Question

a 12kg uniform disc has a radius of 25cm and spins on an axis through it's centre and perpendicular to it's plane find the radius of it's gyration

Answer 1

The moment of inertia of a disc of mass $M$ and radius $R$ about an axis through its center and perpendicular to its plane is given by

$I=\frac{1}{2}MR^2$ ..............(1)

In terms of radius of gyration, $I=MK^2$ ................(2)

Here, $I$ is the moment of inertia and $K$ is the radius of gyration.

From (1) and (2),

$MK^2=\frac{1}{2}MR^2\\ \Rightarrow K^2=R^2/2\\ \Rightarrow K=R/\sqrt 2$

The radius of the disc is $R=25\ cm$

Therefore, the radius of gyration is $K=\frac{25\ cm}{\sqrt 2} = 17.7\ cm$

Answer: The radius of gyration of the disc which spins on an axis through its centre and perpendicular to its plane is 17.7 cm.