- #1
Cosmos
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Can any object have moment of inertia greater than that of a hoop?
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Can any object have moment of inertia greater than that of a hoop?
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- Thread starter Cosmos
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Discussion Overview
The discussion revolves around the moment of inertia of various objects, specifically comparing the moment of inertia of a hoop to that of other shapes, including spherical bodies. Participants explore the implications of radius of gyration and the parallel axis theorem in relation to these concepts.
Discussion Character
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- Some participants suggest that a hoop can have a greater moment of inertia than other objects, including a spherical body, depending on the mass and radius.
- One participant questions whether the radius of gyration of a spherical body can exceed its radius, indicating a specific interest in the relationship between these measurements.
- Another participant emphasizes that the moment of inertia of a hoop is larger around its symmetry axis compared to a spherical body of the same mass and radius.
- There is a mention of the parallel axis theorem, which could increase the moment of inertia when considering different axes of rotation.
- One participant asserts that the hoop may have the highest intrinsic moment of inertia due to its mass distribution being further from the center of mass compared to other shapes.
- A later reply discusses the relationship between angular momentum and the radius of gyration, questioning if the angular momentum about the point of contact can be greater than that about the center of mass if the radius of gyration is larger than the radius.
- Another participant notes that the axis through the center of mass has the minimal angular momentum at a given angular velocity, referencing the parallel axis theorem as a basis for this claim.
Areas of Agreement / Disagreement
Participants express differing views on the moment of inertia of hoops versus spherical bodies, with no consensus reached on whether any object can have a moment of inertia greater than that of a hoop. The discussion remains unresolved regarding the implications of radius of gyration in this context.
Contextual Notes
Some assumptions about the definitions of moment of inertia and radius of gyration are not explicitly stated, and the discussion does not resolve the mathematical relationships involved in comparing these quantities.
- #2
mfb
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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.
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
Cosmos
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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
Vanadium 50
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- It's not mfb's fault if you asked an unclear question.
- Spherical? Hoop? Make up your mind!
- #5
Cosmos
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sorry for that brother....
consider a spherical body...forget the 1st comment...
consider a spherical body...forget the 1st comment...
- #6
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This might be related to your question:
https://www.physicsforums.com/threads/moment-of-inertia-and-mr2.785794/
My comment is in post #3 there.
https://www.physicsforums.com/threads/moment-of-inertia-and-mr2.785794/
My comment is in post #3 there.
- #7
mfb
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A hoop has a larger moment of inertia around its symmetry axis than a spherical body of the same mass and radius.
- #8
Limmin
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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.
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
Cosmos
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robphy said:
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
mfb
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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.
If you compare different angular velocities, you'll have to calculate it.
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