Radius Of Gyration
Sometimes the moment of inertia of a body about a specified axis will be given using the radius of gyration, k
. Given the value k
and the mass of the body (m
) we can calculate its moment of inertia (I
), using the following formula:
Consequently, the radius of gyration is given by
The physical interpretation of the radius of gyration is that it is the radius of a uniform thin hoop (or ring), having the same moment of inertia (about an axis passing through its geometric center — shown below), as the given body about the specified axis.
The moment of inertia of the thin hoop about the blue axis passing through its geometric center is:
The radius of gyration can be useful for listing in a table. If you want to know the moment of inertia of a complex shaped body about a given axis you simply look up its radius of gyration, and then (knowing its mass) apply the above formula to find the moment of inertia.
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