Mass Moment of Inertia - Thin - Cylinder

[erobz]

Homework Statement

Apparently the Mass moment of inertia of a cylinder about the axis shown is $I = \frac{1}{4}MR^2$

Relevant Equations

$\int_V \rho r^2 dm$

The integral is a bit nasty.

$$ I = 4 w \rho \int_0^R x^2 \sqrt{R^2-x^2} dx $$

Just inquiring if I try it, I'm not chasing an approximation, or verify someone gets/has gotten the result.

 

[erobz]

Never mind- I figured out how to confirm it with symbolic calculator. It does appear to be equivalent.

 

[Walter Black]

Homework Statement: Apparently the Mass moment of inertia of a cylinder about the axis shown is $I = \frac{1}{4}MR^2$
Relevant Equations: $\int_V \rho r^2 dm$

View attachment 359392

The integral is a bit nasty.

$$ I = 4 w \rho \int_0^R x^2 \sqrt{R^2-x^2} dx $$

Just inquiring if I try it, I'm not chasing an approximation, or verify someone gets/has gotten the result.

Well you can substitute x for Rcos$ and it would become way easier , i got the final value after putting in the limits (πR^2)/16 . Thanks