MDJH

Not sure whether to post this here or in the physics board, but I will post it in both for now. I have been falling severely behind in physical oceanography and optical physics. I got an exam on the former in 6 days, an exam on the latter in 11, and I would appreciate suggestions for advice on cramming either of them, especially on where to go for online tutorials. (I have found that MathTV sometimes helped save my neck in math cramming.)

I meant to link to it in the original post. Yeah, I multiplied f by pi and by r, but forgot to multiply by 2. That's a pretty big mistake. I suppose I should remove and replace the comment, then.

So basically I posted the following analysis as a comment on this cat video on youtube. "At about 2 minutes in, the fan circles 4 times in 5 seconds. That's 0.8 cycles per second. If we assume the cat's spinning an average distance of a metre from the centre of the fan, that means it's moving at 2.5 metres per second. (v=2*pi*f*r) Also, the circular acceleration would be (v*v)/r, which would mean a velocity change of 6.25 metres per second every second. And so, to the cat, the pull of the rope probably feels like two thirds of the pull of gravity." What say you, Science Forums? Is my analysis valid?

So I was thinking about the idea that light is pulled by gravity... if my understanding (the analogy of light in an accelerating elevator being treated as equivalent to light accelerating due to a force acting on it) is close enough to accurate my logic here should work. Ok, so basically energy is proportional to the product of mass and the square of the speed of light; this resembles the formula for centripetal force, which is proportional to the product of mass and the square of the speed of light, except also divided by the radius of the circle. So according to this logic, the centripetal force that pulls on a photon of light would be proportional to the ratio dividing the energy of the photon by the radius of a hypothetical circle it would be spinning in. This in turn suggests that said radius would be proportional to frequency of the photon, and inversely proportional to the gravitational force. Therefore, how sharp the bending of the light is depends not only on the gravity, but also on how low-frequency the light is. Would I be correct in assuming, therefore, that given approximately equal gravitational forces on each, a longer-wavelength photon would be more easily pulled in by gravity than a shorter-wavelength photon would? Is this why morning/evening sunlight is safer than early-afternoon sunlight?

This fall I plan on doing a physics course which uses Mathematica; more specifically, a mechanics course involving differential equations. Some, but not many, of the computers on campus have Mathematica installed on them, so if I were to use Mathematica outside of class time, I would need to either have access to those computers, or to have access to Mathematica at home. I do not plan on buying the actual program, (I have not completely ruled that out though) but I have heard that they offer a trial version that lasts two weeks; if I start now this should give me time to familiarize myself with Mathematica before the semester starts, making that physics course a little bit easier. This raises a couple questions: 1. Is the windows version of Mathematica enough like the mac version that practicing with one can help me use the other? 2. Is it best to practice Mathematica BEFORE the semester starts, or to wait until the semester DOES start so that I will be able to practice it AFTER classes for the first couple of weeks? (Or to wait until the middle of the semester, or near the end of it, etc...)

Let's say someone were holding an object (like a pencil) at a position away from the centre of mass, such that it would rotate from the gravitational torque if held still. Would there be a way to spin it (as in, about an external axis, while the line from the centre of mass to the pivot is in the same direction as the radius) such that the torque from the centripetal acceleration would just cancel out the gravitational torque?

Ok, so with electricity we have a charged particle creating an electric field, wherein a test charge further from a field-generating particle has a higher potential energy than a test charge closer to it, and so far this is analogous to gravity, in which case we have an object creating a gravitational field, and a test mass further from it has a higher potential energy than a test mass closer to it. In electricity, the test charge's ratio of potential energy to charge is known as electric potential. In gravity, I assume that analogous to this would be the ratio of gravitational potential energy to mass for a test mass, which would be the product of the gravitational constant and the distance from the centre of the source of the gravitational field. Would I be correct in assuming this? Furthermore, this suggests that the gravitational equivalent of voltage would be the difference in the gravitational potential over a distance, and hence would be proportional to whatever difference there would be in gravitational constant and whatever difference there would be in distance from the centre... but since gravitational constant itself is a function of distance from the centre, would it be redundant to include?

Seeing as how the extent to which we could stop it is already in dispute, I would think it would be more practical to try to adapt to it instead.

But would both motions tend to come to a stop at the same time, or at different times?

Ok, so supposedly white light is a combination of red, green, and blue light... but programs like MS Paint treat it like the amount of light goes from 0 to 255; in theory, could brightness of light be infinite? If so, would that imply that brightness of the components would be infinite? If so, then, would a better representation of light be a 3-dimensional graph, wherein one axis represents the intensity of red light, another the intensity of green light, another the intensity of blue light... and based on the intensity values for these three component colours, a position in 3-space on the graph would represent a particular colour, so as for colour to be seen as a linear combination of red, green, and blue light?

Ok, so first off, angular momentum doesn't need to involve rotational motion, and a particle can have "angular momentum" with respect to an axis if it is moving in a straight line that doesn't pass through the axis, right? Also, if the particle had a constant speed and constant mass, then moving along the axis, its angle with respect to the axis would be perpendicular when the distance TO the radius is the lowest... does this imply that the angular momentum of such a particle would be constant? Also, as for the angular momentum of something thrown into the air... let's say we had a water bottle that was filled part way. It was thrown into the air such that its plane of rotation was parallel to the long end of the bottle. While the bottle would be rotating, the water itself would be moving from one side to the other, and flowing along the edge on the way. Would the moment of inertia in such a case be constant or changing, and as such, would the angular velocity (assuming angular momentum is constant; neglecting influence of air friction) itself be a function of time while the bottle is in the air? And another thing, presumably air friction would act to slow down a rotating object, since air molecules are constantly in random motion and the number of collisions with air molecular will be higher in the direction of motion than away from it, right? And if an object were rotating AND translating, would friction stop both rotation and translation at the same time, or could it stop one before stopping the other?

So supposedly angular momentum of a system is conserved, right? Well, consider this video: If, hypothetically, the cat jumped while the roomba was rotating, would the cat be spinning at an angular velocity equal to whatever the angular velocity of the rotating roomba was when the cat jumped?

I wasn't saying it was CENSORED. Again, the concern is that the influence of the dairy industry might be part of the reason milk is even considered a health food in the first place.

Who's "we"? From my recollection of the article, it argues that some of the medical community HAS noticed, and that the influence of the dairy industry tends to suppress such findings. If you're referring to the general public, how on Earth is the average person supposed to know if something everyone consumes, that they're told is healthy, is a major contributing factor in common diseases?

Are you suggesting that the pharmaceutical industry deliberately avoids curing this disease to keep type 1 diabetics like myself dependent on insulin? If so what proof do you have? And as for diabetes research being underfunded, Marat, do you mean in comparison to other diseases, or disease research in general to the war on drugs?

I'm guessing it was that my initial uv term was supposed to be x*Ln(2x+1) as opposed to just Ln(2x+1) itself?

Fair enough. Let's say M represents mass, A represents acceleration, G represents gravitational accelration, U represents frictional coefficient, (same for both objects) and Fg, Fn and Ff represent gravitational, normal, and frictional forces respectively. Each term will be followed by a number that refers to the object. For example, assume object 1 has k times as much mass as object 2. Therefore, M1 = k*M2 Per object, Fg and Fn cancel out, hence A = (Ff / M) for each object. However, Ff = U*Fn, which is mathematically equivalent to Ff = U*Fg. Seeing as how Fg = M*G, we can assume that (Ff1 = U*M1*G) and (Ff2 = U*M2*G) Therefore, A1 = (U*M1*G)/(M1) and A2 = (U*M2*G)/(M2) Therefore, because mass cancels out in this case, the differences in mass cancel, and they therefore accelerate at the same rate, thus take equally long to stop. Did I miss anything?

It obviously isn't making people violently ill immediately. But that's not what's being alleged. What's being alleged is that it has long-term links to diseases like cancer and heart disease. Obviously the effects of this aren't going to be immediate, and I don't think it would necessarily be apparent, to the individuals affected, that the milk contributed to it. Milk having massive health hazards wouldn't necessarily imply people would stop drinking it; smoking has massive health hazards and people still smoke. Of course, that may seem like a false equivalence. We are told that milk is good for you and cigarettes are bad for you; the former is consumed for belief in its benefits, the latter is consumed initially out of curiosity and later out of addiction. However, the point remains; you can't assume something has no health hazards just because people consume it. With the quantity of milk sold and drank everyday, it's hard to tell which diseases it may or may not contribute to, because so many diseases have such uncertain causes. But this isn't a reason to assume milk is safe either. ... Oh, and Cuthber, the reasons are given in that video and in the article.

A math professor of mine was recommending that I go over integration techniques before doing courses involving differential equations. Since I plan on doing at least 3 such courses in the fall, (comp. mechanics, classical mechanics, and diff. eq. itself) I need to catch up on this stuff. So, I was doing some integration by parts practice problems, and I've run into trouble already. One such problem was to find the indefinite integral of LN(2x+1)dx with respect to x. So I set up u = LN(2x+1) and dv = dx, implying v = x and du = 2/(2x+1) Using the formula INT(u)dv = uv-INT(v)du, this yielded LN(2x+1)-INT(2/(2x+1))dx So for the integral within an integral, I used parts again. u = 1/(2x+1) and dv = 2dx implies du = -2dx/((2x+1)^2) and v = 2x Using the same formula, this yielded (2x)/(2x+1)-INT((2xdx)/(4x^2+4x+1)) So I tried a w-substitution. If w=4x^2+4x+1, then dw=(8x+4)dx; if it were just 8xdx I could substitute it, but that +4 part makes it seem like it would be mathematically improper. What did I do wrong?

Let's say two objects of unequal masses were accelerated to the same velocity on separate flat, horizontal surfaces with the same coefficient of kinetic friction. Assume neither object was lifted off the ground and that neither went through a surface or over its edge. Which object would be the first to come to a stop? My tentative guess for this is that they'd come to a stop at the same time. Here's why I guess that. The forces on each object include forces of gravity, friction, and the normal force; force of gravity would be directly proportional to mass, normal force would be identical to force of gravity (given the lack of vertical motion) and friction would be the product of normal force and the coefficient of kinetic friction. Since friction is the only unbalanced force, it would be the only one responsible for acceleration of the object. Friction would be proportional to normal force, which is equal to gravitational force, which is proportional to mass. Therefore, frictional force would be, by extension, proportional to mass. However, acceleration would be given by the ratio of force divided by mass. Since frictional force is proportional to mass, the ratio of frictional force divided by mass would cancel out any differences in mass regardless of the actual mass of the object. Therefore, without knowing the difference in mass, one can safely conclude they take equally long to stop. Did I miss anything? o.o

What do you mean, "no apparent ill effects?" What is your basis for this?

... I see. Well, now I know. In any case, are there any other feasible ways of removing water from the planet? EDIT: Or of storing them in such a way as not to go back into the ocean? Such as sucking it out of the ocean and storing it in some closed container?

I notice that if I hold something in front of but somewhere between my eyes, even something in the middle will be further displaced from the center of my field of vision (assuming that's what it's caused) from closing one eye than from closing the other. Why is that?

Or somewhere between the two? One concern related to climate change is the notion that the melting ice caps would cause rising ocean levels to flood coastal communities. This is used as a reason to cut back on fossil fuel emissions, but there's also some uncertainty as to whether or not such cutting back would stop this problem. So why not address the global flooding issue more directly with a container of some sort? More specifically, my idea was that a large quantity of whatever material was practical for this (if any) would be formed into a gigantic container, filled with ocean water, and then tied to a space shuttle (or maybe a series of space shuttles) and carried through the atmosphere into space and released. This way, the water would go up but WOULDN'T have to come back down. I guess if it was a good idea someeone else would have thought of it. I guess the question now is what are the exact problems with that?

Although I'm used to hearing from doctors and nutritionists about milk being good for you, I've come across some almost convincing arguments for the idea that it isn't. Here's an article, though it's a bit long: http://www.notmilk.com/kradjian.html And for those who don't want to bother with the article, here's a video: It's a bit disturbing to think that even nutritionists would be misinformed on this subject; but the arguments for why they would be sound somewhat plausible. As a type 1 diabetic, I hope they find out what's causing this disease, and if it really is milk, I hope the diary industry gets punished for it.