Just ask this scientician

[Melville]

(phd actually make me stupider. i used to be able to do such problem with ease.)

Yeah, I'm totally going to fail my defense. I don't remember how to do anything. Gah. Anyway, the answer I get is the same as for a physical pendulum. But I'm probably wrong.

Say the line between the center of mass and the point of contact with the ground has a length L and makes an angle x with the vertical. Then the torque T about the point of contact is -MgLsin(x), where M is the mass of the half-sphere and g is the acceleration due to gravity. Since x is small, L is approximately R-r, and sin(x) is approximately x, so T=-Mg(R-r)x. I'm not sure what axis of rotation your moment of inertia is defined with respect to, so I'll introduce a new one, I. Then the equation of motion Ix''=T becomes x''=-Mg(R-r)x/I, where a prime indicates a time-derivative. This is the equation for a simple harmonic oscillator with frequency sqrt(Mg(R-r)/I).

In order to fully solve the problem in terms of given quantities, I'd need to relate I and M to J. If J is defined with respect to an axis through the center of mass and parallel to the actual axis of rotation, then I=J+M(R-r)^2, according to the parallel-axis theorem. Relating M to J seems to require evaluating an integral, which I can't be bothered with.

Did you get the same answer as me? There's something weird about the way the pivot point is constantly moving, so I'm not sure that I set up the problem correctly.

[Spun Lepton]

Can you explain what Dark Matter and Anti-Matter are in a way that doesn't make my brain hurt? (If you've already covered this, apologies. I haven't read through the entire thread, yet.)

[Melville]

Can you explain what Dark Matter and Anti-Matter are in a way that doesn't make my brain hurt? (If you've already covered this, apologies. I haven't read through the entire thread, yet.)

Given your user name, I figured you already knew this stuff.

Nobody knows what dark matter is. Currently, the most popular theory is that it consists of some unknown, heavy, slow-moving particles that are outside the realm of the standard model of particle physics. The basic idea with dark matter is that galaxies seem to contain more matter than what we can see. (By "seeing" matter, I mean detecting electromagnetic waves that it emits. Some of those waves are visible light, some are infrared, etc.) Based on what we can see, we can estimate the amount of visible matter in a galaxy. But then based on the motion of matter in and around the galaxy, we can estimate the gravitational force the galaxy exerts on that matter. The strength of gravity turns out to be larger than it would be if only the visible matter were present, so we infer that there must be some invisible matter in there. Actually, we infer that there must be a lot of invisible matter—about five times as much as there is visible matter. We don't know what that invisible matter is; all we really know is that since we can't see it, it can't interact with electromagnetism.

An alternative explanation is that there is no dark matter, but that our basic gravitational theories are incorrect when applied to the large size of a galaxy. Most people don't care for that alternative.

Regarding anti-matter: The name is misleading. Anti-matter is just regular matter. Basically, in quantum field theory, each type of fundamental particle has a bunch of numbers (called quantum numbers) that define its properties. Each type of fundamental particle has a corresponding type of antiparticle that has opposite quantum numbers. (I'm simplifying things here, but that's the basic idea.) For example, an electron has a negative electric charge, and an anti-electron (aka a positron) has a corresponding positive charge. An antiparticle always has the same mass as its corresponding particle. In any quantum process, the quantum numbers in the final product must be the same as those of the initial system of particles. Since a particle and its antiparticle have opposite quantum numbers, when you add them up you get zero. This means that they can interact with one another to form a final particle that has zero quantum numbers. So when an electron and positron interact, they can annihilate one another to produce nothing but photons (i.e. electromagnetic waves), which have zero charge. That's what people mean when they say that anti-matter annihilates matter to create pure energy.

[Spun Lepton]

Given your user name, I figured you already knew this stuff.

I have an interest in it, but no real education. I typically can't wrap my head around the math, because I suck at math. :P

I've considered going back to my old alias of REverend Ruin, but that would be too much of a pain in the ass.

[Melville]

I have an interest in it, but no real education. I typically can't wrap my head around the math, because I suck at math. :P

Ah. Sucking at math seems to be a very common condition. :P

Faraday, one of the founders of the theory of electromagnetism, was famous for using almost no math. (And rather than trusting other scientists, any time he was interested in their results, he would repeat their experiments himself!) Too bad that's impossible in modern physics.

[lovejuice]

Yeah, I'm totally going to fail my defense. I don't remember how to do anything. Gah. Anyway, the answer I get is the same as for a physical pendulum. But I'm probably wrong.

Did you get the same answer as me? There's something weird about the way the pivot point is constantly moving, so I'm not sure that I set up the problem correctly.

my friend and i come up with the same answer, but we too are worry about the constantly moving pivot point. i wish i still remember my lagrangian mechanics.

i am going to teach the first two year of college physics, and realize how much i've forgotten basic elements.

when is your defense? i wish you all the luck. you're probably doing fine, though. the worse that can happen is they'll have you rewrite some parts of your thesis. that's what happen in my university. does your department have a long history of failing phd candidate?

[lovejuice]

Ah. Sucking at math seems to be a very common condition. :P

Faraday, one of the founders of the theory of electromagnetism, was famous for using almost no math. (And rather than trusting other scientists, any time he was interested in their results, he would repeat their experiments himself!) Too bad that's impossible in modern physics.

it has been said that einstein is a rather poor mathematician. i find that hard to believe, but you probably know more about this.

[Qrazy]

it has been said that einstein is a rather poor mathematician. i find that hard to believe, but you probably know more about this.

Someone told me for his later work (I don't know if it's true or not) he worked with a mathematician but in terms of his early life...

"Alas, Einstein’s childhood offers history many savory ironies, but this is not one of them. In 1935, a rabbi in Princeton showed him a clipping of the Ripley’s column with the headline “Greatest living mathematician failed in mathematics.” Einstein laughed. “I never failed in mathematics,” he replied, correctly. “Before I was fifteen I had mastered differential and integral calculus.” In primary school, he was at the top of his class and “far above the school requirements” in math. By age 12, his sister recalled, “he already had a predilection for solving complicated problems in applied arithmetic,” and he decided to see if he could jump ahead by learning geometry and algebra on his own. His parents bought him the textbooks in advance so that he could master them over summer vacation. Not only did he learn the proofs in the books, he also tackled the new theories by trying to prove them on his own. He even came up on his own with a way to prove the Pythagorean theory."

[Spun Lepton]

Someone told me for his later work (I don't know if it's true or not) he worked with a mathematician but in terms of his early life...

"Alas, Einstein’s childhood offers history many savory ironies, but this is not one of them. In 1935, a rabbi in Princeton showed him a clipping of the Ripley’s column with the headline “Greatest living mathematician failed in mathematics.” Einstein laughed. “I never failed in mathematics,” he replied, correctly. “Before I was fifteen I had mastered differential and integral calculus.” In primary school, he was at the top of his class and “far above the school requirements” in math. By age 12, his sister recalled, “he already had a predilection for solving complicated problems in applied arithmetic,” and he decided to see if he could jump ahead by learning geometry and algebra on his own. His parents bought him the textbooks in advance so that he could master them over summer vacation. Not only did he learn the proofs in the books, he also tackled the new theories by trying to prove them on his own. He even came up on his own with a way to prove the Pythagorean theory."

What an amateur.

:|

[Melville]

my friend and i come up with the same answer, but we too are worry about the constantly moving pivot point. i wish i still remember my lagrangian mechanics.

i am going to teach the first two year of college physics, and realize how much i've forgotten basic elements.

when is your defense? i wish you all the luck. you're probably doing fine, though. the worse that can happen is they'll have you rewrite some parts of your thesis. that's what happen in my university. does your department have a long history of failing phd candidate?

I remember my Lagrangian mechanics, and I tried the problem that way, but it's actually more difficult, because it's tricky (or at least it seemed to be) to write down the translational kinetic energy of the center of mass in terms of the angle of oscillation.

Yeah, I kind of wish that I had done more TAing during my graduate program. (I only taught for one year out of almost five.) That seems to be the best way to maintain your memory of basic physics. But I hate and suck at teaching. What kind of position do you have? Just a teaching contract, or are you doing research too?

I don't have a set date for my defense, but it'll probably be at the end of March or beginning of April. It was supposed to be at the beginning of January, but my girlfriend-related semi-breakdown delayed everything for a few months. As far as I know, only one person in the recent past has failed their defense here, and I'm pretty sure my supervisor wouldn't let me fail, so I'm not too worried about actually failing. But I am deathly worried about not being able to properly answer any questions, given how much I've forgotten and how bad I am at oral exams. My Master's defense was agonizing because one of the examiners asked me to give an intuitive explanation of a bunch of things using Newtonian mechanics, and I couldn't remember at all how to do it.

[Melville]

Someone told me for his later work (I don't know if it's true or not) he worked with a mathematician but in terms of his early life...

Working with a mathematician doesn't suggest he was bad at math; it just wasn't his focus of study, so he knew less than a mathematician. Also, no matter how smart you are, you can generally accomplish more through collaboration. I guess I'm stating the obvious.

Even though he was innately really good at math, it is true that he largely ignored it throughout university. So when it came time for him to invent general relativity, he had to catch up on the math and learn a whole lot of stuff that he was supposed to already know. At least that's how I remember the story going.

[lovejuice]

What kind of position do you have? Just a teaching contract, or are you doing research too?

I don't have a set date for my defense, but it'll probably be at the end of March or beginning of April. It was supposed to be at the beginning of January, but my girlfriend-related semi-breakdown delayed everything for a few months. As far as I know, only one person in the recent past has failed their defense here, and I'm pretty sure my supervisor wouldn't let me fail, so I'm not too worried about actually failing. But I am deathly worried about not being able to properly answer any questions, given how much I've forgotten and how bad I am at oral exams. My Master's defense was agonizing because one of the examiners asked me to give an intuitive explanation of a bunch of things using Newtonian mechanics, and I couldn't remember at all how to do it.

just a teaching contract.

and i fail my first master's defence. the question is kinda mean though. it's taken from a material briefly talked about in class.

phd defense, i think, is kinda different. it's about your own work, so you are supposed to be the one who knows the topic best. in fact, think of it this way, you are about to educate a bunch of simpletons who might only by chance ask some penetrating questions.

[Melville]

just a teaching contract.

and i fail my first master's defence. the question is kinda mean though. it's taken from a material briefly talked about in class.

phd defense, i think, is kinda different. it's about your own work, so you are supposed to be the one who knows the topic best. in fact, think of it this way, you are about to educate a bunch of simpletons who might only by chance ask some penetrating problems.

Oh, in Canada the Master's defense is also about your own work. That was part of what made it so awful. The examiner wanted me to explain a feature of some graphs I had made, and like a year earlier I had actually written down exactly how to explain that feature. But by the time I got to my defense, I had completely forgotten ever having thought about it, and I fumbled around for like twenty minutes as the examiner tried to lead me toward the answer.

Did you do your Master's in the U.S., or in Thailand?

[Winston*]

What is the secret to personal happiness?

[lovejuice]

Oh, in Canada the Master's defense is also about your own work. That was part of what made it so awful. The examiner wanted me to explain a feature of some graphs I had made, and like a year earlier I had actually written down exactly how to explain that feature. But by the time I got to my defense, I had completely forgotten ever having thought about it, and I fumbled around for like twenty minutes as the examiner tried to lead me toward the answer.

Did you do your Master's in the U.S., or in Thailand?

my master is in the u.s., at the same university as my phd.

[Melville]

What is the secret to personal happiness?

You're asking me this? I'm the guy with the depressed Peanuts avatar. Whatever I do, you should do the opposite.

[Melville]

my master is in the u.s., at the same university as my phd.

Oh, someone from the U.S. told me that they got their Master's just by checking a box on a form when they were one year into their PhD. Sounds like your university was a bit tougher!

[Winston*]

You're asking me this? I'm the guy with the depressed Peanuts avatar. Whatever I do, you should do the opposite.

So I should have a Garfield avatar?

[Melville]

So I should have a Garfield avatar?

Bad taste is the secret to happiness! Why didn't I think of it before?!

[Winston*]

Bad taste is the secret to happiness! Why didn't I think of it before?!

Joking aside, in my experience people with bad taste do tend to seem happier than people with good taste.

[Melville]

Joking aside, in my experience people with bad taste do tend to seem happier than people with good taste.

:lol: Even when you put joking aside, you're funny. You're like Seinfeld.

[Qrazy]

Working with a mathematician doesn't suggest he was bad at math; it just wasn't his focus of study, so he knew less than a mathematician. Also, no matter how smart you are, you can generally accomplish more through collaboration. I guess I'm stating the obvious.

Even though he was innately really good at math, it is true that he largely ignored it throughout university. So when it came time for him to invent general relativity, he had to catch up on the math and learn a whole lot of stuff that he was supposed to already know. At least that's how I remember the story going.

Yeah I just meant the way it was told to me suggested he wasn't great at very advanced math. That's all I meant.

[Melville]

Yeah I just meant the way it was told to me suggested he wasn't great at very advanced math. That's all I meant.

Yeah, don't mind me. I was just rambling.

[Qrazy]

Does the plot to Primer hold together well in the eyes of a physicist? Because I have a friend who's getting a statistics masters who says it doesn't hold together, and that he doesn't like the film because 'he's smart'. Now I could understand disliking the film for dramatic reasons but I want to prove the bastard wrong on the conceptual/narrative level.

[bac0n]

You'll appreciate this: my father in law is a high energy physicist at Rice who spends a significant amount of time when he's not teaching working on the Hadron Collider in Geneva. He's been going there for periods of months at a time for at least ten years. Pretty much started going there right after the big collider in Texas lost its funding mid-project and was abandoned (he's still sore about that whole affair).

Anywho, he recently had to get a pacemaker put in his heart, which means he can't go into certain sections of the thing due to the magnetism stopping the pacemaker and therefor killing him. :cry: