Moment of Inertia, difference between Ixc, Ix, and Io?

In summary, Ix is the moment of inertia around the defined x-axis, Ixc is the moment of inertia around an axis parallel to the x-axis through the center of mass, and Io is the moment of inertia around an axis through the origin for an object that is symmetric in all directions. This distinction helps to understand the differences between Ixc and Io.
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Femme_physics
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So I understand that Ix resistance to rotation around the X axis, Ixc is resistance to rotation around the center of gravity of the shape on its X axis, and Io I was told is also resistance to rotation around the object's center of gravity. So, I'm completely confused as to the difference between Ixc and Io. Except that Io don't seem to define an axis. Can anyone help me understand it?
 
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Femme_physics said:
So I understand that Ix resistance to rotation around the X axis, Ixc is resistance to rotation around the center of gravity of the shape on its X axis, and Io I was told is also resistance to rotation around the object's center of gravity. So, I'm completely confused as to the difference between Ixc and Io. Except that Io don't seem to define an axis. Can anyone help me understand it?

I is always the moment of inertia around some axis.
The index denotes which axis is meant.
Sometimes people get creative how to denote a specific axis.

Ix for instance is around the defined x-axis, which may or may not be through the center of mass.

Ixc would be around an axis parallel to the x-axis, which is through the center of mass.

Io would be the moment of inertia around an axis through the origin. The fact that no distinction is made about which axis seems to imply that the object is symmetric in all directions around the origin, which will be its center of mass as well.
 
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1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated based on the mass and distribution of mass around an object's axis of rotation.

2. What is the difference between Ixc, Ix, and Io?

Ixc, Ix, and Io are different moments of inertia that are used to describe an object's rotational motion. Ixc is the moment of inertia about the centroidal x-axis, Ix is the moment of inertia about a specific x-axis, and Io is the moment of inertia about the object's center of mass.

3. How do I calculate moment of inertia?

Moment of inertia can be calculated using the formula: I = Σmr², where I is the moment of inertia, m is the mass of the object, and r is the distance from the axis of rotation to the mass.

4. Why is moment of inertia important?

Moment of inertia is important because it determines how difficult it is to change the rotational motion of an object. It is used in many applications, such as calculating the torque required to rotate an object and predicting how an object will behave when subjected to external forces.

5. How does the distribution of mass affect moment of inertia?

The distribution of mass around an object's axis of rotation affects its moment of inertia. Objects with more mass concentrated farther away from the axis of rotation will have a higher moment of inertia, making them more difficult to rotate. Objects with more mass closer to the axis of rotation will have a lower moment of inertia and will be easier to rotate.

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