This site (as does Wikipedia) gives a good definition and development.  The operative word is, “defined”  and it looks like it comes from the concept of a “distance from the neutral axis”, i.e. a “radius”.  It gives the measure of distribution of area, mass, etc across a section.  Don’t know from where it originated but I’d say it’s a result of “defining” mathematically.
http://www.efunda.com/math/areas/RadiusOfGyrationDef.cfm
Thor A. Tandy P.Eng, C.Eng, Struct.Eng, MIStructE
 Victoria, BC
 Canada 
From: Richard Calvert [mailto:RichardC@lbbe.com] 
 Sent: Saturday, June 20, 2009 11:59 AM
 To: seaint@seaint.org
 Subject: Radius of Gyration
Does anyone know the origin of this term?  Why it refers to a radius and/or what is gyrating? It just seems to specific to be simply obscure… yet I’ve never found anyone who knows. So, anyone on here know?
Richard Calvert, EIT 
Lindemann Bentzon Bojack 
Architects & Engineers
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