# Why is the moment of inertia of a rod not the same as that of a disk?

Take a disk and cut it to the centre like you'd do with scissors, and bring the cut sides to each other taking along all the mass in the middle. you'd have a rod. This should work because $R$ for the individual particles don't change when you're squeezing (moment of inertia of two particles of mass m on opposite sides of diameter of a circle is $2m R^2$, like one particle of mass $2m$).

This works for a ring and a point mass, why not for a disk?