
		The radius of gyration is defined as a measure of the average distribution of the mass of an implement.
		It is part of the implement's rotational inertia, thus, the greater the radius of gyration, the greater the inertia and the smaller the angular velocity generated by a given torque.
	instruct.uwo.ca /kinesiology/241b/mj.htm (1797 words)

	Lecture 30: Radius of Gyration & Buckling
		The radius of gyration (r) describes the way in which the area of a cross-section is distributed around its centroidal axis.
		This is because it has an equal radius of gyration in all directions and it has the its area distributed as far away as possible from the centroid.
		is the buckling length and r is the radius of gyration.
	darkwing.uoregon.edu /~struct/courseware/461/461_lectures/461_lecture30/461_lecture30.html (652 words)

	Proprg.htm (Site not responding. Last check: 2007-11-03)
		A bifilar pendulum was constructed to measure the radius of gyration of each propeller.
		The propellers selected for measurement of radius of gyration had both 2 and 3 blades and ranged from 6 to 11 inches in diameter, A substantial amount of time was spent measuring the balance tray by itself because for small propellers it will add significantly to the inertia.
		The moment of inertia, I of the propellers in terms of the mass, m and the radius of gyration r
	www.geocities.com /AMA271/Aeronotes/proprg.htm (263 words)

	Radius Of Gyration Definition
		The Radius of Gyration of an Area about a given axis is a distance k from the axis.
		The Radius of Gyration of a Mass about a given axis is a distance k from the axis.
		This is equivalent to using the general Radius of Gyration equation on a rectangle.
	www.efunda.com /math/areas/RadiusOfGyrationDef.cfm (187 words)

	Radius of Gyration (Site not responding. Last check: 2007-11-03)
		The radius of gyration is defined as (I/M)^1/2, or the square root of the moment of inertia divided by mass.
		Conceptually, the radius of gyration is the distance that, if the entire mass of the object were all packed together at only that radius, would give you the same moment of inertia.
		That is, if you were to take the entire mass of the disk-shaped flywheel with some radius and pack it into a narrow donut whose radius is the flywheel's radius of gyration, they'd both have the same moment of inertia.
	van.hep.uiuc.edu /van/qa/section/Making_stuff_move/Stuff_that_Spins/976820467.htm (231 words)

	Catsailor.com: Finally a carbon mast also on the Olympic Tornado! (Site not responding. Last check: 2007-11-03)
		Boat B has smaller radius of gyration with respect to it's three rotational axes: pitch, roll, and yaw (this is the technically correct term in continuum mechanics in this country).
		Point of this example is that a similar reduction in radius of gyration can be had by both increasing and decreasing weight; both leading to better performing and worse performing boats.
		Radius of Gyration, although technical useable, is therefor a traiterius principle to use.
	www.catsailor.com /forums/showflat.php?Cat=&Board=Test&Number=34682&page=0&view=collapsed&sb=5&o=&fpart=5 (1346 words)

	[No title]
		Radius of gyration: 0.355752392535 (m), 35.575239 (cm) Moment of inertia: 0.153175543915 (kgm^2), 1531755.439148 (gcm^2) 6/7.5/11in.
		Radius of gyration: 0.000000000000 (m), 0.000000 (cm) Moment of inertia: 0.000000000000 (kgm^2), 0.000000 (gcm^2) 6/7.5/11in.
		Radius of gyration: 0.108816964229 (m), 10.881696 (cm) Moment of inertia: 0.009788358412 (kgm^2), 97883.584118 (gcm^2) 75mm MMT Public Missiles Ltd. - PT-3.0 - Airframe tube, Material: Kraft phenolic OD: 3.126 In.
	www.highrf.com /Rockets/Parts%20Listing.txt (521 words)

	Radius of gyration
		The radius of gyration of an area with respect to a particular axis is the square root of the quotient of the moment of inertia divided by the area.
		In other words, the radius of gyration describes the way in which the total cross-sectional area is distributed around its centroidal axis.
		The radius of gyration of a mass is similar except that the moment of inertia of the mass is involved.
	www.fastload.org /ra/Radius_of_gyration.html (248 words)

	Catsailor.com: Finally a carbon mast also on the Olympic Tornado! (Site not responding. Last check: 2007-11-03)
		The boat radius of gyration is directly related to the amount of energy it takes to move a boat through waves (reduces pitching moment and rolling moment).
		In short the lever (or radius of gyration for that particular element or part) is squared while the mass is not.
		It is a fictitous radius that when squared and multiplied by the mass of a body produces the same moment of inertia as acquired by integrating the elements of a body times the radius squared to each element over the entire length of the body from some reference axis.
	www.catsailor.com /forums/showflat.php?Cat=&Board=Test&Number=34682&page=0&view=collapsed&sb=5&o=&fpart=4 (3591 words)

	Rectangular Cross-Section
		Similarly, the radius of gyration about a vertical axis passing through the center of the cross-section is
		The radius of gyration can be thought of as the ``effective radius'' of the mass distribution with respect to its inertial response to rotation (``gyration'') about the chosen axis.
		A circular cross-section has only one, and its radius of gyration is equal to half its radius, as shown in the next section.
	www-ccrma.stanford.edu /~jos/waveguide/Rectangular_Cross_Section.html (125 words)

	PS674 (Site not responding. Last check: 2007-11-03)
		The squared radius of gyration depends on the coordinates of all of the atoms and on their masses.
		The radius of gyration can be defined for any collection of points, without the need to specify their connectivity.
		For a polyethylene chain with a molecular weight of 100,000, these two extremes for the radius of gyration are about 2.2 nm and 180 nm.
	gozips.uakron.edu /~mattice/ps674/endv.html (422 words)

	[trikes] Trice Micro/16 inch trike wheels (Site not responding. Last check: 2007-11-03)
		The radius of gyration is the radius at which most of the mass can be considered to be located.
		Now in cycle wheels the radius of gyration will be close to the rim as this is where most rotating mass is located, so the 349 wheel will have a smaller radius of gyration than a 406 wheel.
		So although a 406 wheel may be the same mass its radius of gyration will be bigger, thus the moment of inertia will be larger, thus the wheel will accelerate slower for a given torque.
	www.ihpva.org /pipermail/trikes/2000q3/003313.html (446 words)

	Longitudinal Radius of Gyration
		We have been able to make numerous measurements of the longitudinal radius of gyrationsthrough the center of graity of the bike/rider, Kx.
		The bike swing is used to determine Kx for the class project bikes.
		FInding Kx The radius of gyration is an important value for the designer.
	www.calpoly.edu /~wpatters/wave4.html (390 words)

	Perfection Clutch: CALCULATING CLUTCH TORQUE CAPACITY
		The second variable is the mean radius of the of the friction material in feet.
		The Radius of Gyration in Feet = Square Root of (Outer Radius in Feet Squared + Inner Radius in Feet Squared / 2).
		The Radius of Gyration in Feet = Square Root of (0.348' squared + 0.246' squared / 2).
	perfectionclutch.blogspot.com /2005/07/calculating-clutch-torque-capacity.html (711 words)

	SPIDER: CG 3 (Center of Gravity - radius of gyration) (Site not responding. Last check: 2007-11-03)
		Compute center of gravity and radius of gyration of a 3-D density distribution.
		The coordinates of the center of gravity, with respect to the center at (NSAM/2 + 1, NROW/2 + 1, NSLICE/2 +1), and the radius of gyration are printed out and put into the first four (optional) registers appearing on the command line.
		For the definition of the radius of gyration, see International Tables of Crystallography, vol.
	www.wadsworth.org /spider_doc/spider/docs/man/cg3.html (110 words)

	PS674
		What is the radius of gyration of a uniform sphere of radius 10 nm?
		A monodisperse polybutadiene fraction with M = 50,000 has a root-mean-square radius of gyration of 6.8 nm.
		If a linear poly(1,4-cis-butadiene) chain has a root-mean-square radius of gyration of 50 nm in dilute solution in a Theta solvent, estimate the root-mean-square end-to-end distance in the bulk polymer, in the absence of solvent:
	gozips.uakron.edu /~mattice/ps674/qnum.html (643 words)

	A Method for Determining Transmembrane Helix Association and Orientation in Detergent Micelles Using Small Angle X-Ray ...
		to be parallel by radius of gyration analysis.
		The measured apparent radius of gyration is (Yeager, 1976
		of gyration of SN was 32 ± 2 Å.
	www.biophysj.org /cgi/content/full/77/2/1064 (4635 words)

	Dymag at Streetfighters USA - Streetfighter Parts & Accessories (Site not responding. Last check: 2007-11-03)
		The mass of a wheel is deemed to act at a certain radius from the center of the wheel (radius of gyration).
		Hence reducing the radius of gyration, improves the manoeuvrability of the motorcycle.
		This is achieved by lightening the rim as this is on the extreme radius, and designing the spoke system with minimal weight at the extreme, whilst maintaining the required strength and stiffness.
	www.streetfighters-usa.com /store/dymag.html (715 words)

	Effective Dimensions of Oligomers in Size Exclusion Chromatography. A Molecular Dynamics Simulation Study (Site not responding. Last check: 2007-11-03)
		At the same radius of gyration, the retention radii order is found to be PS > PIB > PE.
		The approach of the mean-square radius of gyration and mean-square end-to-end distance dependence on chain length to limiting long-chain behavior is discussed.
		]M) as a measure of radius of gyration, the radius of gyration determined independently, and the retention radius from simulation as criteria for equal retention times is made.
	pubs.acs.org /cgi-bin/abstract.cgi/mamobx/1996/29/i04/abs/ma9508663.html (504 words)

	Definition of Gyration from dictionary.net
		The act of turning or whirling, as around a fixed center; a circular or spiral motion; motion about an axis; rotation; revolution.
		If a burning coal be nimbly moved round in a circle, with gyrations continually repeated, the whole circle will appear like fire.
		Radius of gyration the distance between the axis of a rotating body and its center of gyration.
	www.dictionary.net /gyration (88 words)

	BYU DIPPR Forums - measurement units of tha radius of gyration
		BYU DIPPR Forums - measurement units of tha radius of gyration
		my query is this....i am using the dippr database but i dont know the measurement units of the radius of gyration for organic compounds...can i have some help on this please?
		Default Unit of the radius of gyration in DIPPR 801 database is "m" (meter).
	dippr.byu.edu /forums/topic.asp?TOPIC_ID=53& (56 words)

	Half Cylindical Shell (Site not responding. Last check: 2007-11-03)
		If it is not, calculate the surface area of the Circular Cylinder (lateral + base) using the outer radius of the base circle.
		Subtract the volume calculated by using the inner radius from the volume calculated by using the outer radius and divide the result by two.
		For none constant density see the general integral forms of Mass, Mass Moment of Inertia, and Mass Radius of Gyration.
	www.engineering.com /content/ContentDisplay?contentId=41005046 (199 words)

	[No title]
		Given the information in Problem 1, estimate the radius of gyration of a polystyrene with molecular 46,000,000 (this is the largest PS I know).
		Consider a thin solid disk of radius R and uniform thickness and uniform density.
		Obtain an expression for Rg of such a stack in terms of the radius of each disk, R, and the number of disks, N, each of thickness t.
	www.chem.lsu.edu /htdocs/people/psrusso/4595/f96set3.doc (610 words)

	Small-Angle Neutron Scattering from Single Arm Labeled Polybutadiene Star Polymers in Dilute Solution (Site not responding. Last check: 2007-11-03)
		No dependence of the radius of gyration on star polymer concentration was noted, but the radius of gyration of the labeled arm increased as the functionality of the star increased from 3 to 12, the increase in dimensions in the 12-arm star being ca.
		In these dilute solutions the radii of gyration were larger than obtained for the bulk melt state of the stars.
		The data have been compared with theoretical predictions, but generally a much stronger dependence of the radius of gyration on star functionality is observed than is predicted.
	pubs.acs.org /cgi-bin/abstract.cgi/mamobx/2001/34/i16/abs/ma010048c.html (284 words)

	Percolation and cluster structure parameters: The radius of gyration
		The squared radius of gyration of percolation clusters are determined in terms of the clusters' second spatial moments using the enhanced Hoshen - Kopelman algorithm for square and triangular lattices containing
		Correlation length exponents and related exponents as well as their corresponding amplitudes are calculated in terms of the squared radius of gyration above and below the percolation threshold.
		A coefficient for cluster compactness that is based on the squared radius of gyration of a cluster is introduced.
	stacks.iop.org /0305-4470/30/8459 (256 words)

	center of gyration - Definitions from Dictionary.com
		Center of gravity (Mech.), that point of a body about which all its parts can be balanced, or which being supported, the whole body will remain at rest, though acted upon by gravity.
		Center of gyration (Mech.), that point in a rotating body at which the whole mass might be concentrated (theoretically) without altering the resistance of the intertia of the body to angular acceleration or retardation.
		Center of inertia (Mech.), the center of gravity of a body or system of bodies.
	dictionary.reference.com /search?q=center%20of%20gyration (658 words)

	Radius of gyration and second moments of area (Site not responding. Last check: 2007-11-03)
		What are the pratical applications of the radius of gyration and the second moments of area and volume.
		Both the radius of gyration and the second moment of area are used to help us describe how objects rotate.
		The moment of inertia is computed by weighting the second moment of the area with the density of the material the object is made from.
	van.hep.uiuc.edu /van/qa/section/Making_Stuff_Move/Stuff_that_Spins/20020604164241.htm (184 words)

	Circular Cross-Section
		radius of gyration about any line passing through the center of the cross-section is given by
		Thus, the radius of gyration about any midline of a circular cross-section of radius
		, the radius of gyration is given by
	ccrma-www.stanford.edu /~jos/waveguide/Circular_Cross_Section.html (96 words)

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