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Simply marvelous ! In this solution, I've noticed that the main task was to represent R(n) as a division between P(n) and Q(n). From that, the remainder seems to be something straightforward. What was your insigth about that? Is It a common practice when dealing with recurrence relations?

amazing special cases --- Physics WORKS!

thank you Dr.!

omg thanks for your video , I've searched through so many materials about this , and honestly, this is the best video I've found.

What exactly is the difference between the natural length (l) and d? Thank you for sharing this video.

Finally...something regarding complex analysis...love the video....I would greatly appreciate it if you would make more videos on this topic...especially branch cuts of more complicated functions....

First!

Very well presented mathematics too, thanks.

Don't we need to specify that the rope is massless? (that is an implicit assumption, right?) Or is there some reason that your infinitesimal free body diagram did not incorporate the gravitational force of mass?

This seems like the opposite of alpha decay. In an alpha decay situation, there is an alpha particle trapped inside the attractive nuclear force region that eventually tunnels to the outside world.

Thank you for your explanation!

Good explaination

Very cool and good job, but... I'm pretty sure in the case of these high altitude ice crystals, causing halos, sun dogs etc, were considering hexagonal crystals, right? I suppose in some way its related because those can be made of, be composed of triangles, so maybe it works the same, I'm just wondering if this is the same or if the math is actually a bit different since its hexagons.

Great 👍

Thank you. Absolutely what I wanted.

Was a huge confusion before this video, now crystal clear, love from Türkiye.

Hi Dr Ben, thank you for this brilliant lecture. At 4:35, would you please elaborate how to solve the arbitrary constants A and B here if really want to solve to the end? Thanks a lot!

👍

This will help me defend my PhD thesis!

Thank you ! Very useful

Thank you! Could you also make a video in which you derive a formula for the stress acting on a balloon such that the express only depends on the thickness, the radius of the sphere and the material properties? If this is possible, of course

Would you care to explain the meaning behind the differential values? I am confused because in a math course I have never seen a differential element used on its own like this, but it is all over engineering and physics courses. I understand it is meant to represent an "infinitesimal" value, but such isn't defined in mathematics and is considered non-rigorous. I am an engineering student btw, but we were never explicitly taught how we may or may not treat infinitesimals by our lecturers. What does it actually represent in equations such as this? Should I consider it just a very small value (ie. a shorthand for a delta approaching 0)? I understand the hand-waviness behind the differentials in physics and engineering is fine as long as you are dealing with single-variable calculus, but problems will arise without proper mathematical treatment of such elements in multivariable calc. (multivariable chain rule just to name one - can't simply cancel the differentials out as if they were parts of a fraction).

Thank you very much, in A/l's we solve these kind of sliding wedge problems - through : Newtonian perspective : but trust me, Lagrangian perspective is awesome, No tedious equations or forces : i am tired of applying, the principle of, relative acceleration : in more complicated wedges, please upload more wedge problems and solve them using Lagrangian.

Thank you for this amazing video! As a high school student, your content is invaluable for my preparation for the physics olympiad. I truly appreciate it! I would also love to see a video discussing a conducting hemisphere placed on an infinite conducting plate under a uniform electric field.

Another beautiful video! Weel done!

Came across the video by chance. The clarity of your teaching is among the highest. Thank you very much and hope you will make more videos.

Hi sir, is ut possible to prove it by using conservation of momentum?

But wouldn't this just be the force required to raise the wheel a tiny bit off the ground? That's not the force required to get it all th eway over the step, is it?

I don’t get why E inside like in the middle isn’t drawn??? It should be proportional to D-P and because like I understand D is zero inside and the E should be -P inside then? If I’m wrong please correct me and if I’m right why didn’t you draw the lines inside in the middle?

great explanation of why m+dm instead of m-dm.

excellent approach, thanx Dr Ben....however i could use a little voice loudness...i was barely hearing you with the computer volume on Max....so this means i really found your video useful and interesting till the end despite my suffering lol.

Very cool

Could you discuss about optics in the upcoming videos? My test on my physics camp is about diffraction 😊

Thank you! This is the infinitesimal derivation I was looking for.

this is honestly my favourite youtube video ever. thank you so much.

Another problem could be to properly solve for kh, I remember doing it 2 years back, and the results surprised me. Both components of velocity after collision are independant of radius of the ball, so any problem where a ball is spinning and collides with a surface, or even not spinning and collides obliquely with a surface has to be dealt with properly by finding angular velocities after collision and taking care of rotational energy and energy loss when it is slipping against the surface during collision, NO MATTER HOW SMALL THE BALL IS. Any problem that tells you to ignore these effects by assuming the ball is small is essentially made in the wrong light. Very interesting I might say.

Can someone explain to my why assuming conservation of angular momentum and assuming the ball will stop are not at odds? Surely if the ball stops it has no angular momentum about the pivot point (or any point) However the AM is clearly nonzero before contact? (I have a final tomorrow so if anyone can tell me quickly thay would be grreeat!)

3:20 What about torque due Mg?

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Why can't we simply equate the rotational and translational kinetic energy prior to the collision to potential energy after?

It's very refreshing to watch these contents of yours. Thanks

Love your content .thanks for sharing ❤

You're my hero