Question

What is the radius of gyration of a disc of radius 20 cm, rotating about an axis passing through its center and normal to its plane?

Answer 1

Let the radius of gyration is k. Then for the disk,
$$\begin{gathered} m{k}^2=I \\ \Rightarrow m{k}^2=\frac{1}{2}m{r}^2 \\ \Rightarrow k=\frac{r}{\sqrt{2}}=\frac{20}{\sqrt{2}}=10\sqrt{2}cm \end{gathered}$$