Understanding the Meaning of Radius of Gyration in Spinning Wheels | Explained

[helpinghand]

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

 

[PhanthomJay]

For an area, A, with an area moment of inertia of I, the radius of gyration, r, is $r = \sqrt {I/A}$.
For a mass, m, with a mass moment of inertia of I, the radius of gyration, k, is $k = \sqrt{I/m}$.
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 $L/\sqrt 3$, which implies that a point mass located a distance $L/\sqrt 3$ from the end has the same moment of inertia (I = mr² = mL²/3).