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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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In summary, the conversation discusses the moment of inertia of various objects, specifically a hoop, a more massive hoop, and a larger hoop. The conversation also touches on the relationship between moment of inertia and radius of gyration, and the parallel axis theorem. It is mentioned that a hoop has a larger moment of inertia compared to a spherical body of the same mass and radius, and that the axis through the center of mass always has the minimum angular momentum.
- #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...
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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.
1. Can any object have moment of inertia greater than that of a hoop?
Yes, it is possible for an object to have a moment of inertia greater than that of a hoop. The moment of inertia of an object is dependent on its mass and distribution of mass around its axis of rotation. Therefore, an object with a greater mass and a larger distance from its axis of rotation can have a greater moment of inertia than a hoop.
2. How is moment of inertia calculated?
Moment of inertia is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. It is represented by the symbol I and its unit is kilogram-meter squared (kg·m²).
3. What is the significance of moment of inertia?
Moment of inertia is an important concept in physics and engineering, particularly in the study of rotational motion. It determines how much force is needed to change the rotational motion of an object and is used to calculate the angular acceleration of an object.
4. Can the moment of inertia of an object change?
Yes, the moment of inertia of an object can change if its mass or distribution of mass changes. For example, if an object's mass is redistributed further from its axis of rotation, its moment of inertia will increase.
5. How is moment of inertia related to an object's shape?
The moment of inertia of an object is directly related to its shape. Objects with more mass distributed further from their axis of rotation will have a greater moment of inertia, while objects with more mass concentrated closer to their axis of rotation will have a smaller moment of inertia.
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