disk with inertia, finding angular velocity final with two disks

Question

A disk of moment of inertial 625 kg m² is rotating in a horizontal plane about an axis through its center with an angular speed of 13.0 rad/s. If a second, identical, but not rotating disk, is placed on top of the rotating disk, what will be the new rotation speed when the two disks rotate together?

𝜔_final =  rad/s

Answer 1

This is a question about conservation of angular momentum:

The angular momentum of the two disks together will be the same

as the original angular momentum of the single disk.

The general expression for angular momentum is

L = Iω

where I is the moment of inertia and ω is angular velocity.

You can rewrite it as

ω = L/I

In general, if you keep the angular momentum L the same, but double the moment of inertia I,

then the angular velocity ω is cut in half.

So your problem can be solved without actually knowing the moment of inertia

given to you.