Question

Calculate moment of inertia of a disc about its diameter having a R?

Answer 1

Answer:

The moment of inertia of a disc about one of its diameter is I. The mass per unit area of disc is proportional to the distance from the centre. ...

We can calculate the mass moment of inertia along the axis through the centre, perpendicular to the plane of the disc by integrating...

Answer 2

let the radius is=R

and mass=M

therefore. area of the disc=πR²

mass per unit area=M/πR²

.......

now...a small ring of width dx and of radius X is taken ...

therefore area of that ring=2πx.dx

therefore mass of the ring$=\frac{2M}{R {}^{2} } \times x.dx$

now ..the moment of inertia of that ring is

$= \frac{2M}{R{}^{2} } \times x.dx \times x {}^{2}$

therefore..the moment of inertia of the disc is..

I= ∫ $\frac{2M}{R {}^{2} } \times x.dx \times x {}^{2}$

(range from 0 to R)

$=\frac{2M}{R {}^{2} }\frac{R^{}{4}}{4} \\\\\\ I=\frac{MR{}^{2}}{2 }$

$\:\:\:\: \: \: \: \large\mathfrak{\underline{\huge\mathcal{\bf{\boxed{\boxed{\huge\mathcal{I=\frac{MR{}^{2}}{2 }}}}}}}}$

••••hope this helps you.........••••