Is it possible for two objects with the same mass to have different rotational inertias?

Question

Is it possible for two objects with the same mass to have different rotational inertias?

_____ Yes, if the two objects of the same mass are rotating with different angular velocities then they will have different rotational inertias.

_____Yes, if the same mass is distributed at different distances from the axis of rotation in the two cases.

_____No, two objects with the same mass will always have the same rotational inertia because only the total mass not the distribution of mass determines the rotational inertia.

There may be more than one answer.

Answer 1

The (scalar) moment of inertia of a point mass rotating about a known axis is defined by

I = m R^2

m is the mass
R is the (perpendicular) distance of the point mass to the axis of rotation.

http://en.wikipedia.org/wiki/Moment_of_inertia

two objects who have the same mass can have different moment of inertia if they are at different distances

Yes, if the same mass is distributed at different distances from the axis of rotation in the two cases.

Answer 2

Sure, look at 2/5 mr^2 = I for a ball and 1/2 mr^2 = I for a solid disk; where the I's are respective moments of inertia where L = Iw; where L = angular momentum and w is the angular velocity around the major axis of rotation.

So there you have it, two shapes (ball and disk) of the same mass m. But they clearly have different L's for the same w becaise their I's are different. So here are the answers:

_____ Yes, if the two objects of the same mass are rotating with different angular velocities then they will have different rotational inertias.

Nope, rotational moments of inertia depend solely on the shape, mass m, and torque arm r from the axis of rotation. Angular momentum L = Iw does depend on both I and the angular velocity w. But if L(ball) = 2/5 mR^2 w = 1/2 mr^2 W = L(disk), we can find 2/5 2/1 R^2w = 4/5 R^2 w = r^2 W, so that W = (4/5) w (R/r)^2 and different angular velocites yield the same angular momentum for the same mass. In fact, the torque arms need not be the same length.

__X___Yes, if the same mass is distributed at different distances from the axis of rotation in the two cases.

Set I(ball) = 2/5 mr^2 = 1/2 mR^2 = I(disk); this is clearly doable for the different mass distributions (aka shapes) as 4/5 r^2 = R^2 and the two torque arms are not equal even though their I's are.

_____No, two objects with the same mass will always have the same rotational inertia because only the total mass not the distribution of mass determines the rotational inertia.

Nope, see the source for the effects of mass distribution (shapes).

Answer 3

specific. Angular momentum relies upon on how the mass is dispensed besides because of the fact the fee of the mass and the rotational speed. A wheel wherein all the mass is on the exterior would have so plenty extra momentum than one the place all the mass is focused on the centre.