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Bignose physically rotated the vectors, rather than rotating the reference frames but leaving the vectors the unchanged. Those are very different concepts. Physically rotating the vectors: It takes a whole lot more work to lift a car vertically 100 meters than to roll it horizontally 100 meters. Rotating the reference frames: Whether you decide your x, y, and z unit vectors are directed north, east, and down versus east, north, and up versus whatever does not change the amount of work needed to push a car 100 meters north, but it sure does change the representation of the force vector needed to do accomplish that goal.

I gather that Gareth is assuming that since work can be positive or negative it cannot be a scalar. The answer is that the word "scalar" has multiple meanings, only one of which is a quantity with magnitude only. Another meaning: A vector can be multiplied by a scalar (google "algebra over a field"). For example, the vector (1,2,3) can be scaled by 2, yielding the vector (2,4,6) or by -2, yielding the vector (-2,-4,-6). Here a scalar is any real number, and that is the context in which work is a scalar. Note that for a complex vector space, complex numbers act as scalars. Physicists have yet another definition of scalar: Something that isn't changed by rotation of coordinates. A vector doesn't satisfy this, but work does.

A scalar is any real number, not a non-negative real number.

Whoa, whoa, whoa! Do not extrapolate on top of something that is already just a hypothesis. One billion years represents about 2/9 of the age of the Earth. The Moon moved from wherever it formed (and we do not know that) to where it is today over a period of 4.5 billion years. Well over 7/9 of that migration occurred during the first 7/9 of that 4.5 billion years because, as Mokele noted, the tidal recession of the Moon is not linear. Not even close. As I noted, tidal forces are inversely proportional to the cube of the separation distance.

I am so embarrassed: My representative. At least I had the rare opportunity to vote against him three times last year, twice in the primaries (he ran as a congresscritter and for President) and once in the general election. I used all three opportunities.

That is a 22 year old article you cited, Mokele. In this case it is the Nature article that is wrong, not the History Channel. The History Channel is merely reciting the currently favored hypothesis regarding the origin of the Moon -- the Giant Impact Hypothesis. In a nutshell, a large Mars-sized body collided with the recently-formed Earth about 4.5 billion years ago. The iron core of this body fell into the Earth while the mantle material rebounded into orbit. The Moon quickly coalesced from this ejected mantle material. The angular momentum inparted by the collision made the post-collision Earth day a mere 5 hours long. The Moon was a lot closer (a whole lot closer) to the Earth than it is now. Since tidal forces are inversely proportional to the cube of distance, a factor of 10 reduction in the Earth-Moon distance would yield tides 1000 times higher than present. Unlikely as it seems, this hypothesis is a lot less far-fetched than any other explanation. It explains lots of wierd characteristics of the Earth and the Moon: the Earth's rather large and the Moon's rather small iron cores; the common oxygen isotope ratios on the Earth and Moon; and the presence of potassium, rare earths, and phosphorus in some lunar rocks (google KREEP) that suggest the Moon was once largely molten. References (just a few; google "Giant Impact Hypothesis" for more): http://www.nature.com/nature/journal/v412/n6848/full/412708a0.html http://www.nature.com/nature/journal/v437/n7063/full/nature04129.html http://physicsworld.com/cws/article/news/17802 http://arxiv.org/abs/astro-ph/0405372 In this case, Mokele is reciting the currently favored hypothesis regarding the formation of life. Moreover, those huge tides in primordial times may well have helped life along rather than having hindered it. More references: http:// http://hal.archives-ouvertes.fr/docs/00/33/03/10/PDF/bg-2-97-2005.pdf http://arxiv.org/abs/astro-ph/0112399

As mentioned above, [math]W=F*d[/math] is a simplification of the concept of work. It assumes that the force is constant and that the displacement is a straight line path parallel to the force. How much work is done in making a 1 kg mass move 1 meter horizontally? The gravitational force acts on the mass throughout. Since [math]{\boldsymbol F}_g = m {\boldsymbol g} \approx m*9.81\,\text{m}/\text{s}^2[/math] downward, that simple formula suggests that the work done is about 9.81 joules. It is in fact zero. Why? The correct interpretation in this case is [math]W= {\boldsymbol F} \cdot {\boldsymbol d}[/math], where both the force and displacement are vectors. The work is identically zero in the above example since the displacement vector is normal to the force vector. If the path is not a straight line or if the force is not constant one must resort to the integral definition, [math]W=\oint {\boldsymbol F} \cdot d{\boldsymbol l}[/math].

Reference please, particularly regarding the claim of small arms fire. Also, please do not reference the canceled Mobile / Tactical High Energy Laser (M-THEL) Technology Demonstration Program. Blowing up a large object filled with explosives is one thing. Blowing up a bullet is quite another. Blowing up a chip of paint is yet another (you have to be able to see it, for one thing). Now imagine blowing up the hundred-plus thousand pieces of debris estimated to be in low Earth orbit. Blowing up a big chunk of space debris is in a way even more problematic. How do you vaporize it rather than just blowing it up and creating tens of thousands of pieces of debris that now must be dealt with individually? That said, a google search on "laser removal of space debris" yields a lot of hits. For example, http://books.google.com/books?hl=en&id=Lg3AxhNFtEoC&printsec=frontcover. The proponents of laser removal of space debris in my opinion vastly underrate the complexity of the problem and overrate the ability of lasers to solve the problem. These problems plague the high energy laser community in general, and are a big part of the reason that the M-THEL was canceled.

There is nothing that can be done about the existing space debris other than to let atmospheric drag slowly solve the problem for us. That debris is spread out amongst a wide variety of orbits. Collecting it somehow is an insurmountable problem. The long-term solution is to not let it accumulate in the first place. Vehicles must safe themselves at the end of their life by performing one last set of burns that either place them on a safe reentry trajectory or move them well out of harm's way. The Space Treaty suggests, but does not require, this treatment. Even then, some vehicles will (and do) fail. There will still be some accumulation of space debris.

The title of the thread ("formulas I should know") and the opening sentence of the OP ("hey, i want to be an aeronauticall engineer, and im just wondering if any one would be nice enough to type down any formulas i should know to help me out.") That is exactly why Bignose and I tried to steer him away from this idea. Cameron, read this page "What is Aerospace Engineering". Some highlights: Who are Aerospace Engineers? Aerospace Engineers are involved in all aspects of aeronautics (working with aircraft) and astronautics (working with spacecraft). They conduct research, and design and develop vehicles and systems for atmospheric and space environments. These engineers often specialize in one of many areas such as aerodynamics, propulsion, flight mechanics, orbital mechanics, fluids, structures, guidance & control, and computation. That final sentence lists several specialties within aerospace engineering. It is a very broad list, and it is not complete (navigation and rendezvous aren't on the list, for example). There is no way one person can be an expert in every single aspect of aerospace engineering. More from the UT web page : Recommended High School Preparation Courses The UT Aerospace Engineering Department likes to see completion of high school courses in the following subjects: Mathematics courses including: Algebra Geometry Trigonometry Mathematics Analysis Calculus [*]Computer Science [*]Natural Science courses including: Biology Chemistry Physics [*]English [*]History [*]Foreign Language Note that I highlighted English. I not only am an aerospace engineer (my specialties: orbital mechanics, guidance, navigation, rendezvous), I hire them -- and I don't hire them if they do not possess good communication skills, written and verbal.

That's putting it mildly. That didn't just sour the tone. It spoiled the whole works. Try to look at things from their perspective. The Republicans think they lost the election because (a) the economic collapse right before the election was just a case of incredibly bad timing, and (b) they lost their way in the last eight years. They admit they deviated from their roots from 2000 to 2008: They stopped being Republicans. In their mind, the 2008 defeat was a clear message that they had to return to their conservative roots. With this mindset, voting for the stimulus plan would have been hypocritical. Particularly so with Polosi's souring of the works.

Just a quick note before I go: It is much, much more important to understand concepts and to understand how equations are derived than to memorize random equations. Autistic savants are great at memorizing things but can't generalize because they don't understand what's in their heads. Geniuses can get by with very little memorization because they can derive things on the fly.

Read Shelly Taylor's own website. Read the paper that started this whole imbroglio. The links are right there in post #16. Quoting from her UCLA website, "This tend-and-befriend account of social responses to stress is the theoretical basis for our work. ... Our previous research suggests that oxytocin and endogenous opioid peptides are implicated in these responses, especially in women." Quoting from the 2000 paper, "We propose that human female responses to stress are not well characterized by fight-or-flight, as research has implicitly assumed, but rather are more typically characterized by a pattern we term 'tend-and-befriend.'" I am of the opinion "Vive la Différence." Men and women are a bit different, mentally and physically. Thank god for that. Usually. Exception granted for those occasions when my wife remembers one of my transgressions from 25 years ago.

The other way around, ParanoiA. Females are better than males. This is exactly the crap that the social scientists (Taylor et al) and even more so those who exaggerate/extrapolate from her writings claim: If women had been leading the banking institutions our country wouldn't be in the mess it is in now. Which is of course a pile of hogwash.

Not really. Laws are short and simple and are often in the form of a purely empirical relation expressed in terms of a single mathematical formula. Newton's second law of motion: [math]F=ma[/math]. Short, simple, without rationale. Newton's Principia was a theory that bound his laws of motion in a theoretical context. The same goes for modern theories. Planck's law, [math]I(\nu,T)=((2h\nu^3)/c^2)* 1/(e^{h\nu/(kT)}-1)[/math], and the Stefan-Boltzmann law, [math]j^* = (2\pi^5k^4)/(15c^2h^3)* T^4[/math], are simple empirical relationships. Planck developed the former as an empirical relationship. The theory of blackbody radiation ties these laws and other concepts together and gives meaning to the magical numbers that underly those empirical relationships. In a nutshell, theories are greater than laws.

Oh, really? Tend and Befriend In threatening times, people seek positive social relationships, because such contacts provide protection to maintain one’s own safety and that of one’s offspring. This tend-and-befriend account of social responses to stress is the theoretical basis for our work. Until recently, the biosocial mechanisms underlying human affiliative responses to stress have remained largely unknown. Our previous research suggests that oxytocin and endogenous opioid peptides are implicated in these responses, especially in women. This isn't some journalist mangling Shelly Taylor's words. This isn't even some other researcher mangling Shelly Taylor's words. These are Shelly Taylor's words, from http://taylorlab.psych.ucla.edu/research.htm. Need more? From SE Taylor, LC Klein, BP Lewis, TL Gruenewald, "Biobehavioral Responses to Stress in Females: Tend-and-Befriend, Not Fight-or-Flight" Pyschological Review, 2000, http://bbh.hhdev.psu.edu/labs/bbhsl/PDF%20files/taylor%20et%20al.%202000.pdf Survival depends on the ability to mount a successful response to threat. The human stress response has been characterized as fight-or-flight (Cannon, 1932) and has been represented as an essential mechanism in the survival process. We propose that human female responses to stress (as well as those of some animal species) are not well characterized by fight-or-flight, as research has implicitly assumed, but rather are more typically characterized by a pattern we term "tend-and-befriend." Specifically, we suggest that, by virtue of differential parental investment, female stress responses have selectively evolved to maximize the survival of self and offspring. We suggest that females respond to stress by nurturing offspring, exhibiting behaviors that protect them from harm and reduce neuroendocrine responses that may compromise offspring health (the tending pattern), and by befriending, namely, affiliating with social groups to reduce risk. We hypothesize and consider evidence from humans and other species to suggest that females create, maintain, and utilize these social groups, especially relations with other females, to manage stressful conditions. We suggest that female responses to stress may build on attachment-caregiving processes that downregulate sympathetic and hypothalamic-pituitary-adrenocortical (HPA) responses to stress. In support of this biobehavioral theory, we consider a large animal and human literature on neuroendocrine responses to stress, suggesting that the tend-and-befriend pattern may be oxytocin mediated and moderated by sex hormones and endogenous opioid peptide mechanisms. ================================= This is politically motivated pseudoscience, pure and simple. Find a study that suggests males are better than females in any way intellectually (e.g., the highest scoring males outscore the highest scoring females in math) and you will find article after article that attack that study as being biased, or just plain wrong. Continue to state that males (top males, not average) are better than females (top females, not average) at math and you may, as Larry Summers found out. lose your job. On the other hand, if you state the females, on average and in aggregate, are much better at leading everything from households to nations to the world, (a statement with much broader impact than being a better mathematician) and the politically correct audience will sing your praises.

ParanoiA: Correct me if I'm wrong. Mokele: I gather that the author ParanoiA was talking about was the author of the study (Lauren A. McCarthy, and by inference, Shelley Taylor), not the author of the unreferenced quote in the OP. Given the statements in that report (see ParanoiA's post), this has the look and feel of politically motivated pseudoscience.

Experiment: Throw a spider on your girlfriend/wife/whatever. (It's Friday the 13th, after all. You can make up for it tomorrow on Valentine's Day.)

Here is a nice (where is that tongue-in-cheek smiley?) piece of bipartisan legislation: The Fair Copyright in Research Works Act. It would remove restrictions on federally-funded research that requires researchers to make their publications publicly available (e.g. PubMed, arXiv). The galling title of the thread is a statement by Allan Adler, Association of American Publishers VP for government and legal affairs to the House Judiciary Committee last week. Some reading: http://paulcourant.net/2008/09/17/fair-copyright-in-research-works/ http://www.libraryjournal.com/article/CA6595774.html http://scienceblogs.com/gregladen/2009/02/open_access_the_time_to_act_is.php?utm_source=sbhomepage&utm_medium=link&utm_content=channellink Googling the Fair Copyright in Research Works Act results in a lot more hits, none of the favorable to the publishing industry. I made my opinion known by calling Adler's statement galling. Any other opinions?

You are wrong. The inertial mass is still Ma. You are getting into trouble by looking at things from the perspective of a non-inertial frame. A frame with origin at the center of object B is a non-inertial frame. The gravitational force acting on object A due to object B is [math]\frac {G M_b M_a}{r^2}[/math]. An inertial observer will see object B accelerating toward object A with an acceleration of [math]a_b = \frac {G M_b}{r^2}[/math]. This inertial observer will also see object A accelerating toward object B with an acceleration of [math]a_a = \frac {G M_a}{r^2}[/math]. The relative acceleration is indeed [math]a_{rel} = \frac {G (M_a+M_b)}{r^2}[/math]. So, who sees this acceleration? Answer: An observer fixed with respect to object A or with respect to object B. That observer is not in an inertial frame. ================================ Thread moved to pseudoscience.

Yep. http://nbcsports.msnbc.com/id/6437288/

There's a big difference between natural selection and artificial selection. Nature tends to select favorable mutations. We tend to select recessive mutations that in nature would be extremely disadvantageous: Wolves that don't mature properly (dogs), bovines with ridiculously large udders (milk cows), grasses that don't scatter their seeds properly (almost all grains, corn or maize being the worst).

This is Not Even Wrong. It is trash.

Yes.

You're mixing theories here. Gravity is a real force in Newtonian mechanics and causes an acceleration from the perspective of an inertial frame. Gravity is a pseudo-force in general relativity and does not cause an acceleration from the perspective of an inertial frame. An inertial frame in general relativity is a frame whose origin is free-falling with respect to the local gravity field. An object close to the origin of the frame (inertial frames do not have infinite extent in GR) that is in free-fall will not be measurably accelerating with respect to the inertial frame origin. You have to look at the object from the perspective of a non-inertial frame to see an acceleration. =========================================== To the OP: I realize that English is not your first language. The paper has quite a few grammar and wording errors that make the paper rather hard to read. I suggest you get the assistance of someone to help you in this regard. More importantly, your paper has a number of logical flaws. It is a purely classical, pre-relativistic description. We already know Newtonian mechanics is wrong on many fronts. Your paper starts on the wrong footing by assuming Newtonian mechanics as a foundation. Your understanding of the equivalence principle is fatally flawed. You get into trouble by erroneously treating a body-centered frame as an inertial frame. Newtonian mechanics strictly applies in inertial frames only. As soon as you go to non-inertial frames you have to add fictitious forces. None of this is new; physicists (particularly d'Alembert and Euler) developed the mathematics underlying non-inertial frames. The equivalence principle is one of the most accurately verified principles in all of physics.