- #1
RaamGeneral
- 50
- 1
Hello, sorry for this stupid question.
I struggled to find the moment of inertia of half solid thin disk (about the center of the disk) through an integration, but I couldn't get the right value.
I'm pretty sure it has to be [tex]MR^2/4[/tex], but
[tex]
I=\int r^2 dm \\
dm=(M/A)dS[/tex]
With [tex]A=\pi R^2/2[/tex]
I compute the integration in polar coordinates, where [tex]dS=r dr d\theta[/tex] with 0<r<R and 0<theta<pi:
[tex] 2M/(\pi R^2) \int_0^R \int_0^\pi r^3 d\theta dr=MR^2/2[/tex]
Where am I wrong?
I struggled to find the moment of inertia of half solid thin disk (about the center of the disk) through an integration, but I couldn't get the right value.
I'm pretty sure it has to be [tex]MR^2/4[/tex], but
[tex]
I=\int r^2 dm \\
dm=(M/A)dS[/tex]
With [tex]A=\pi R^2/2[/tex]
I compute the integration in polar coordinates, where [tex]dS=r dr d\theta[/tex] with 0<r<R and 0<theta<pi:
[tex] 2M/(\pi R^2) \int_0^R \int_0^\pi r^3 d\theta dr=MR^2/2[/tex]
Where am I wrong?