Inertia Tensors for Fractional Volumes: How to Calculate?

In summary, "Moments of inertia of halves" refers to the calculation of the moment of inertia of a solid object when it is split into two equal halves, and is a measure of an object's resistance to rotational motion around a specific axis. The moment of inertia of a half is calculated by dividing the moment of inertia of the entire object by two, and is affected by the mass and distribution of the object's mass. This property is useful in various applications of physics and engineering and cannot be negative.
  • #1
springo
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Homework Statement


How do you find the tensor of inertia for fractions of the usual volumes?
(like half of a sphere, half of a cylinder, half of a disk, quarter of a disk, etc.)

I already know the tensor of inertia for the whole volume.
Take M as the fraction of the volume's mass, not the whole volume's.

Homework Equations



The Attempt at a Solution


I have no idea where to start...

Thanks.
 
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Related to Inertia Tensors for Fractional Volumes: How to Calculate?

1. What is the definition of "moments of inertia of halves"?

"Moments of inertia of halves" refers to the calculation of the moment of inertia of a solid object when it is split into two equal halves. It is a measure of an object's resistance to rotational motion around a specific axis.

2. How is the moment of inertia of a half calculated?

The moment of inertia of a half is calculated by dividing the moment of inertia of the entire object by two. This assumes that the object is symmetrical and the axis of rotation passes through the center of mass of the object.

3. What factors affect the moment of inertia of halves?

The moment of inertia of halves is affected by the mass and distribution of the object's mass. Objects with more mass and concentrated mass distribution will have a higher moment of inertia of halves compared to objects with less mass and more spread out mass distribution.

4. How is the moment of inertia of halves useful in science?

The moment of inertia of halves is useful in various applications of physics and engineering, such as calculating the rotational energy and stability of objects, as well as designing structures and machines that require precise control of rotational motion.

5. Can the moment of inertia of halves be negative?

No, the moment of inertia of halves cannot be negative. It is a physical property that represents an object's resistance to rotational motion and is always a positive value. A negative moment of inertia would imply that an object has negative mass, which is not possible.

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