Question

1. Find the radius of gyration of a uniform disc about an axis perpendicular to its plane and passing through its center.

Answer 1

To find:

Radius of gyration of a uniform disc about an axis perpendicular to its plane and passing through its center.

Calculation:

First of all, moment of inertia of the disc along the specified axis will be :

$\rm\therefore \: MI = \dfrac{m {r}^{2} }{2}$

• Here, m is mass , r is radius of disc.

Now, radius of gyration is defined as:

• The radius of a ring having the same moment of inertia as that of the disc along that specified axis.

• Let radius of gyration be x :

$\rm \therefore \: MI_{ring} = MI_{disc}$

$\rm \implies \: m {x}^{2} = \dfrac{m {r}^{2} }{2}$

$\rm \implies \: {x}^{2} = \dfrac{ {r}^{2} }{2}$

$\rm \implies \: x = \dfrac{r}{ \sqrt{2} }$

So, radius of gyration is r/√2.