Question

Calculate the radius of gyration of a uniform circular disk of radius $r$ and thickness t about a line perpendicular tothe plane of this disk and tangent to the disk as shown in figure.

Answer 1

We know that

$Moment$ $of$ $Inertia$ $=Mass\times Radius$ $of$ $Gyration$

Since

Moment of Inertia of disc (With axis passing through COM) = $\frac{1}{2}M{R}^2$}

Radius of Gyration of disc = $\frac{1}{2^{\left(0.5\right)}}R$

Applying Parallel Axis Theory

$K^2=K_C^2+d^2$

here $K_C=$ Radius Of Gyration about axis passing through COM

$d=$ Distance between Axis

$K^2=$ $\frac{1}{2}{R}^2+R^2$

$K^2=$ $\frac{3}{2}{R}^2$

$K=$ $\sqrt{\frac{3}{2}}R$