Visual physics derivation! (Centripetal acceleration)

The most logical explanation for why centripetal acceleration formula has a v^2/R.
The centripetal force given by mv^2/R appears in most places in mechanics. However, it's not very straight forward as to why the equation has a speed squared in it, or why it's inversely proportional to the radius of the turn. In this animated video, we will get the intuition behind this.
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Chapters
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00:00 Visualising change in velocity
01:00 Doubling speed
03:40 Tripling speed
05:00 Why V^2
05:25 Doubling radius
07:25 Tripling radius
08:03 Why 1/R

[@Mahesh_Shenoy]

First! Also, if you like such videos and haven't already consider subscribing - lnkd.in/ggwZxJNk A new intuitive physics video every weekend (Almost). Next up - Biggest confusions on centripetal and centrifugal forces!

[@SyedShaan-ib4bv]

This is the most intuitive reasoning for centripetal acceleration that I’ve seen, I think I’m finally satisfied

[@SureshBabu-et8zb]

Sir I can confidently say that you are the best teacher on the platform

[@xsli2876]

Thank you! Using the same trick, we can derive another version of centripetal acceleration: omega^2 x radius. In terms of why the direction of centripetal acceleration is always pointing toward the center, because the magnitude of velocity doesn't change. It is not getting faster or slower. If the acceleration(which is a vector too) has some component on the direction of velocity, then velocity magnitude will change. Therefore, centripetal acceleration must be perpendicular with the velocity.

[@Mahesh_Shenoy]

Love it!

[@user-gi6mj9zb4o]

one of the best explanation I've had in a long time

[@phannamanh]

This formula makes me feel confused. I always set the question (Why) in my mind. I tried to prove it by using calculus but it is so complicated. I figured out a lot of explanations about it and afterwards i am disappointed. Fortunately, I came across your video and it is the best thing I've seen. Thank you very much. It helps me a lot.

[@noelfuentes2810]

Wow bro, I never comment on videos, but this was exactly what I needed, great job. I finally understand the concept now! Thanks!

[@MalikIstiakAhamedRohan]

This video really make my concept clear as water...... Thank you very much, sir

[@rufaidasheikh2725]

hi sir ...... I watched ur videos at khan academy... and fell in love with your teaching ..... and here I am, feeling guilty for stalking you on youtube ...... i really want to thank you for making me fall in love with science... luv yuh

[@Mahesh_Shenoy]

Thanks a lot for reaching out, Rufaida :)

[@davidogbija5806]

🎉🎉🎉 This teaching worth celebrating. Thank you so much Sir.

[@MDE123]

Thank you! Best explanation I have seen. I get it now

[@joshita_alapati]

Best explanation I got to understand its derivation in visual senses

[@ARN48411]

Now, It makes more sense to me!! 🎉❤

[@himanshupandae]

Loved it !

[@pralay1762]

Great video 😍❤️❤️

[@letsdance8045]

You are the greatest teacher that I never see

[@pranavpriy8108]

Superb sir🔥🔥🔥

[@thuppunathodachipoam51]

Ayyyy mahesh sir is back 🔥

[@mesganawoldeselassie4267]

You really helped me as I am visual learner...thank you so much again!!

[@valli474]

Your explanations are the best, i always wonder how learning here is made so easy and very enjoyable, thanks a ton sir :)

[@Mahesh_Shenoy]

Thanks a ton, Valli! :)

[@samarth2410]

Wow , how simply you explained it.This is awesome!👍

[@Mahesh_Shenoy]

Glad you liked it!

[@MalikIstiakAhamedRohan]

Very good video + animation

[@divyakumar8147]

great video

[@akyatwinejoshua9234]

You are just the best

[@ImiGamlin-qf6ss]

that way a great explanation sir thankyou soo much

[@user-xl5gu3cy5x]

smart explanition!!!!!!!!!!!!!!! thank you

[@swetha9115]

You are really amazing sir ☺,

[@sinah8151]

Thanks that was great !

[@snowdenkhaw5799]

Good video man, keep it up!!!

[@Mahesh_Shenoy]

Thanks!!

[@omkarreddydevarapalli130]

Nice explanation

[@cartoonic6039]

I have a very simple but intuitive question. Why doesnt the object collapse into the point. Since the centripetal force is an acceleration is increasing with time it should get to a point where its high enough to pull the object towards its centre. For example: The electron in an atom if not for its stationary state it should be pulled towards the nucleus since the proton and nucleus attract but what keeps it moving in a circular path is the fact that they have fixed energy called stationary States so they can't lose energy. But objects in the real world dont have fixed energy level so what keeps them in circular path? Another example is that if we change the mechanics occurring on the body interms of force, The centripetal force will be the F=m×a but converting the objects tangential velocity into force its F=0 since it has no acceleration.Resolving the 2 forces the object is supposed to move towards the center so why does it still move circular

[@RajaBabu-ur5kf]

Loved your video!

[@Mahesh_Shenoy]

Thanks!

[@jlpsinde]

AMAZING

[@amanbajracharya7403]

Finally!❤️❤️❤️

[@Morax___]

Ah I love this video

[@fire..fly23]

Thank you so much sir

[@MRKS8]

Terrific

[@mesganawoldeselassie4267]

It is amazing!!

[@Mahesh_Shenoy]

Thanks 🙏

[@Forever._.curious..]

Thanks 😊 sir

[@obanijesuadufe8827]

I really love how you explained things but I have a question. If you remove the proportionality sign, we still have to deal with constant k. Is that constant k simply 1?

[@Adil_LC]

thank you

[@Yohanmiracle]

Awesome sir

[@Mahesh_Shenoy]

Thanks

[@praveenkumarmorabad1358]

As a teacher You inspired me alot 🙏🎁 thank you sir 🙏🙏

[@Mahesh_Shenoy]

You are welcome :)

[@raghavg5847]

thanks sir , great video but does this mean that if two cars travelling in a straight line (at different speeds) turn such that their velocities after the turn are in the same direction,then the change in velocity of the faster car will be more? (i dont know why but i expect them to be equal) Also sir please check the book Pathfinder for Physics, it has unique problems especially MCQs section

[@Mahesh_Shenoy]

Yes! Longer vectors means bigger change.

[@swetha9115]

I got it 👍🔥

[@rajeevkumarsam5499]

Nice explanation.. kindly cover all lectures of physics clsss 11..

[@borkata7935]

I don't really understand why the change in time is cut in half when the velocity is doubled, can't the velocity have changed by giving it increasing the displacement twice? Could anyone explain?

[@crazyexperimentalinfinite]

Hi at 01:16 you changed the vectors of inital velocity to but it shall remain same

[@prakashraj4348]

Super animation, curious voice , and amazing explanation!

[@Mahesh_Shenoy]

Glad you liked it :)

[@appoliticalfacts2515]

sir please be regular In this make more and more videos like this

[@Mahesh_Shenoy]

Yup, that's the plan for this year!

[@aryanraj441]

@@Mahesh_Shenoy you're planning to stop making content for class12 physics on khan academy India?

[@whiteseashells7513]

Sir Projectile motion please make a video.

[@uzairhussain4856]

Great Animations and intuitive explanation. Which software?

[@Mahesh_Shenoy]

Thanks, Uzair! I used Keynote for this

[@uzairhussain4856]

@@Mahesh_Shenoy Thank you. Keep doing the great work. ♥️

[@aleksandarslozenjicin2511]

Hi, When we double the size of radius, the car passes longer arc length (new distance A to B) in same time as first car which is moving shorter arc length (old distance A to B), why is the change in velocity identical...

[@Mahesh_Shenoy]

Because change in velocity only depends on how much velocity vector has turned! And in both cases, they have turned by the same amount!

[@shaktikashyap6]

No no no, time taken is not the same.. the time taken increase as the length of arc increase and that's why the ratio of distance/time is same as before, which means the velocity is same as before...

[@Aliha_Mushtaq]

Thank you sir 🥹🙌🏻

[@danielaschalew]

you are a genus.

[@darshi2185]

No he is species

[@shethkv812]

Direction?

[@Forever._.curious..]

Yu serve true potential junior Physicist rather than those ratifying stupid students

[@GianiPritpalsingh-pj2ig]

❤❤❤❤

[@anjaligarg8709]

I had a doubt regarding magnetic field lines We say that field lines never cross since at the point of intersection the magnetic field will have two different directions, but why can't we take the vector sum of the field and calculate the resultant direction since they are vector quantities? I am a 10th grade student please help me out

[@sakettrivedi6995]

"Two field lines never cross eachother other " means while crossing they do not have individual independent existence at same point. They actually merge ( add up According to vector sum ) to give a single new field line. Hope that helps

[@anjaligarg8709]

Ohkk thanks!

[@Mahesh_Shenoy]

Great question, Anjali. I too had that exact same question. Thanks Saket for clarifying. Let me know if you have some follow up questions!

[@aftabmohd8783]

But why is it V squared. Does it mean that the energy needed to equate acceleration centripetal for a velocity v would be equal to the same velocity but v^2.

[@singh2702]

For example, an object moves in a circular motion at a speed of 5m/s, this is the position vector. The velocity vector has magnitude of 5m/s and is tangential to the circle. The reason why acceleration is V squared is because the velocity vector is moving 5 times faster than the position vector hence 5^2.

[@kgpokebro8466]

I am student of class 9 thanks for explaining

[@amysleftelbow4253]

I love you

[@mridulacharya8250]

1:46...did U assume that new delta V is parallel to V...since u said corresponding angles r equal...

[@pranavsisodia1257]

It must be parallel as only magnitude of velocity is doubled direction of vectors still remain the same hence only length increases and new delta v is parallel

[@Mahesh_Shenoy]

Yea, what he said :)

[@abdulwajeed9619]

Friend: Bruh physics is tough Me:No thats the easiest subject(because of mahesh shenoy sir)

[@Mahesh_Shenoy]

Oh wow, what a motivation booster. Thanks!

[@chienbin4813]

+ 1 sub

[@aftabmohd8783]

Wouldn't Delta V be zero.

[@Robinhood-rj3rt]

there is no way.... most of the normal people can understand this....may God give strength for them....

[@wikdipr2944]

You should see the calculus proof

[@in_essence_codm]

Im in only 9th grade but I understood it clearly

[@TanmayGaude23e4]

​@@in_essence_codmhe is talking about ppl who came up with the formula at first.

[@ashutosh-kumar]

Sir, Please make a course on KZbin or Udemy, Paid or Free, How to make videos like you?

[@Mahesh_Shenoy]

I plan to make a few videos on just that!

[@adityadixit2024]

Sir, I have a doubt Power =VI So V is inversely proportional to I But V=IR Here V is directly proportional to I Why such a paradox?

[@anjaligarg8709]

Voltage is directly proportional to current. The formula of power just states that power is the product of voltage and current but it does not mean that if we increase the voltage, the current will decrease. This is because power is not a constant and thus when voltage increases, current also increases. Thus, if we double the voltage, the current will also be doubled and power will be 4 times the original magnitude.

[@Mahesh_Shenoy]

Thanks Anjali. Aditya, I am wondering if this question came up while learning about transformers. In an ideal transformer, the input power = output power. And hence, when we step up the voltage, the current steps down - apparently at odds with Ohm's law. Is that the doubt, Aditya? If yes, Anjali I would love if you think you can deep dive into it.

[@anjaligarg8709]

@@Mahesh_Shenoy Yes sir, as far as I know, Ohm's Law is applied when we are considering only one circuit, and thus we should not compare the current generated in the primary and secondary coil by using Ohm's law. Here, the law of energy conservation steps in; the energy that each coulomb of charge gains in a second in the secondary coil is equal to the energy lost by each coulomb of charge in the primary coil each second. Thus, if the voltage is 5 times lesser in the secondary coil than the primary coil, the current needs to be 5 times faster than the current in the secondary coil. This is explained much more intuitively in a video on transformers by Mahesh Sir himself.

[@Mahesh_Shenoy]

@@anjaligarg8709 Loving this community. Thanks a lot, Anjali!

[@Frankly747]

B R I L L I A N T ! ! ! !

[@fazeelmohammad8236]

Great sir..pls give us your introduction

[@shaktikashyap6]

Ok but the truth is that the centripetal acceleration is directly proportional to Radius so how your intuition explanation in which you said that Centripetal acceleration is inversely proportional to radius will satisfy that..?

[@Mahesh_Shenoy]

Ah, I think we need to be careful when we say it's 'directly proportional' to something. For a given linear speed, as you increase the radius, the centripetal acceleration decreases. It is inversely proportional. What you are probably talking about is when we consider a constant 'angular speed'. Like on a spinning disk. That's different. Because, on a spinning disk, things at different radii are moving with different velocities.

[@griffithfimeto3387]

You didn't relate the number square to the speed yes we get square number multiply by velocity by time not velocity square

[@singh2702]

The reason Velocity is squared is because the velocity vector changes at a rate x times the rate of the position vector and the position vector changes x times the rate of time, hence acceleration x^2 or v^2.

[@user-mr5cm7yh6h]

Exactly 💯 you are a good teacher And I am hoper you are Islamics man...

[@demiyo8424]

But how do we show a=v²/r?didn't you only show that a is proportional to v²/r

[@singh2702]

The reason Velocity is squared is because the velocity vector changes at a rate x times the rate of the position vector and the position vector changes x times the rate of time, hence acceleration x^2 or v^2. With an increasing radius, the angle which the velocity vector changes decreases , so if radius is doubled, angle by which velocity vector changes is halved.

[@gilbertengler9064]

second part to explain time is unclear for me! bigger radius will push to do a longer distance in the same time! so speed should increase????? Visual proof in Khan University is better according to me!

[@GaleWinged]

Why same time duh? The Speed is constant, the distance increased so time should increase too.

[@qualquan]

there are better videos

[@Mahesh_Shenoy]

O’course there are!

[@MaximusAurelius1987]

Thumbnail - pointing to head -> has occult knowledge. Are you planning on going on spaceship in 2024? Tier 2 Satanists don’t get to go. Sorry take it up with your boss.

[@saddatsabanature4307]

🥺❤‍🩹❤

[@cartoonic6039]

I have a very simple but intuitive question. Why doesnt the object collapse into the point. Since the centripetal force is an acceleration is increasing with time it should get to a point where its high enough to pull the object towards its centre. For example: The electron in an atom if not for its stationary state it should be pulled towards the nucleus since the proton and nucleus attract but what keeps it moving in a circular path is the fact that they have fixed energy called stationary States so they can't lose energy. But objects in the real world dont have fixed energy level so what keeps them in circular path? Another example is that if we change the mechanics occurring on the body interms of force, The centripetal force will be the F=m×a but converting the objects tangential velocity into force its F=0 since it has no acceleration.Resolving the 2 forces the object is supposed to move towards the center so why does it still move circular

[@singh2702]

Acceleration is not increasing firstly , it is constant. The reason an object is not pulled into the center of the circle is because centripetal force is balanced with centrifugal force.