Spinning People

Can we find Moment of inertia of humans??
- Rohan (age 19)
Pune

Sure, but the moment of inertia depends on what axis you spin someone about, how they hold their arms, etc. Very roughly, you’d expect moments of around 10 kg-m^2, just from the size and weight of a typical person. The moment about an axis running top to bottom is obviously much smaller than those about axes running front-to-back or sideways. The vertical axis moment goes way up when you hold out your arms.

That’s how skaters spin so fast. They start spinning with their arms out, then pull them in while spinning on a tiny contact. The contact exerts very little torque, so the angular momentum doesn’t change. Since the moment goes down, the rotation rate has to go up.

The different moments about different axes are a reminder that the moment of inertia is actually not just a number but rather a tensor: a matrix of numbers used to convert the 3-d rotational velocity vector to the 3-d angular momentum vector. If you spin someone about some diagonal axis, you’ll find that their angular momentum keeps changing because it doesn’t point along the spinm axis. You have to keep exerting torques to keep them spinning smoothly on that axis.

Mike W

(published on 10/22/2007)