The final lesson keeps each source claim tied to a readable diagram. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The energy source ledger shows the spin square
The checked rotational-energy ledger stores inertia 8, spin 3, and energy 36.
8,3,36
The rolling source ledger keeps both energy parts
The rolling ledger keeps 9 joules rotational, 9 joules translational, and 18 joules total.