This video explores the fundamental nature of buoyancy, and how it arises from molecular collisions and the weight of stationary water. Along the way we will meet some concepts from vector calculus, which will be useful for understanding buoyancy, and which we will also see again in future videos.

Please do not be discouraged if you are seeing some of these ideas for the first time, and are confused by them. That’s totally normal when learning new kinds of math. You’ll find that over time these ideas become very natural.

Three concepts central to this video are:

1. The dot product. This is the simplest way two vectors can be multiplied. Two vectors go in and one scalar number comes out, which relates to the vectors’ size and the extent to which they align.

https://en.m.wikipedia.org/wiki/Dot_p...

2. The divergence theorem. This is a very versatile theorem in vector calculus that lets you turn flux integrals into volume integrals, and vice versa. Basically it equates the flux through a closed surface to the extent to which the vector field has a source or a sink inside the region bounded by the surface. We used this theorem twice in this video, in two different directions and contexts, so that should tell you something about how widely applicable this theorem is!

https://en.m.wikipedia.org/wiki/Diver...

3. The normal vector. This is just a vector which is perpendicular (in physics, “normal” is often used to mean “perpendicular”). Typically the vectors are defined to point outward from a surface. Often the normal vectors have length 1, which makes them normalized another sense of the word (vectors with length 1 are often called “normalized”). It’s actually a confusing terminology, some to think of it! But the concept is straightforward.

https://en.m.wikipedia.org/wiki/Norma...)

Please let me know if you have any questions, comments, or suggestions for future videos, and thanks for watching! :)

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Thanks to fesliyanstudios.com for the background music! :)