Radius of Gyration: Solving Inertia Discrepancies

[theBEAST]

Homework Statement

The Attempt at a Solution

Alright, so the solution manual shows that the intertia of the disk is:

I = m * k², where k is the radius of gyration​

However why can't the inertia of the disk be:

I = 0.5 * m * r², where r is the radius of the disk​

This is the formula for the inertia of a rotating disk... However when I plug in all my numbers I get a different inertia value when compared to the inertia value that I got using the radius of gyration.

 

[haruspex]

Because the spool is not a uniform disk. You don't need to know why it's not uniform, just accept that you are given the effective radius.

 

[theBEAST]

Because the spool is not a uniform disk. You don't need to know why it's not uniform, just accept that you are given the effective radius.

Ah okay, I wish it said that the density is not uniformly distributed... But thanks!