I Calculating Mass Inertia Product - Examples 1 & 2

AI Thread Summary
The mass inertia product is calculated by considering the shape and orientation of the object in question. In the provided examples, different methods are used to determine the moments and product of inertia for a cylinder. The discussion emphasizes the importance of accurately identifying the geometry and alignment of the object to ensure correct calculations. Clarity on these factors is crucial for achieving precise results in mass inertia product calculations. Understanding these principles is essential for applications in physics and engineering.
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How is the mass inertia product calculated? I have two examples and each one uses something different.
How is the mass inertia product calculated? I have two examples and each one uses something different.

Example 1:
1.png


Example 2: moments and product of inertia of the cylinder
2.png
 
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What is the shape and orientation of Example 1?
 
scottdave said:
What is the shape and orientation of Example 1?
That's it, I got it, thank you!
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
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