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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?

بتبرم كتيير لسانك طويل

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

This is ipho 1990 !!!!

Still wrestling with the fact that initial angular velocity or acceleration does not change the horizontal distance.( In tennis for example is obvious that it does(?))

Wow! Thank you, professor! I hope one day I get such a physical intuition as yourself, so that I could solve hard problems like this. If not for this video, it would've taken me months to come out with your solution! Are there any tips you would want to share to this end? Or is it just time and doing lots and lots of physics? Haha! I send you my highest regards! I love your channel!

Well done, thanks!

Thanks professor Ben for sharing this question physics. From the Brazil here

Nice problem but the whole "ignore \delta t" thing seems a little deus ex machina. Don't you need some kind of estimate of \delta t to justify your neglecting of it? And its magnitude would strongly depend on the value of \mu, I think, as well as maybe trickier stuff like the modulus of compressibility.

Great video! Now it will be interesting to consider non uniform mass distribution in the chain or the case where different parts of the chain are accelerating at different rates. Your thoughts?

Interesting that the situation naturally imposes constraints on k. E= hmg KE (post) = ½m(v²+w²) v²= 2ghk; w² =μ²2gh(1+sqrtk)² KE = mgh(k+μ²+2μ²sqrtk+μ²k) <= hmg ==> k(1+μ²)+2μ²sqrt(k)+μ²‐1<=0 ==> sqrt(k) <= (1-μ²)/(1+μ²) = -1+2/(1+μ²) ~ 1-2μ²

It seems to me that the fact about the time interval related to the contact with the ball and the ground should be mentioned in the problem's heading too. Something like "the time the ball is in contact with the ground is very small" . Anyways, great video, it is a very challenging problem 😊😊

Thank you so much for the help sir ❤

8:24 how can we do this calculation and what information would we need ?

This is all in the absence of drag/air forces right? Could be interesting to include the Magnus force which propels the object forwards as it rotates. Does there exist an angular velocity where the magnus force pulls it back to where it was dropped from? Also, by assuming negligible contact time with the ground, does this mean the angular velocity of the ball doesn’t change? What’s the minimum angular velocity for skidding? So many questions sorry! It’s an interesting problem as always. Let me try answering my own qs: If contact time is zero, there is a horizontal impulse on the ball at the ground equal to mw. Therefore there is an angular impulse (change in angular momentum) of mwr, where r is the radius of the ball. So using angular momentum, mwr = I(omega_0 - omega), and we can solve for omega after the bounce so yes it changes. My guess: if we let omega equal zero, we can solve for the minimum allowable omega_0 to stay skidding.

In the final calculations as n approaches infinity, correct me if I'm wrong, but it appears you applied the limit partially, meaning you deemed the organs which wouldn't cancel out as ones approaching zero as n approached infinity, but did not do the same for those that did cancel each other out. I know that they didn't approach zero, but still, applying the limit calculation not on the entire expression is a bit mathematically questionable. I can see why that would be the final result, but if there is a more precise way of reaching it I'd be glad to know.

Where is this question taken from?

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in 10:13 shouldn't the Z component be 2vx cos(lamda)-g

thank you sooo much sir ❤❤

Very cool! Thx!

Thanks doc, you're a life saver. I was trying to find a mistake in my calculation for hours and your video poped up after the search, solving it

What is the free charge here?, Where it will be,1) inside the dielectric, if yes then it will be a conductor not a dielectric or 2) the outside charges that produce es the polarization in the dielectric, but why the name free?

OMG!!! Such an amazing explanation!!! Have'nt found a video that better explains this concept in such an easy way! Thanks a lot!!

Electronics & Telecomunication student here, while explanation is pretty clear and i understand where does it come from, im kinda confused. We had to made a model of cable with two parallel wires and find value of capacitance. The model is maded in FEMM and using values from program i get different value of capacitance and now im curious which value is closer to be real. Is there any way to find out? Using values from femm, im just dividing charge over voltage difference between two wires, is that good way or not?

My own understanding H = 1.028334744 meters .

Nice one! As you said it's doable using Newton's 2nd law, but tbh I prefer lagrangian mechanics for these type of problems (easier to manage the fact that the FOR relative to the slope is non-inertial), and it shows just how powerful it is here. Same stuff with coupled oscillators (springs, pendulums... we often had those in exams, I think once there was even a charged pendulum or smtg lol)

11:00

I don't follow why you multiply |P| by delta x, delta y and delta z. Shouldn't it only be P times separation which is delta y. So shouldn't it only be |P|*delta y ?

Well done, many thanks!

is it coincidence that the plane of potential zero is a sphere? If I had for example a grounded cube, how would that translate to the problem?