Radius of Gyration

  • #1

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Hey Guys,

I having trouble with understanding radius of gyration, could someone please explain what it is? I have just never understood it's full meaning. So for example, the radius of gyration of a spinning wheel of a car is ....some value... What does that mean?

Thanks
 

Answers and Replies

  • #2
PhanthomJay
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For an area, A, with an area moment of inertia of I, the radius of gyration, r, is [itex]r = \sqrt {I/A}[/itex].
For a mass, m, with a mass moment of inertia of I, the radius of gyration, k, is [itex]k = \sqrt{I/m} [/itex].
In either case, it represents the distance of an equivalent line area or point mass , respectively, to the axis about which the moment of inertia is taken, to yield an equivalent moment of inertia. For example, a thin rod of length L has a mass moment of inertia about an axis perpendicular to one end of mL2/3. It's radius of gyration is thus [itex]L/\sqrt 3 [/itex], which implies that a point mass located a distance [itex]L/\sqrt 3 [/itex] from the end has the same moment of inertia (I = mr2 = mL2/3).
 

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