Moment of inertia of 3 disc system

[Rosengrip]

Homework Statement

We have 3 discs, arranged as the sketch below shows. Find the moment of inertia of the whole system around the axis, passing horizontally through center of the bigger disk:

1. Two smaller disks are fixed and cannot rotate around their axes.

2. Two smaller disks can rotate freely around their axes.


R is the radius of big circle
r is the radius of 2 smaller disks
L is the distance between COM and axes of smaller disks.
M is the mass of bigger disk
m is the mass of 2 smaller disks

[PLAIN]http://www.shrani.si/f/3L/Os/9CLgTJj/rotacija.jpg

Homework Equations

I = (1/2)*m*R^2 ---> moment of inertia for disk
Parallel axis theorem

The Attempt at a Solution

For the 1st point, my solution would be:
I = (0.5)*M*R^2 + 2*((0.5)*m*r^2 + m*L^2)

However I am not sure about the 2nd one, any hints? Thanks in advcance

 

[tiny-tim]

Hi Rosengrip!

(try using the X² icon just above the Reply box )

We have 3 discs, arranged as the sketch below shows. Find the moment of inertia of the whole system around the axis, passing horizontally through center of the bigger disk:

2. Two smaller disks can rotate freely around their axes.
…
For the 1st point, my solution would be:
I = (0.5)*M*R^2 + 2*((0.5)*m*r^2 + m*L^2)

However I am not sure about the 2nd one, any hints? Thanks in advcance

Your 1 looks fine.

For 2, I think you're meant to assume that the small discs do not rotate on their own axes (ie they always face the same way).

 

[Rosengrip]

Hm, I don't have the right formula just yet but I somehow think that system moment of inertia in 2nd scenario would be bigger than one in 1st. Is that the correct assumption?

From center of bigger disk POV, the smaller disk rotates in point 2., whereas in point 1. it stands still. The situation is reversed from outside POV (in point 2. vertical line drawn on the smaller disk would always point downwards).

What bothers me is that I can't really formulate the problem under 2nd point, since all we did were cases which fall under point 1 :(

 

[tiny-tim]

Hi Rosengrip!

Hm, I don't have the right formula just yet but I somehow think …

erm … physics is equations!

stop philosophising, and do the equations …

if necessary, go back to the definition and do an ∫ (do it for something easier, like a rod!)