Moment of inertia depends on the axis

The mistake

Treating I as a fixed property of the object.

Why it feels right

Mass is a single number, so rotational inertia seems like one too.

How to catch it

You reused I from a table without matching the axis.

The first principle

I depends on how mass is distributed about the chosen axis. Use the parallel-axis theorem I = I_cm + Md² to shift axes.

worked mini-example

A rod spun about its center versus its end — same I?

Common wrong move

Yes, it's the same rod.

Correct

No: I_end = ML²/3 is four times I_center = ML²/12.

Test the repair ROT-03 · transfer
A thin hoop has I = MR² about its central axis. What is I about a parallel tangent axis?

Make a fresh prediction before referring to the worked example.