Find the radius of gyration of a disc of mass M and radius R rotating about an axis passing through the center of mass and perpendicular to the plane of the disc.

Explanation

The moment of inertia of a disc about an axis passing through the center of mass and perpendicular to the disc is, `I=(1)/(2)MR^(2)`
In terms of radius of gyration, `I=MK^(2)`
Hence, `MK^(2)=(1)/(2)MR^(2), K^(2)=(1)/(2)R^(2)`
`K=(1)/(sqrt(2))RorK=(1)/(1.414)RorK=(0.707)R`
From the case of a rod and also a disc, we can conclude that the radius of gyration of the rigid body is always a geometrical feature like length, breadth, radius or their combinations with a positive numerical value multiplied to it.