Mechanical Engineering: Centroids & Center of Gravity (11 of 35) C. G. of a General Spandrel 1

[@murky499]

Greetings Prof. van Biezen, Periodically, I try and re-learn subjects from my college years. For the last year or so I have been going over calculus based on the text from the 1960’s by George Thomas “Calculus with Analytical Geometry”. I am doing all the problems as I proceed and have made it through >250 pages and hundreds of problems (he gives the answers to all the problems in the Appendix-which is key) but I have encountered one that eludes me. I have watched most of your videos on centroids and volumes generated by rotating areas around an axis. What has stumped me, I believe, is quite simple: I cannot analytically prove that the y-coordinate of the centroid of the volume generated by rotating y=x about the x-axis is zero. I know from symmetry that this is the case but can’t make the math prove it. I keep arriving at some small, finite value (for x=1). I have solved numerous centroid and volume problems with no issue-but not this one. Your videos are excellent, easy to follow and cover quite an extensive array of problems. Having access to this type of information and knowledge is one very positive aspect of social media and I am very grateful that you take the time to share your expertise (mine is in semiconductors, detectors and instrumentation for NASA missions). Your insight would be most appreciated and would definitely retire quite a bit of frustration. Best regards, Murzy Jhabvala

[@caitlinmilne6365]

Sir, would you be able to (a) determine the centroid of a spandrel formed by the removal of a quarter circle radius r from a square with side r? (b) would you be able to calculate the second moment of area of this circular spandrel about it’s centroid ?

[@MichelvanBiezen]

We have a number of examples of how to find the centroid of such an object (or similar objects)

[@williamlema01]

you are a lifesaver!

[@dipeshlamichhane1272]

Can we find out the x coordinate using the same vertical strip (i.e not considering the horizontal strip).If yes,please say it kindly sir

[@MichelvanBiezen]

To find the x-coordinate of the center of mass you must use horizontal strips.

[@iheyinwadavidmicheal6552]

Sorry sir ....what's the difference between this general squandrel and the previous squandrel of the last video

[@MichelvanBiezen]

The equation of the lins is different. In this example we did th general case.

[@iheyinwagrace2882]

@@MichelvanBiezen thank you so much I'm learning a lot from you

[@MichelvanBiezen]

We are glad the videos are helping.

[@jfk7936]

Hi Sir, How come in the previous videos you have "A" as your denominator which is the area of the whole shape but in this question you have your denominator as integral of " y" or "x" which is the area of the section rather than the whole shape ?

[@MichelvanBiezen]

Both denominators represent area. If you know the area (from the shape) you don't need to calculate it with an integral.

[@jfk7936]

No I got it, thank you !

[@H.E.N_21]

sir,i need a quick response im writing exam tomorrow.....my question is when do we take horizontal elements or verticle? can we as well use the verticle element for both x and y centroids or horizontal for both

[@MichelvanBiezen]

It depends. If you are finding the x-coordinate of the centroid, then you need horizontal strips. If you are finding the y coordinate of the centroid, then you need the vertical strips.

[@H.E.N_21]

@@MichelvanBiezen thank you sir

[@Gio_lk]

Hi Sir, what's the difference if thickness is included and what method will we need to use?

[@MichelvanBiezen]

If the thickness is uniform, then it can be solved the same way. If the mass is known you can replace the area with mass. If the density is not uniform, you have to include the density function.

[@Gio_lk]

Can you explain a bit more on the bit that you said 'It could be solved as the same way when thickness is uniform', and I come across with something called lamina modelling assumption, can you please explain that too. Many thanks.

[@MichelvanBiezen]

If the thickness is uniform, then the mass is proportional to the area, so we can substitute area for mass.

[@brianramz6681]

proff. moment of inertia?

[@VibudaJayathilake]

learning in 2021! (5/1/2021)

[@ing.hugoadrianhp3596]

gracias estubo intendible ,,mejor aun si ubiese estado en español