Question

Use equationI=∫r2dmto calculate the moment of inertia of a uniform, solid disk with mass M and radius R for an axis perpendicular to the plane of the disk and passing through its center. Express your answer in terms of the variables M and R.

Answer 1

`I = (1)/(2)MR^2`

Step-by-step explanation:

Let say the ring is made up of small rings of radius "r" and thickness "dr"

so here we have

`dm = \rho (2\pi r dr)`

so we have

`dm = (M)/(\pi R^2)(2\pi r dr)`

`dm = (M(2rdr))/(R^2)`

now from above formula we have

`I = \int r^2 dm`

`I = \int r^2((M(2rdr))/(R^2))`

so we have

`I = (1)/(2)MR^2`