Solving Inertia of a Record Homework

[pucr]

Homework Statement

A turntable for playing records has a moment of inertia of 5.2 kgm^2 and is rotating with an angular velocity of 36 rpm. A record, initially at rest is dropped straight down onto the rotating turntable. The record and turntable rotate together at 33 rpm. Find the moment of the inertia of the record.

Homework Equations

$$\omega_{i} = \frac{6\pi}{5} \frac{rad}{sec}$$
$$\omega_{f} = \frac{11\pi}{10} \frac{rad}{sec}$$

The Attempt at a Solution

I really don't have a clue about how to solve this. It's a problem on a practice exam, not homework. I thought I could solve it with torque, but then there is no coefficient of friction to calculate force.
The only thing I can think to do is to calculate the difference in kinetic energy but that didn't give me the right answer.
If someone could give me some direction that would be amazing. Thanks.

 

[LowlyPion]

Rotational Kinetic Energy looks to be the key.

You have something rotating with a known I*ω²/2

And you are given a modified I*ω²/2 (the added mass of the record - distributed in the same manner as the turntable)
that yields a new I*ω²/2 where they give you the new ω.