Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated. Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application, it is the perpendicular distance from point mass to the axis of rotation. One can represent a trajectory of a moving point as a body. Radius of gyration can be used to characterize the typical distance travelled by this point. Suppose a body consists of n particles each of mass m. Let r 1, r 2, r 3, …, r n be their perpendicular distances from the axis of rotation; the moment of inertia I of the body about the axis of rotation is I = m 1 r 1 2 + m 2 r 2 2 + ⋯ + m n r n 2 If all the masses are the same the moment of inertia is I = m. Since m = M / n, I = M / n From the above equations, we have M R g 2 = M / n Radius of gyration is the root mean square distance of particles from axis formula R g 2 = / n Therefore, the radius of gyration of a body about a given axis may be defined as the root mean square distance of the various particles of the body from the axis of rotation.

Known as a measure of way in which the mass of rotating rigid body is distributed about its Axis of Rotation. In structural engineering, the two-dimensional radius of gyration is used to describe the distribution of cross sectional area in a column around its centroidal axis with the mass of the body; the radius of gyration is given by the following formula: R g 2 = I A or R g = I A Where I is the second moment of area and A is the total cross-sectional area. The gyration radius is useful in estimating the stiffness of a column. If the principal moments of the two-dimensional gyration tensor are not equal, the column will tend to buckle around the axis with the smaller principal moment. For example, a column with an elliptical cross-section will tend to buckle in the direction of the smaller semiaxis. In engineering, where continuous bodies of matter are the objects of study, the radius of gyration is calculated as an integral; the radius of gyration about a given axis can be computed in terms of the mass moment of inertia I axis around that axis, the total mass m.

In polymer physics, the radius of gyration is used to describe the dimensions of a polymer chain. The radius of gyration of a particular molecule at a given time is defined as: R g 2 = d e f 1 N ∑ k = 1 N ( r k − r m e a

USS McFaul is an Arleigh Burke-class destroyer in the United States Navy. She is named for U. S. Navy SEAL Chief Petty Officer Donald L. McFaul; this ship is the 24th destroyer of her class. USS McFaul was the 11th ship of this class to be built at Ingalls Shipbuilding in Pascagoula and construction began on 26 January 1996, she was launched on 18 January 1997 and was christened on 12 April 1997. On 25 April 1998 she had her commissioning ceremony at the Garden City Terminal in Savannah, Georgia. On 22 August 2005, McFaul was involved in a minor collision with the destroyer USS Winston S. Churchill off the coast of Jacksonville, Florida. Both ships suffered minor damage, no injuries were reported. Both ships returned to their homeport at Naval Station Norfolk under their own power. On 16 February 2007, McFaul was awarded the 2006 Battle "E" award. On 24 August 2008, McFaul arrived in Batumi, Georgia, as part of Operation Assured Delivery to "deliver humanitarian relief supplies... as part of the larger United States response to the government of Georgia request for humanitarian assistance" in the wake of the 2008 South Ossetia war.

McFaul offloaded nearly 155,000 pounds of supplies—including hygiene items, baby food and care supplies, bottled water, milk—donated by the United States Agency for International Development. On 5 April 2010, McFaul responded to a distress call from the merchant vessel MV Rising Sun after she was attacked by pirates. McFaul was able to neutralize the threat, captured ten suspected pirates and rescued eight crewmembers from on board a dhow near Salalah, Oman; the pirates were transferred to the destroyer USS Carney for a week before they were transferred back to McFaul where 30 days they were turned over to the Somali Transitional Federal Government for subsequent prosecution. On 12 September 2012, McFaul was ordered to the coast of Libya in what the Pentagon called a "contingency" in case a strike was ordered; this was in response to the 2012 diplomatic missions attacks. The ship may have been assigned to Carrier Strike Group Ten in the 2010s. On 12 November 2009, the Missile Defense Agency announced that McFaul would be upgraded during fiscal 2013 to RIM-161 Standard Missile 3 capability in order to function as part of the Aegis Ballistic Missile Defense System.

The shield has background of dark blue with Neptune being pulled by seahorses in a chariot over sea waves. The traditional Navy colors were chosen for the shield because dark blue and gold represents the sea and excellence respectively. Neptune, God of the Sea, symbolizes swift mobilization. Waves represent the coastline and highlight Chief Petty Officer McFaul's enclosure from sea by rubber raiding craft to block General Noriega's escape from Panama; the crest consists of the shape of an array with a gold cross center. The array is split into quarters with palm leaves surrounding; the crests AEGIS shape highlights the USS McFAUL's modern multi-mission warfare operations. The cross honors the Navy Cross awarded to Platoon Chief Petty Officer Donald L. McFaul for extraordinary heroism in action under fire and saving his teammate's life; the quarter colored crest are adapted from the Panamanian flag to represent operation "Just Cause" in the Republic of Panama. The quartered sections honor McFaul's SEAL team, SEAL Team Four.

The laurel symbolizes honor. The palm indicates to the location of Panama; the motto is written on a scroll of blue. The ships motto is "Courage Honor Sacrifice"; the coat of arms in full color as in the blazon, upon a white background enclosed within a dark blue oval border edged on the outside with a gold rope and bearing the inscription "USS McFAUL" at the top and "DDG 74" in the base all gold. This article includes information collected from the Naval Vessel Register, which, as a U. S. government publication, is in the public domain. Official site Naval Vessel Register – DDG-74

Tajuria matsutaroi motokoae is a butterfly of the family Lycaenidae. It is a subspecies of Tajuria matsutaroi; this subspecies is found on Leyte island in the Philippines. Its forewing length is 16–19 mm. Subspecies motokoae is distinguishable from the nominotypical subspecies by the following characters of the upperside: 1) ground colour is decidedly darker and tinged with purple, while only tinged with pale purple in subspecies matsutaroi, 2) black border is broader in spaces 1b, 2 and the upper part of the cell on the forewing, 3) in the female, the upperside costal area is blackish, whereas it is whitish in subspecies matsutaroi. Hayashi, Hisakazu, 1984: A New Tajuria from Mindanao. Tyô to Ga. 34: 127-129.. Hayashi, Hisakazu, 2011: A new subspecies of Tajuria matsutaroi from Lyte Is; the Philippines. Tyô to Ga. 62: 33-34. Treadaway, Colin G. & Schrőder,Heinz,2012: Revised checklist of the butterflies of the Philippine Islands. Nachrichten des Entomologischen Vereins Apollo, Suppl. 20: 1-64