# Rotational

how is moment of inertial related to how spread out something is? can you explain it more in depth?

Hello!

All the moments of inertia have a dependence on mass and radius of the stuff.

To be more specific, I = mr^2 times some fraction depending on the shape. In general, the further away the mass is distributed from the axis of rotation, the greater the moment of inertia. So a ring of mass M, where all the mass is concentrated far away from the axis, has a greater moment of inertia than a disk of the same mass, where itâ€™s all spread out.

how, if possible, would you compare the moment of intertia of a heavier ring to a lighter disk?

Sure thing!

The ring has all of itâ€™s mass as far away from the rotation axis as it can get- it will therefore have a larger moment of inertia than a disk of the same mass.

Itâ€™s also heavier than the disk, so the moment of inertia will be even MORE greater.

In equation terms, the ring has I = MR^2 and the disk has half that with I = \frac{1}{2}MR^2, if they have the same mass. Increase the mass of the ring, and the moment of inertia will be greater than twice as big.

1 Like

ok thank you sm!

1 Like

No problemo!

2550 north lake drive
suite 2
milwaukee, wi 53211

âś‰ď¸Ź help@fiveable.me

*apÂ® and advanced placementÂ® are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

Â© fiveable 2020 | all rights reserved.