I'm trying to understand why the Earth bulges at the equator. But before looking at the Earth, which introduces gravity, I wanted to make sure I understood the shape of some rotating objects and if/why they have a bulge.  A metal sphere: A very rigid object. If this is rotated then there is no bulge because it requires a lot of energy to deform the object.  A ball of sand: Nothing is connected. If this rotated then all the sand is simply thrown off due to inertia, leaving nothing behind after a time.  A ball of dirt: Somewhat rigid. The dirt wants to "fly off" due to inertia but tension keeps the object pulled together, as a result there is bulge at the equator - where the velocity is fastest and thus more "tension" (more bulge) is needed.   Does the "ball of dirt" situation accurately resemble Earth? If so, then does this not suffice to explain why the Earth bulges without even needing to mention gravity? Or is Earth more like the "ball of sand" which is can only be kept together (while rotating) under the force of gravity? Or is it something between or neither at all?  I'm afraid I'm terribly confused as to how the various effects come in to play and interact to create an equatorial bulge. Some sources have tried to explain in terms of an  but I'm not entirely satisfied with that as an explanation (actually that source even indicates the equilibrium approach is not so straightforward).
The earth is not a sphere, because it bulges at the equator.   I tried fiddling with centripetal force equations and gravity, but I couldn't derive why this bulge occurs.    Is there   (a) a mathematical explanation using forces (not energies) and   (b) a simple intuitive explanation to explain to others why the bulge occurs?
Zip a file without including the parent directory Uses of the definite article (the) in generic noun phrases I was reading a paragraph about lions and I came up with a question about the definite article (the).  Let me tell you first what I know about it.     1->We use the before a singular noun (when we are sure about the noun.    And the listener and the speaker both know about it).      2->We use the before a plural noun (again when we are sure about the noun,   and we are not talking generally).   So, my question is why does the writer use the here as we are not talking about any specific lion or lions. We are talking generally.  The Paragraph:     Living in the grasslands, scrub, and open woodlands of sub-Saharan   Africa, the lion is the second largest cat in the world. It is dwarfed   slightly by the tiger, which is closely related and has a very similar   body type.    Can we re-write the paragraph something like this:     Living in grasslands, scrub, and open woodlands of sub-Saharan Africa,   lions are the second largest cat in the world. They are dwarfed   slightly by tigers, they are closely related and has a very similar   body type. How to connect to device via SSH over direct ethernet connection I have, by default, 250MB of swap space in Ubuntu, and I want to expand it to a larger size. I need 800MB, which I think will be enough to open several applications without having to hit the current limit of swap. I hope someone can help me. Java String split is not working I need to save/compile a few times and a bunch of weird files (like foo.tex.Ak6664) appear in my Dropbox folder each time I need to compile between two and four times before I see changes I make in the editor (TeXstudio) and each time I compile, a new .tex file is created with random letters and numbers at the end.   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PS: I still have the old iPhone 6, so it could be used as "temporary storage" if needed.