moment of inertia - 2

[logistic_guy]

Find the moment of inertia \(\displaystyle I\) of a uniform cylinder of radius \(\displaystyle R\), and mass \(\displaystyle M\) if the rotation axis is through its center.

 

[logistic_guy]

In the previous post we found that the moment of inertia of a uniform hollow cylinder is \(\displaystyle I_z = \frac{1}{2}M\left(R^2_2 + R^2_1\right)\).

It can be found here.

moment of inertia

Find the moment of inertia I of a uniform hollow cylinder of inner radius R_1, outer radius R_2, and mass M if the rotation axis is through its center. Hint: I = \int R^2 \ dm

www.freemathhelp.com

The moment of inertia of a uniform cylinder is the same but with \(\displaystyle R_1 = 0\).

Then the answer to this problem is:

\(\displaystyle I_z = \textcolor{blue}{\frac{1}{2}MR^2}\)

Of course it would be more fun to derive it with integration!