Moment of Inertia: Solving Point A from 3r & 1r Up

In summary, the conversation discusses finding the Moment of Inertia of a point A on a graph with x and y axes. The x and y moments have been found, but not the z moment. The z-axis points up out of the page and the moment of inertia can be calculated using the distance of the point mass from the z-axis, which is the hypotenuse of the right triangle formed by its x and y components.
  • #1
Trojanof01
13
0
So I have a point A on a graph with x and y axes. From the origin, the point is 3r to the right, and 1r up. I'm to find the Moment of Inertia along the x, y, and z axes. I've found the x and y moments, but not the z and I'm not really sure on how. I'm not getting any ideas from the graph alone. How do I start?
 
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  • #2
Bump, anybody?
 
  • #3
The z-axis points up out of the page. The moment of inertia of the point mass about the z-axis will be

[tex]I_z = md^2[/tex]

where d is the shortest distance of the point mass from the z-axis. Since the point mass is on the x-y plane d will be the distance that the point mass is from the origin. That is it is the hypotenuse of the right triangle formed by its x and y- components.
 

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 the product of an object's mass and the square of its distance from the axis of rotation.

2. How is Moment of Inertia calculated?

The moment of inertia of a point mass is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. For a system of point masses, the individual moments of inertia can be added together to get the total moment of inertia.

3. What is the significance of solving Point A from 3r & 1r Up?

Solving Point A from 3r & 1r Up refers to finding the moment of inertia of a system of point masses, where one point mass is located 3 times further from the axis of rotation than another point mass. This calculation is important in understanding the distribution of mass in a rotating system and how it affects its rotational motion.

4. How is Moment of Inertia used in physics?

Moment of Inertia is an important concept in physics and is used in many applications, such as understanding the motion of rotating objects, calculating the angular acceleration of a system, and determining the stability of a spinning object.

5. What factors affect the moment of inertia of an object?

The moment of inertia of an object depends on its mass, shape, and distribution of mass relative to the axis of rotation. Objects with larger mass and more spread out mass distribution have a higher moment of inertia, making them more resistant to changes in rotational motion.

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