Two disks with different moments of inertia rotating on a common shaft

[lmc489]

Homework Statement

Two disks with moments of inertia I and 31 are mounted on a common shaft with frictionless bearings. They are initially rotating with angular speeds of w and 2w. They are brought together without being disturbed. What is their final KE as a fraction of their initial KE?

The answer is 49/52 but i don't understand the concept of it.
can someone please explain?

Equations:
Angular Momentum: Iw = Iw

 

[hage567]

You will need to use conservation of angular momentum and conservation of rotational energy.

Start by writing out these quantities for each disk and then when the disks are brought together.