You have an apparatus that spins a horizontal disk and ring which share the same rotational axis.

You have an apparatus that spins a horizontal disk and ring which share the same rotational axis. A string has one end wrapped around the plastic spool (under the disk) and the other end passing over a vertical pulley lined up with the tangent to the spool. A mass is hung from the free end of the string so it can fall past the table, spinning the system.

The spinning disk and ring have some unknown moment of inertia I. The hanging mass set has a known mass m. You will measure acceleration a of the mass as it falls. You will also measure the radius r at which the string is connected to the spool (this connects the linear motion of the mass to the rotational motion of the disk and ring). Find a formula for the unknown inertia I in terms of these quantities you can measure.