Very nice video. An algebraic demonstration is that if you take the dot product of the vector equation u = v + w with itself, you get: u^2 = v^2 + w^2 + 2 v * u And that can only equal the conservation of energy equation if v * u = 0, which means they are orthogonal.
There are some old textbooks by S.L. Loney that I like, you'll find some very interesting problems in there. Over 100 years old, but not much has changed in classical mechanics since then so definitely worth a look!
Very nice video. An algebraic demonstration is that if you take the dot product of the vector equation
u = v + w
with itself, you get:
u^2 = v^2 + w^2 + 2 v * u
And that can only equal the conservation of energy equation if v * u = 0, which means they are orthogonal.
Meant v * w in the last two equations!
@@niconeuman Nice, thanks for sharing!
This approach also gives the angle when the masses are not the same.
thank you so much!
Sir do you know of any books with very difficult classical mechanics ( especially Newton laws and kinematics) questions?
There are some old textbooks by S.L. Loney that I like, you'll find some very interesting problems in there. Over 100 years old, but not much has changed in classical mechanics since then so definitely worth a look!
@@DrBenYelverton Great coincidence I am currently solving SL Looney Trigonometry book 😃
Ah, excellent!
@@DrBenYelverton sir were u referring to SL Looney's Statics and dynamics book ?
That's one of them, there is also another called "An elementary treatise on the dynamics of a particle and of rigid bodies".
Thank you sir.
That really was beautiful.
Thank you!
Nice video 👍
We have
u = v +w.
So
= ||v||² + ||w||² + 2.
So 2 =0, and = 0.
QED