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

AI Thread Summary
To find the Moment of Inertia for point A located at (3r, 1r) in the x-y plane, the z-axis is defined as pointing out of the page. The moment of inertia about the z-axis is calculated using the formula I_z = md^2, where d represents the distance from the z-axis. This distance is the hypotenuse of the right triangle formed by the x and y coordinates. Therefore, d can be determined using the Pythagorean theorem, which yields d = √((3r)² + (1r)²). With this information, the z-axis moment of inertia can be accurately calculated.
Trojanof01
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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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The z-axis points up out of the page. The moment of inertia of the point mass about the z-axis will be

I_z = md^2

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.
 

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