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Dr Ben Yelverton
United Kingdom
เข้าร่วมเมื่อ 11 พ.ย. 2020
Hello! On this channel, I share educational videos about Physics & Maths. I studied at Cambridge for 8 years, first gaining an MSci in Natural Sciences (specialising in Physics) and then a PhD in Astronomy. During my PhD, I also worked as a Physics supervisor for four different Cambridge colleges. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard. More information here: benyelverton.com/
Pressure inside a planet
Finding the pressure inside a spherical planet as a function of radial distance from the centre, by integrating the equation of hydrostatic equilibrium. We assume a uniform density here, but the method can be generalised easily to the non-uniform case.
Deriving the hydrostatic equilibrium condition: th-cam.com/video/rqE6psWXQLA/w-d-xo.html
To support the channel: ko-fi.com/benyelverton
About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#physics #mathematics #pressure #gravity #integration #differentialequation #planet #gausslaw #vectorcalculus #gradient #gravitationalfield #density #fluid #fluids #pressuregradient #hydrostaticequilibrium #hydrostatic #equilibrium #forces #balance #vectors #calculus #physicsproblems #maths #math #science #education
Deriving the hydrostatic equilibrium condition: th-cam.com/video/rqE6psWXQLA/w-d-xo.html
To support the channel: ko-fi.com/benyelverton
About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#physics #mathematics #pressure #gravity #integration #differentialequation #planet #gausslaw #vectorcalculus #gradient #gravitationalfield #density #fluid #fluids #pressuregradient #hydrostaticequilibrium #hydrostatic #equilibrium #forces #balance #vectors #calculus #physicsproblems #maths #math #science #education
มุมมอง: 781
วีดีโอ
Hydrostatic equilibrium: force-based derivation
มุมมอง 4643 หลายเดือนก่อน
Deriving the relationship between pressure gradient, density and gravitational field for a fluid in hydrostatic equilibrium, by considering the balance of forces acting on a small Cartesian fluid element. To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teac...
Fibonacci numbers and resistor networks
มุมมอง 5023 หลายเดือนก่อน
Exploring the relationship between the Fibonacci numbers and the effective resistances of ladder-like resistor networks, using recurrence relations. Full derivation of nth effective resistance: th-cam.com/video/8-Ow1KY0_0A/w-d-xo.html And the nth term of the Fibonacci sequence (note that this starts with 1, 1 instead of 1, 2, but is easily adaptable): th-cam.com/video/14pBNzI-yuw/w-d-xo.html Ab...
Finite resistor ladder: n repeating units
มุมมอง 5693 หลายเดือนก่อน
Finding the effective resistance of a ladder-like resistor network with a finite number of repeating units, n. We need to solve a non-linear recurrence relation, and along the way we make use of matrix diagonalization. At the end, we take the limit as n becomes infinite and see that the golden ratio makes an appearance. Simple derivation in the case of infinite n: th-cam.com/video/7i_PGNp7i1o/w...
Infinite ladder of resistors: general case
มุมมอง 1.2K3 หลายเดือนก่อน
Deriving an expression for the effective resistance of an infinite ladder-like resistor network, in the general case where the repeating unit contains three arbitrary resistors. We finish with some special cases, and see how the golden ratio turns up in the solution. About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent...
When is angular momentum not parallel to angular velocity?
มุมมอง 1.2K3 หลายเดือนก่อน
Developing some intuition about the direction of a rigid body's angular momentum, with the aid of some examples. We focus particularly on the case when angular momentum and angular velocity are in different directions, and discuss how to understand this scenario in terms of applied torque. The discussion is purely in terms of vector cross products, without referring to the inertia tensor. The t...
Understanding surface tension in liquids
มุมมอง 8714 หลายเดือนก่อน
Here we discuss two different (but equivalent) ways of understanding surface tension in liquids, in terms of both forces and energy. We finish by explaining how surface tension causes liquid droplets to take on a spherical shape in the absence of external forces. To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University of Cambridge, then stayed on to get a Ph...
Pressure required to inflate a balloon
มุมมอง 2.3K4 หลายเดือนก่อน
Why does it become easier to inflate a balloon once it grows beyond a certain size? Here we develop a simple model to find the excess pressure required to inflate the balloon to an arbitrary radius r, and use the result to gain some understanding of this effect. Deriving the equation Δp = 2γ/r: th-cam.com/video/CtUetjUX-yY/w-d-xo.html To support the channel: ko-fi.com/benyelverton About me: I s...
Laplace pressure in a bubble: derivation using forces
มุมมอง 1K4 หลายเดือนก่อน
By considering the balance of forces on a surface area element, we derive expressions for the excess pressure inside a spherical bubble in terms of the surface tension. We consider two different cases - a gas bubble surrounded by liquid, and a bubble surrounded by a thin liquid film floating in a gas. To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University o...
Single-slit diffraction using phasors
มุมมอง 5234 หลายเดือนก่อน
Using phasors to investigate the interference pattern I(θ) produced when a wave diffracts through a single slit of finite width a. To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a priva...
Double-slit interference with phasors
มุมมอง 8205 หลายเดือนก่อน
Using phasors to investigate the interference pattern I(θ) produced when a wave diffracts through two narrow slits separated by a distance d. To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working...
Temperature of a planet with an atmosphere: the greenhouse effect
มุมมอง 4725 หลายเดือนก่อน
Finding the equilibrium temperature of a planet heated by a star, including the effects of reflection and re-emission of radiation by its atmosphere (i.e. the greenhouse effect). The result depends on the albedo and emissivity of the atmosphere in appropriate wavelength ranges. To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University of Cambridge, then stayed...
Dust grain heated by a star: equilibrium temperature
มุมมอง 4675 หลายเดือนก่อน
Finding the equilibrium temperature of a dust grain heated by a star, by considering the balance of absorbed and emitted radiation. We first treat the grain as a black body, then consider how the model might be made more realistic. To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I...
Collision between spheres: general result
มุมมอง 7015 หลายเดือนก่อน
Deriving general vector expressions for the velocities of two smooth spheres following a collision. We include both elastic and inelastic collisions, by allowing for an arbitrary coefficient of restitution. Using the zero-momentum frame allows us to simplify the maths a little! To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University of Cambridge, then stayed...
Why do particles of equal mass rebound at 90 degrees?
มุมมอง 2.7K5 หลายเดือนก่อน
When a moving particle collides elastically with a stationary particle of equal mass, the two particles always move away at right angles to each other. In this video we use the conservation of momentum and energy to prove this. An interesting result whose proof is surprisingly simple! To support the channel: ko-fi.com/benyelverton About me: I studied Physics at the University of Cambridge, then...
Drag forces and the Reynolds number: intuitive understanding
มุมมอง 7826 หลายเดือนก่อน
Drag forces and the Reynolds number: intuitive understanding
Why can orbital and spin angular momenta be added?
มุมมอง 1.5K6 หลายเดือนก่อน
Why can orbital and spin angular momenta be added?
Why does Kapitza's pendulum oscillate upside down?
มุมมอง 2.4K7 หลายเดือนก่อน
Why does Kapitza's pendulum oscillate upside down?
What is the electric displacement field?
มุมมอง 6K7 หลายเดือนก่อน
What is the electric displacement field?
Bound charge density: why does ρ = -∇⋅P?
มุมมอง 1.8K7 หลายเดือนก่อน
Bound charge density: why does ρ = -∇⋅P?
Polarisation and surface charge: why does σ = P⋅n?
มุมมอง 2K7 หลายเดือนก่อน
Polarisation and surface charge: why does σ = P⋅n?
Angle at which particle leaves sphere: force-free method
มุมมอง 1.3K8 หลายเดือนก่อน
Angle at which particle leaves sphere: force-free method
Ball and chain projected up a rough inclined plane
มุมมอง 1.4K8 หลายเดือนก่อน
Ball and chain projected up a rough inclined plane
Coiled chain falling off the edge of a table
มุมมอง 1.8K8 หลายเดือนก่อน
Coiled chain falling off the edge of a table
Chain dropped onto scales: finding the effective mass
มุมมอง 8508 หลายเดือนก่อน
Chain dropped onto scales: finding the effective mass
Particle leaving sphere immediately: force-free method
มุมมอง 8718 หลายเดือนก่อน
Particle leaving sphere immediately: force-free method
Slicing cones and the geometry of the discriminant
มุมมอง 5328 หลายเดือนก่อน
Slicing cones and the geometry of the discriminant
Ellipse and hyperbola equations from locus definitions
มุมมอง 4439 หลายเดือนก่อน
Ellipse and hyperbola equations from locus definitions
I really appreciate this! 😊
Will pulley rotate in this case
Thank you so much
❤ from india Sir can u pls make a video to find electric field at edge(vertex) of a triangular sheet(equilateral) with surface charge density sigma and electric field at a point p at a distance above(at z axis) centroid of a equilateral triangular sheet of surface charge density sigma My sir solved this problem by flux method but i wanted a classical integration method
Amazing job! I wish your videos get the attention they deserve! Keep up the work. I'm excited for your next videos :)
You should've mentioned that this is one of several uniqueness theorems (this one is for Dirichlet problem). In particular, in Electrostatics there is another one for the case when the charges on the conductors are fixed . For example, if you place uncharged sphere in the electric field, the theorem you presented is not useful.
It's a very good video
Well made video but I suppose there is one inaccuracy the terms in the first equation should be mv + Fdt = (m - dm)(v + dv) - (dm)(w - v)
The equation in the video is correct - if you start with the equation you suggest, you arrive at the incorrect conclusion that the speed of the rocket decreases as fuel is burnt. Take a look through the comments and you'll find an extensive discussion I had with someone else about this same issue!
Good explanation of a tricky idea!
Is it a pure coincidence that the Y equation is basically the (tangential) velocity head if we use Bernoulli’s equation
Sir ur voice is so calming
Very clear in explaining this chain-scale problem 👍
great videos! These are really helpful please please keep posting!
Thanks for your support, I will!
Does each stage have the same amount of fuel? In real life, rockets stages have different amounts of fuel I think.
This is definitely a simplified model!
Notations are beautiful
Thank you!
woow i found an underrated teacher i mean you can really go to any famous private institute or university and become their main teacher sir thanks for this effort for teaching here
Thanks for your kind words, I'm glad the videos have been helpful!
Solution seems pretty interesting. However I encountered some discrepancy in your solution and mine (I get proportionality 1/r⁴). I consider directly that pressure acting on a small element of a balloon is equal to four tensions projected onto vertical axis(which should give some solid angle ) divided by the surface dS. The rest is just like you did,and at the end I got different formula (dimensions are ok!!). Is my method correct or there's something I miss?
That should get you the same result! I have used a similar method in another video, maybe compare your working against this: th-cam.com/video/CtUetjUX-yY/w-d-xo.html
The result you have used for dipole is for a far away point, I dont see how it makes sense?
Indeed it is, so our conclusion is that the electric field outside the sphere is equivalent to the field that would be produced by a very small dipole at the centre of the sphere.
@@DrBenYelverton what do you mean when you day that the dipole is verysmall? Do you mean the moment of dipole is very small?
Not necessarily the dipole moment - the separation between the two charges is much smaller than the size of the sphere.
@@DrBenYelverton exactly. But the charges are at the circumference of the sphere so doesnt that make the size of the sphere and the distance between the charges comparable?
The actual charges here are indeed on the surface of the sphere, but the result of the video shows that the overall field you get is indistinguishable from the field that would be produced by a small dipole at the centre.
You should have shown us the point at which you have found the potential
It's an arbitrary point.
It's interesting that conservation of energy was not involved in the calculation. I guess that a coeficient of restitution of e = 1 would have been the subrepticious way of introducing it, but this is not immediately apparent. Good video as always.
Thanks - yes, using the coefficient of restitution makes the algebra easier and has the advantage that the result works for both elastic and inelastic collisions!
What is presented here is a very simple approximation. Setting the wave equation to zero is a boundary condition valid at infinity, which does not exist in reality. The correct way to analyse this problem is to set the wave equation to a source and then analyse the propagation of the resultant electromagnetic fields. When this is done a lot of detail overlooked here is revealed. The fields propagate instantaneously when they are created by the source in the nearfield, and they reduce to about the speed of light at about one wavelength from the source, and never becomes exactly c even at extreme astronomical distances from the source. This corresponds to the phase speed, group speed, and information speed. Another important detail that is revealed is that there is a circulation of the electric field in the nearfield. The longitudinal electric field that is launched from the source, curves toward the opposite pole and creates the transverse electric field at about 1/4 wavelength, and launches transverse electric fields back toward the source and also away from the source. These propagating fields in the nearfield completely violates Relativity, which says nothing goes faster than speed c. So the speed of light is not a constant as once thought. Inserting c=infinity into the Lorentz Transformation yields Galilean transformations, where time and space are absolute. These results indicate that if a moving body is observed with nearfield light, then no Relativistic effects will be observed, but if farfield light is used then Relativistic effects will be observed. Since time and space can not depend on the frequency of the light used to observe effects on time and space, then one must conclude the effects of Relativity are just an optical illusion. Any theory based on Relativity such as General Relativity, and Quantum electrodynamics are wrong. See the following short TH-cam presentation for details, as well as the paper it is based on: *TH-cam presentation of above arguments: th-cam.com/video/sePdJ7vSQvQ/w-d-xo.html *More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity,2023: vixra.org/abs/2309.0145 *Electromagnetic pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1
Thank you, sir!
❤❤❤❤amazing stuff.
Thank you!
Can you explain the equality at 7:17 resulting from an integration by parts? I can't quite put together what u, v, du, dv are in this case. Thank you!
I'm a little bit unsure. My intuition tells me that for the vertical major axis that if you smush the ellipse a lot then the top basically turns into a super tight corner. So I would think that there would need to be a lot of force needed to change the direction of velocity. Also in the same example of the super smushed ellipse, the sides will approach vertical walls so would the minimum velocity for not falling off at the top even get up the sides to get to the top(since the derived expression seems to say the min velocity just keeps decreasing. )
Hey thanks for this wonderful video ❤
Glad you enjoyed it!
Only someone who doesn't believe that balances measure mass instead of weight could ever believe in the validity of this experiment. The two sides of a balance incline as one. You can't treat the different sides as independent. More force is needed to incline one side because there is all the mass on the other side.
Except that it actually always rotates because of the rotation of the earth and so one has to calculate out any potential effects. You didn't show any of the data. It actually disproves the equivalence principle.
A really misguided experiment. It does not at all prove what it pretends to prove. It is pretending that the two masses are moving independent from each other.
Hi ben, I am a physical chemistry teacher. I tried to derived a function for the electric field lines for days and finally got it independently by a different method from yours. Then I find your video. I am curious if your method is you own discovery or you used a reference? Another questions is that I haven't figured out what values should A take. To draw a few lines in a figure, they should be reasonablely spaced. Do you have any idea?
As far as I remember I came up with the idea myself, originally for the purpose of making video thumbnails! I'm sure I'm not the first to discover this though. With the field line spacing, ideally in 3D the number of field lines crossing a unit area should be proportional to the field strength. You'd have to think about how to adapt this to make a 2D figure and choose the values of A appropriately.
Thanks for this, your explanation was very clear! I have two questions: 1. Does the graph imply that the balloon's pressure actually goes down as the balloon's radius increases past that tipping point? 2. If you were to tie off the balloon after filling it to a given pressure/radius, and then increase the external pressure (say, in a pressure chamber), the balloon should shrink, right? What equation governs the decrease in radius? How does it interact with the ideal gas law?
I have a doubt that u²=(y²+σ²)/y² then u =+ or - √(y²+σ²)/y so why you rejected -√(y²+σ²)/y ? and only taken +√(y²+σ²)/y in place of u in arccot(2zu/a) ?????
Sir at 03:13 it shouldn't be (u.t).t - (u.n).n due to the n towards the opposite ( not exactly but almost ) way ?
Please don't stop posting these videos i know these are gaining less views but believe you are actually clearing doubts of many people related to real physics.🎉
Thanks for your support! I will get back to making videos soon.
What a great explanation. This should go viral one day
Thanks for your support, let's hope so!
Best proof of this I have ever seen.
Excellent, thanks for saying so!
Neat! I really liked it , it is such a nice observation and much faster than integration by parts
I'm glad you enjoyed it!
@@DrBenYelverton Thank you for the video!! I hope I get to use it on an exam tomorrow 🤞🏻
Good luck, hope it goes well!
Great explanation
Thank you!
excellent, i finally understand
I'm glad this helped!
THANKU SIR 🙏
If you observe a electron, it becomes a particle, so if you observe a phonon, will it become a particle?
Thanks Ben, clear physics and clear mathematics,
Glad to hear it, thanks!
Very nice! It is interesting you did not use the term "no slip condition" at the top surface but tried instead to emphasize its source which is fluid friction (viscosity).
Thanks for watching. Yes, very much an intuition-focused video!
Haven't learnt integration that well yet, however can't we integrate electric field due to line wires(finite) and then as we integrate wouldn't it give us E.F at general point?... If i knew integration that clearly i would definitely try every possibility ..but as i dont know it that well .. can you tell me if what im thinking is possible or not..
That works in principle but I'm not sure if the resulting integral can be done analytically - it's hard enough finding the on-axis field!
Plz provide the proof
I believe this problem is in lev landaus book it's funny all the other classical mechanics texts like morin and goldstein are 600 pages long but lev gets right into he's book is 200 or less
Thank you so much this was unbelievably helpful.
Unbelievably well-made! Thank you.
It would be nice if you solved an example question
See the following video for an example: th-cam.com/video/tdKVnrCpdmE/w-d-xo.html
Hello, for the value of x, why do we utilise both values of lambda? Sorry if its a bad question.