Consider a system composed of two plane disks, which we will designate
as and . Their radii are and respectively . The
disk is fixed over the disk and a distance from the
center, as in the figure. The disk can spin and move freely in a
friction-free platform, while the other disk is fixed on a point
of disk , but can spin freely without friction. No external forces
act on the system. The masses of the disks are and
Demonstrate that the angular velocity of both disks is a constant, in
angles are defined in the figure.
![Two Disks] (https://dl.dropboxusercontent.com/u/38822094/TwoDisks.JPG)
I will start by writing the conservation laws of both disks, in linear
momentum by components we have:
Then the equation for the conservation of energy:
The longest one is the conservation of momentum... (with respect the
origin of the coordinate systems)
Could you tell me if these equations are correct? As a next step I am thinking of deriving each of the equations above and joining them in some way using the fact that ,,.
Is there an easier way?