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Radius of Gyration

  1. Nov 27, 2011 #1
    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?

  2. jcsd
  3. Nov 28, 2011 #2


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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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