Mechanical Engineering: Centroids & Center of Gravity (24 of 35) Pappus-Guldinus Theorem 1 Explained

In this video I will explain the first theorem of Pappus-Guldinius of finding the area of an object.

Next video in this series can be seen at:

[alizakhan]

You explained difficult thing in a very easy way, you are an example of a perfect teacher!

[krishnaSagar]

You explained it like it was damn nothing .... wow ❤️

[francescopiccoli]

WOW. I'm italian and i don't understand this Theorem. I search english videos and now i understand. Thanks

[udayprasadchittiboina]

Well explained sir it became so easy after listening to you

[geraldglennmullet]

A segment of a circle of radius R is bounded by an arc equal to 1/3 the circumference of the circle. Find the volume of the solid generated by revolving this segment about its chord as an axis. (This solid is know as Kepler's Lemon). Note: Do note use integral calculus.

[sushantravva]

Thank you so much sir!
After watching this my assignment problem became too easy☺️

[jaivardhansingh-np]

holy shit !! I am happy, done in seconds now that the teacher I needed to pass my engineering

[blueckaym]

How to determine the centroid of a more complex curve/shape?
For example if we start with a circle rotated around an axis outside of it, so that we get a torus (or donut) shape we can get the volume of the torus by multiplying the area of the initial circle, but the length of the rotation (ie the distance covered by the centroid), but in that case it's the line drawn by the center of the initial circle when being rotated.
But now lets say I want to split the initial circle vertically, and find the volume only of the outer half of the torus (ie a torus with perfectly cylindrical hole).
Btw the volume of the cylindrical hole is trivial to find as it's a ... cylinder :)
But what about the centroid of the outer half of the torus?
if I divide the radius of the initial circle by 2 again, I'll have a shape with larger volume on the inside of that quarter-point/circle, compared to the volume outside of it.
I guess for a semi-circle it's not that difficult to find a chord that splits it (parallel to the diameter it's already split by) in two halves with equal areas (if that's the correct approach?).
But if so, how to proceed with complex shapes? ... For example if you have an S shape rotated in similar way around an outside axis?

[raze]

when rotated at x axis, is the strip dy? When rotated at y axis the strip is dx?

[olympusbiz]

it become very easy after listening to u

[srinivasreddya]

Tq so much sir
Keep making more viedoes for us

[alfiafiyan]

Any highschool student preparing for jee watching this?

[olympusbiz]

do u know how to find moment of inertia of different objects

[frankdimeglio]

What is E=MC2 is consistent with TIME AND what is gravity. (TIME is thoroughly consistent with what is gravity ON/IN BALANCE.) WHAT IS E=MC2 is dimensionally consistent. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! WHAT IS E=MC2 is taken directly from F=ma.

Consider what is the man (AND THE EYE ON BALANCE) who IS standing on what is THE EARTH/ground. Touch AND feeling BLEND, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). CLEAR water comes from what is THE EYE. INDEED, consider what is (essentially and necessarily) BALANCED BODILY/VISUAL EXPERIENCE !!! Lava IS orange, AND it is even blood red. The hottest flame is blue. The hottest lava is yellow. LOOK upwards, ON BALANCE, at what is the TRANSLUCENT AND BLUE sky !! The orange (AND setting) Sun IS the SAME SIZE as what is THE EYE !! NOW, consider what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE. (BALANCE AND completeness go hand in hand.) WHAT IS E=MC2 is taken directly from F=ma, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS the rotation of WHAT IS THE MOON matches the revolution.

WHAT IS E=MC2 is taken directly from F=ma. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites ON BALANCE, as the stars AND PLANETS are POINTS in the night sky. Consider TIME AND time dilation ON BALANCE. c squared CLEARLY represents a dimension of SPACE ON BALANCE. WHAT IS GRAVITY is, ON BALANCE, an INTERACTION that cannot be shielded or blocked (ON BALANCE) !!! E=MC2 is consistent with/AS WHAT IS GRAVITY, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS the rotation of WHAT IS THE MOON matches the revolution. Magnificent. Notice that the curvature or shape of said Moon matches that of what is THE EARTH/ground (that is, given what is a CLEAR horizon, of course.) The diameter of WHAT IS THE MOON IS about ONE QUARTER that of WHAT IS THE EARTH/ground ON BALANCE. Excellent !!! It ALL CLEARLY makes perfect sense ON BALANCE. Consistent WITH WHAT IS TIME, WHAT IS E=MC2 IS GRAVITY ON BALANCE. Finally, the average ocean tide is about 6 feet; AND said Sun manifests or forms at what is EYE LEVEL/BODY HEIGHT. The tidal range on the open ocean is about 3 feet. Notice, what is THE EARTH is ALSO BLUE ON BALANCE. Outstanding. Again, ON BALANCE, consider what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE. The BULK DENSITY of WHAT IS THE MOON is comparable to that of (volcanic) basaltic lavas on THE EARTH/ground. The surface of WHAT IS THE MOON is chiefly composed of pumice. Excellent. ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE), AS the rotation of WHAT IS THE MOON matches the revolution; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS WHAT IS E=MC2 is taken directly from F=ma.

By Frank Martin DiMeglio