Thanks so much 😁

Thank you so much for your kind words 😁 I'm glad it's helped you out.

Brilliant ☺ I found Physics hard when studying and I didn't always understand topics straight away so make sure you keep going with it; it does all come together in the end ☺ And, I have a more detailed video that goes into Dimensional Analysis in a bit more depth. I think I explain it better in this video kzfaq.info/get/bejne/qdFpdbh-p7GamIk.html and do ask questions if you have any. Take care!

You're very welcome. I had the exact same question when I was studying physics back in high school. Take care.

Thank you so much 😄.

Hi thanks for watching the video 😁. The constant of proportionality can be found through performing an experiment on the system that your trying to model mathematically. So, in the above example, we really want to discover how the angular acceleration will change if, say, we shorten the length of the string (r) or if we increase the particles velocity (or both). What we can do is take many measurements of the angular acceleration with various values of r and v. When we plot these measurements on a graph (with "a" on the y axis and "v^2/r" on the x axis) we should get a straight line. The gradient of this line is the value of k. Acc | | * | * | * | * |*________________ V^2/R Something like that 😄... Let me know if this wasn't clear or didn't fully answer your Question.

So, if the gradient = 1, our mathematical model becomes: a = 1*(v^2/r) we can exclude the "one" because it's redundant

Brilliant 😀 I'm glad it's helped.

You're most welcome Sarthak. 😊

I'm glad it's helping ☺

You're welcome 😊 The constant of proportionality (k) represents the gradient when you plot the centripetal acceleration against V^2/R: Acc | | * | * | * | * |*______________ V^2/R What we're doing here is making an assumption about what physical quantities may effect an object's centripetal acceleration while it's being spun around in a circle. We've assumed that the distance from the center of the circle and its velocity may have an impact, but the problem is: we don't yet know how they might effect the acceleration. Dimensional analysis helps us find out that increasing the velocity raises our object's acceleration by a power of 2, but the acceleration is inversely proportional to the distance from the center of the circle. However, the equation doesn't finish there so we add k as a placeholder to say that some constant is needed to complete this equation. k doesn't have any units and, therefore, cannot be represented by any of the fundamental dimensions like Length (L), Time (T) etc. You can find the value of k through experimentation or by looking at 2d velocity and position vector diagrams and a bit of mathematics (I might cover this in a future vid). In this case, however, we find vector mathematics concludes that k is equal to 1 I hope this helps. Do ask more questions if I haven't explained it clearly enough 😊

Thank you, that's really kind. 😊

Brilliant 😊 I'm glad it's helping.

Thanks 😊 I use Photoshop

With physics & engineering, 'dimension' refers to the measurable aspects associated with fundamental physical quantities. These dimensions, such as length, time, and temperature, etc. are the building blocks upon which physical systems are described and analyzed. When I was studying AI at Uni, one of the goals was to train a neural network. Each parameter on the neural net could be considered as a unique dimension in a "solution landscape". This solution landscape could have many dimensions. Each point on this landscape would be a unique neural net configuration. The goal was to find the best point on the solution landscape... In both cases, dimensions represent the fundamental components that define our system of interest.

Good question. When the dimensions on both side of the equal sign are "not" the same, this means the equation has been written or derived incorrectly. We're all human, and when we do maths we can often make mistakes (especially when the maths gets complicated). So, one quick test to see if our equation is correct is to see if the units on both side of the equation are equal. Say if our equation calculates the velocity of an electron undergoing some acceleration over a certain time period: "vf = vi + at" vf -> electrons final velocity vi -> electrons initial vel a -> the electron acceleration t -> the time the electron undergoes a constant acceleration This equation "wants" a velocity of the electron on the Left hand side. The Right hand sides job is to work together to produce a velocity when all the variables are added or multiplied together. If the Right hand side doesn't deliver, then it hasn't done its job properly - in other words, the equation is not correct! It's time to go back to the blackboard and double check our maths. Take care - if you have further questions, don't hesitate.

Thank so much I was beyond thrilled to see that you took the time to respond and provide such a thorough and insightful answer. Your dedication to your craft and your commitment to fostering a community of learners is truly commendable. Thank you for all that you do, and I eagerly await your next video!❤❤

@@sarosaeed857That is such a lovely comment - thank you so much 😊 Funnily enough, my next video will cover some example exam questions on dimensional analysis. But, I am also working on more classical mechanics and will navigate towards quantum mechanics... eventually. I'm glad I could help.

Thank you so much Emma 😊

I'll be making another video soon about how to answer Dimensional Analysis Exam questions. I've also got a more detailed video here that might help you kzfaq.info/get/bejne/qdFpdbh-p7GamIk.html Take care and keep trying 😊

So our equation is: a = (r^n)(v^m) where "a" represents an acceleration, "r" is a distance and "v" is a velocity. We then convert these measurements into their respective dimensions - a distance (r) is simply a length (L) a velocity is a length divided by time (L/T) and an acceleration is a length over time squared (L/T^2) These Length (L) and Time (T) dimensions MUST be the same on both sides of the equation (the equals sign). @3.50 I'm using the law of indices i.e. the Product of Powers: L^n * L^m = L^(n+m) to simplify our Dimensional equation. @4:29 - the dimensions MUST balance on both sides of the equation meaning the powers must be the same. This gives us two simultaneous equations which we solve for to get m and n. If this is still confusing, you'll need to learn about the laws of indices in algebra class and how to solve simultaneous equations which you'll also study in algebra class. But again, do talk to your teacher because you may have not learned all the maths required yet for solving Dimensional analysis problems. Good luck and take care!

Also, m is positive 2 because when: -2 = -m then we can multiply both sides of the equation by -1 to get: +m = +2 or m=2

​@@PhysicsTutoringHub why should we need to multiply it by -1? Is there any rule?

​@@PhysicsTutoringHub Thanks for clearing out:)

@@user-ex3sq1xi8lWell, if we have an equation that looks like this: -x = 2 (negative x is equal to 2) We could leave it like this if we wanted but, normally we'd like to express our variable x as a positive variable rather than a negative one. If we multiply both sides of the equation by negative one (-1) it flips the sign of -x to +x. You can do this on your calculator. if you type in (-1 * -1), you get a +1 as an answer. But whatever calculation we perform on one side of the equal sign we have to do the exact same thing on the other side. So, our equation is -x = 2 I now decide to multiply both sides by negative one because I've decided it looks better to express our variable x as a positive value: (-1) * -x = (-1) * 2 +x = -2 or x = -2 The same can be applied to -m = -2 I hope this helps. 😊

I don't think I learned DA as early as that when I was at school! They definitely come up in AS and A-level exams though - I've checked the past AQA maths(Mechanics) papers from the last couple of years. But, it's also useful to learn as early as possible if you decide to study Physics or Maths in A-level (you may have not decided yet!). I'm going to make a video soon that covers example exam questions you may find in AS and A-level. They may help you with GCSE as well. If you have any questions, do ask me 😊

TLDR: Ask your teacher because it depends entirely on your curriculum, exam board etc. It depends if your curriculum teaches this in high school - talk to your teacher. In the UK, You'll find Dimensional Analysis (DA) questions in AS and A-level Maths (mechanics) papers but this also depends upon the exam board. When I was in High School over 20 years ago, I don't remember learning DA but I did cover it in the first year of my undergraduate Physics course.

​@@PhysicsTutoringHub We do have these in our textbooks...for exams our question paper follows a acute pattern, Like previous year questions will be repeated...thus, we only need to practice PYQ's . But this year they are including High level and out of syllabus questions! We can't predict what it would be! It'll be tough to score A grades! So I decided to watch classes from where I can understand the basic concepts well...

@@user-ex3sq1xi8lBrilliant😊. I found exams preparation very stressful when I did them and I had the same concerns as you. It's very difficult to know what to focus our time on when studying for these tests. Previous years questions are good to look at to get a rough guide on what may appear. But, your teacher should be preparing you and your fellow students for these exams too. It's part of their job to do so. Take care and good luck with your studies 😊

​@@PhysicsTutoringHub Tysm