Rotational Inertia
Spin up a solid disc, a hoop, and a solid sphere — all sharing the same mass and radius — under the same applied torque, and watch them visibly pull apart purely because of how each one's mass is spread out from the axle.
Preview — sign up free to change the numbers yourself
What you can adjust
- Mass (each body)
- 0.5 – 4 kg
- Outer radius (each body)
- 0.05 – 0.3 m
- Applied torque
- 0.02 – 0.5 N·m
- Run duration
- 2 – 12 s
All three bodies share this same mass. Mass alone does not decide how hard something is to spin up — where that mass sits relative to the axle matters just as much, which is exactly what this run demonstrates.
All three bodies share this same outer radius. A bigger radius makes every body harder to spin up, but never changes which one wins — that's decided by how the mass is distributed within the radius, not the radius itself.
The same twisting force is applied to all three axles at once. A bigger torque spins every body up faster, but never changes the ORDER they finish in.
How long the torque is applied for. A longer run gives the slower bodies more time to visibly fall behind the faster ones.
About this simulation
What it shows
A solid disc, a hoop and a solid sphere with the same mass and radius are each spun by the same torque. They gradually pull apart in spin speed.
The key idea
How hard something is to spin depends on where its mass sits, not just how much there is. Spin-up is torque divided by rotational inertia, and the hoop (all mass at the rim) has the most.
Try this
Raise Applied torque from 0.05 to 0.2 N·m: every body spins up four times as fast, but the order stays sphere, disc, hoop.