# B Can any object have moment of inertia greater than that of a hoop?

1. Mar 27, 2016

### Cosmos

Can any object have moment of inertia greater than that of a hoop?

Last edited by a moderator: Mar 28, 2016
2. Mar 27, 2016

### Staff: Mentor

Two hoops.
A more massive hoop.
A larger hoop.

I could speculate what you actually want to know, there the answer would be "no", but currently the answer is a clear yes.

3. Mar 27, 2016

### Cosmos

But,sir/mam what I really want to know is whether........When you have been given a spherical body with a radius R (say) then can its radius of gyration be larger than R????????????

4. Mar 27, 2016

Staff Emeritus
1. It's not mfb's fault if you asked an unclear question.
2. Spherical? Hoop? Make up your mind!

5. Mar 28, 2016

### Cosmos

sorry for that brother.............
consider a spherical body........forget the 1st comment.......

6. Mar 28, 2016

### robphy

7. Mar 28, 2016

### Staff: Mentor

A hoop has a larger moment of inertia around its symmetry axis than a spherical body of the same mass and radius.

8. Mar 28, 2016

### Limmin

Don't forget the parallel axis theorem. Increases moment of inertia by rotating the hoop about another axis entirely.

Meanwhile...I basically agree, the hoop may be the shape with the highest intrinsic moment of inertia. Because all the mass in a hoop is some distance away from the center of mass. In any other body, much of the mass of closer to the center, which decreases your rotational inertia.

9. Mar 29, 2016

### Cosmos

Thanks Robphy......
Well then if i have a spherical body of radius R that rolls on a horizontal surface with linear velocity v and angular velocity ω. Let L1 and L2 be the magnitudes of angular momenta of the body about centre of mass and point of contact respectively.Then is it true that L2 greater than L1 if K(radius of gyration) is larger than R....??????????

10. Mar 29, 2016

### Staff: Mentor

At the same angular velocity, an axis through the center of mass is always the axis with minimal angular momentum. This is a direct consequence of the parallel axis theorem.
If you compare different angular velocities, you'll have to calculate it.