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Differential Sums?!?!?!?!?!
We would like to find
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uNeXpEcTeD uSeS oF mAtH
Suppose we want to find
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Why You Should Stop Calling People Smart
Note: this isn’t a traditional physics post. If you want more of that, come back later or read some of my older posts.
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Using Lots of Geo in Physics
Physics Cup 2012 Problem 10: A thin rod of mass $m$ and length $L$ is placed into a corner formed by a vertical wall and a horizontal floor so that the rod forms an angle $\alpha$ with the floor and is perpendicular to the line where the floor and the wall meet. The static coefficient of friction of the rod against the wall and against the floor is $\mu=\tan\beta$, which is not large enough for keeping the current position – as long as the only forces applied to the rod are the normal and and friction forces applied to its endpoints, and the gravity force $mg$ applied to its centre. What is the minimal additional force $F$ needed for maintaining the current position of the rod (assuming that its direction and application point are optimal)? Express your answer in terms of $m$, $g$, $\alpha$, and $\beta$.
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On Symmetry
Apparently symmetry really helps in physics problems. I was too close-minded to realize this lol. Sometimes it stares at you like ( ͡°( ͡° ͜ʖ( ͡° ͜ʖ ͡°)ʖ ͡°) ͡°), and sometimes its more discreet like ┬┴┬┴┤(･_├┬┴┬┴. Sometimes, its more dependent on your own training materials. For example, consider this problem:
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A Nice(ish) Eigenvalue Problem
So I came across a problem when I was doing some EM that I want to share with you today.
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USAPhO 2012 A2
We’re gonna do another one of my favorites today: USAPhO 2012 A2!.
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Science Bowl and Giving Back
Science Bowl has always been a part of my life. It’s been there for me through life’s great ups and downs, the twists and turns, the random times I feel like a poet and defy grammar. It’s always been a vent for my anxiety. I decided to apply to be captain and got in a while back and everything changed.
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An Attempt at a Graduation Speech
I’ve realized that I’ll probably never get to give a graduation speech, so here it is: a little early though.
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Rotating Special Relativity
When in the course of doing physics problems (man, I should really stop listening to Hamilton), you find yourself at the intersection of what seems to be two different fields. For example, consider the following problem, at the intersection of special relativity and oribital mechanics.
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A USAPhO Problem
Today, we will be doing one of my favorite problems of all time: USAPhO 2011 A2!.
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A Physics Analogy of School Starting Again
It’s been a great summer, and I hope I really get to interact with the people I talked to over the summer.
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Another, Another One
Let’s keep our pattern of posting Princeton’s Graduate Qualifier exams. Today, we’ll do J09M.1, which is entitled “Coupled Pendula” because its literally solving the system where two pendula are coupled together with a spring at their midpoints.
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Another Princeton Problem
Turns out Princeton makes some really, really good problems to do if you like doing physics. So, just like when your binge-watching a good TV show, I need another one, another one, another one…
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An Interesting Kinematics Problem
I was reviewing kinematics (for fun, of course) because its my favorite physics topic because of its extreme relevance to the real world. After all, who hasn’t dropped something or pushed something off a table. I was grinding some problems and came across a really interesting one.
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Why Boundary Conditions Matter
In this article, we are going to talk about some boundary conditions. I sound (▀̿Ĺ̯▀̿ ̿) when I’m talking about this lol. But in reality, I just go like ༼ つ ◕◕ ༽つ with the physics and hope for something to happen. (~^)
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Using the Equipartition Theorem on Photons
I’ve realized that there are very few topics of physics covered on this site, so this post is meant to fix it a little bit. Let’s do a thermodynamics problem today then. So let’s start with some discussion of the equiparition theorem: what exactly is it and why should you really care? After all, equipartition is a pretty big word and you would have probably tuned out by now if a professor was lecturing about this. This is important some problems, like the one we will solve today! Let’s get started, shall we?
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USAPhO is Cancelled
For context, I’ve been preparing for the USAPhO (United States of America PHysics Olympiad) for the past 2 years. Due to COVID-19, its now cancelled.
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More Plasma, More Captain Phasma
These are my notes for Chapter Two of Introduction to Plasma Physics and Controlled Fusion by Francis F. Chen. Its really a great book and its available online, so I would recommend that you check it out!
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Princeton Makes Good Problems
First of all, happy Pi Day!!! Time to get to the physics. I found this Princeton problem looking at old quals for fun.
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Damped, Driven Oscillator
Alright, so we’ve all seen what a simple harmonic oscillator is and how to solve its equation (I hope). So let’s move into more spicy territory, shall we?
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Earnshaw's Theorem
So it’s come to my attention that my blog doesn’t really have that many EM problems on it, so I decided to prove Earnshaw’s theorem. But what really is Earnshaw’s Theorem and why should you care? That’s what we talk about in this blog post.
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My First Experience With Plasma Physics
These are my notes for Chapter 1 of Introduction to Plasma Physics and Controlled Fusion by Francis F. Chen.
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Target Acquired: Plasma Physics
I’m beginning a new adventure!
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A Poem
E̓rͯro͙rs͒ ̲aͪreͭ ̮r̠ed
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High School Pt. 3 + AP Exam Results
School just started again!!!! Yayyyy!