How to Calculate Moment of Inertia about x=y=z Line?

In summary, the conversation is about finding the moment of inertia of a solid about the line x=y=z and the difficulty in determining the formula for the distance between a point and the line. The suggestion given is to find the plane perpendicular to the line and project the vector from the origin to the point onto this plane. This will give the vector between the point and the line, allowing for the calculation of the distance. Eventually, the person was able to figure it out with the help of the suggestion.
  • #1
Stevecgz
68
0
I'm attempting to find the moment of inertia of a solid about the line x=y=z, but cannot figure out a formula to for distance between a point and the line x=y=z. I tried to simply by first looking at it in two dimensions, but I still haven't come up with anything. Any suggestions are appreciated.

Steve
 
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  • #2
So, the distance between a point and a line is measured perpendicular to the line. So the first thing you should do is find the plane perpendicular to the line. Then project the vector from the origin to the point onto this plane. The projection is just the vector between the point and the line.
 
  • #3
Thanks StatusX, I was able to figure it out.
 

1. What is the moment of inertia about x=y=z?

The moment of inertia about x=y=z is a physical quantity that describes how an object's mass is distributed around a certain axis or point in space. It is a measure of an object's resistance to rotational motion.

2. How is the moment of inertia about x=y=z calculated?

The moment of inertia about x=y=z can be calculated by using the formula Ix=y=z = m(d^2) where m is the mass of the object and d is the distance from the axis or point of rotation.

3. What is the significance of the moment of inertia about x=y=z?

The moment of inertia about x=y=z is an important concept in physics as it helps to determine an object's rotational motion. It is also used in engineering applications such as designing structures that need to withstand rotational forces.

4. How does the moment of inertia about x=y=z affect an object's rotational motion?

The moment of inertia about x=y=z determines how much torque is needed to rotate an object around that axis or point. Objects with a larger moment of inertia will require more force to rotate compared to objects with a smaller moment of inertia.

5. Can the moment of inertia about x=y=z change?

Yes, the moment of inertia about x=y=z can change depending on the distribution of mass around the axis or point of rotation. It can also change if the object's mass or shape is altered.

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