We can write the moment of inertia I of a body as
(1) where
is the mass and
is the radius of gyration of the body about the same axis from which the radius of gyration was calculated. For a uniform disc of radius
about an axis through the centre perpendicular to the disc the moment of inertia is
and equating this to (1) gives
The radius of gyration can be defined concisely as as the distance from the centre of rotation of a rotating body to the point where the mass can be considered to be concentrated, as if the body were a single particle of massat a distance equal to the radius of gyration from the axis of rotation.
The radius of gyration of some other simple solids are given in the table below.
Solid | Radius of Gyration |
Uniform thin rod of length l fixed at one end |
|
Uniform thin rod of length l about the middle |
|
Solid cylinder of radius |
|
Hollow cylinder of radius |
|
Solid sphere of radius |
|
