- #1

Nexus99

- 103

- 9

- Homework Statement:
- A rigid body consists of two thin and coaxial disks having the same density and thickness. One disk has a radius ##R##, while second has a radius of ##2R##. The total mass is ##m##. Calculate the total moment of inertia respect to an axis passing through the center of the rigid body and perpendicular to the disk surfaces

- Relevant Equations:
- density, lenght of a circumference ecc.

The total moment of inertia is:

##I_{tot} = 2 M_1 R^2 + \frac{1}{2} M_2 R^2##

We have ## M_1 = (4 \pi R^2) \sigma ## and ##M_2 = (\pi R^2) \sigma ## , where ## \sigma ## is the density of the disks.

We also know that:

## \sigma = \frac{m}{ \pi 5 R^2} ##

this leads us to say that:

##I_{tot} = \frac{17}{10} m R^2 ##

Is it ok?

##I_{tot} = 2 M_1 R^2 + \frac{1}{2} M_2 R^2##

We have ## M_1 = (4 \pi R^2) \sigma ## and ##M_2 = (\pi R^2) \sigma ## , where ## \sigma ## is the density of the disks.

We also know that:

## \sigma = \frac{m}{ \pi 5 R^2} ##

this leads us to say that:

##I_{tot} = \frac{17}{10} m R^2 ##

Is it ok?