Timeline for Why perpendicular axis theorem is applicable only for laminar (2-D)objects?
Current License: CC BY-SA 4.0
5 events
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| Jul 10, 2018 at 0:00 | comment | added | BioPhysicist | @sammygerbil We take each lamina and apply the perpendicular axis theorem to each of them separately to get a $I_z$ for each. That is the end of using the perpendicular axis theorem here. Then we stack the lamina such that their z-axes are aligned. Now we have a 3D object. What is $I_z$ of this new object? Well it is just the sum of all of the $I_z$'s we found previously. Performing this sum is not using the parallel axis theorem. It is just from the definition of $I_z$ and how the integral is a linear operation. | |
| Jul 9, 2018 at 22:12 | comment | added | BioPhysicist | @sammygerbil the parallel axis theorem is for finding $I$ given a known $I$ for the same body. In this case we are finding $I$ for a composite body by adding up all of the $I$'s from each separate body. This is why I do not think the parallel axis theorem is applied here. As for the perpendicular axis theorem, it is being applied separately to each separate body (thin sheet) in order to find $I$ of the whole body. Adding up multiple $I$'s due to composing multiple bodies is not the parallel axis theorem. | |
| Jul 9, 2018 at 18:50 | comment | added | BioPhysicist | @sammygerbil I don't think this is the case. He could use the parallel axis theorem if he knew $I_z$ for each sheet but did not align each sheet when stacked. Then $I_z=\Sigma (I_n+md_n^2)$. But if we are stacking each sheet with everything aligned I do not see how he must be using the parallel axis theorem. He is just using the fact that we can add each separate $I_z$ together since translation in the z-direction does not change $I_z$. | |
| Jul 9, 2018 at 17:21 | history | edited | BioPhysicist | CC BY-SA 4.0 |
added 241 characters in body
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| Jul 9, 2018 at 17:16 | history | answered | BioPhysicist | CC BY-SA 4.0 |