Two bodies of identical mass spin about the same axis. Only the shape factor k and the axis position differ, so every change you see in I = k m r² comes from where the mass sits — never from how much of it there is.
Moment of inertia I = k m r² + m d²
Hoop0.5000 kg·m²
Disc0.2500 kg·m²
A is 2.000 times B
Shape factor k
Hoop1.000
Disc0.5000
Mass is identical for both — only k and the axis move I.
Parallel axis term m d²
0.0000 kg·m²
Axis is through each centre, so nothing is added yet.
Rotational energy KE = Iω² ÷ 2
Body A100.0 J
Body B50.00 J
Angular acceleration α = τ ÷ I
Body A20.00 rad/s²
Body B40.00 rad/s²
The same torque spins the smaller I harder.
Body A shape
Body B shape
Mass m (both)2.00 kg
Radius r0.50 m
Axis offset d0.00 m
Spin rate ω20 rad/s
Applied torque τ10.0 N·m
Both bodies always carry the same mass and the same size. A rod uses its length L where the round shapes use radius r.
Try it: put A on Rod ctr and B on Rod end and note B's reading while d = 0. Now slide d to half the length — A climbs to exactly that number. Shifting the axis by L/2 is precisely what turns mL²/12 into mL²/3. (B keeps the same offset, so it moves further still.)