- #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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SUMMARY
The discussion centers on the moment of inertia of various shapes, specifically comparing hoops and spherical bodies. It is established that a hoop has a greater moment of inertia around its symmetry axis than a spherical body of the same mass and radius. The parallel axis theorem is crucial in understanding how the moment of inertia can increase when rotating about different axes. Additionally, the conversation touches on the implications of radius of gyration in relation to the radius of the spherical body.
PREREQUISITES- Understanding of moment of inertia
- Familiarity with the parallel axis theorem
- Knowledge of angular momentum concepts
- Basic principles of rotational dynamics
- Study the parallel axis theorem in detail
- Explore the concept of radius of gyration in various shapes
- Learn about the relationship between angular momentum and moment of inertia
- Investigate the moment of inertia for different geometric bodies
Physics students, mechanical engineers, and anyone interested in the principles of rotational dynamics and moment of inertia calculations.
- #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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