Rolling kinetic energy is a sum of checked rotational and translational parts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Matched translation and rotation give eighteen joules
Rotational energy 9 J plus translational energy 9 J gives total kinetic energy 18 J.
9+9=18
Faster rolling squares both energy ledgers
Rotational energy 16 J plus translational energy 16 J gives total kinetic energy 32 J.
16+16=32
Heavier matched rolling doubles the base total
Rotational energy 18 J plus translational energy 18 J gives total kinetic energy 36 J.