Comparisons between the Chinese and US education systems seem to be coming up a lot recently in the news thanks to the rapid growth in China. However, it would be nice if they stuck to per capita numbers, as some of the absolute numbers seem to be misleading. At least this story seems to be better and discusses things like graduation rates which are more relative, unlike some other stories that seem to be more about people being scared that China now grants more college degrees than the US. That shouldn't be too surprising for a country that has more than four times the population.
Any frequency with a clean ratio to the camera frame rate should do something interesting, within some limits. If you went with half the frequency, 12 Hz, you could see something more like this (alternating between the two curves each frame), and at a third the frequency, 8 Hz, you could get something like this (cycling over each curve, for a three frame cycle). If you doubled the frequency to 48 Hz, you could get something that looks the same frozen in time, but with twice as many peaks and troughs to the wave. Same goes with higher multiples in principle. Non-integer ratios may work, such as 32 Hz looking like a squished version of the 8 Hz one.
There were a bunch of "could"s and "may"s in there though, because in the end, the pattern may become too messy to be seen due to the thickness of the water (e.g. take one of the linked graphs and imagine the lines becoming really thick), it starting to break up into droplets, or issues with consistency. And for the lower frequencies and ratios that produce a cycling of frames, the brain will pretty quickly interpret cycling more than 2 or 3 frames as smooth motion.
I would do this myself some weekend to double check I am thinking clearly about it... but my old camera does only maybe 0.2 FPS depending on how fast I can push the button and wait for it to focus.
Formal math is rarely open to interpretation (ZF vs. ZFC aside...), however, a communication about math is, especially depending on the care/forethought put into making things clear. Informal math can be a different story, and there are plenty of "paradoxes" and "controversies" that amount to arguments on the internet, potentially from loose definitions and/or intuition, that have no actual question or uncertainty in answer in formal math.
There is an ISO standard for brewing tea and for what number to assign in a database for a person's sex (the actual English+French standard is 24 pages long... with ~2 paragraphs of standard, and the rest boiler plate). A standard for use in mathematical writing becomes less surprising at some point.
Wouldn't being a software programmer be at odds with being a mathematician though? At least in all the languages I know, the answer from typing "6/2*(1+2)" would be 9 (except Scheme without an infix macro... because it would probably complain 1 is not a function). Which would be different than what I would expect if I saw that in a math paper.
And it only takes one end, either writer or reader, to realize there is more than one convention. Ideally the writer should be aware and write things such that it is not ambiguous (unless trying to start arguments...). But even if not, the reader can still realize it is not written clearly. Or at the very least, seeing an obelus in use is a red-flag, as it is rarely used beyond the arithmetic level. Its use suggest the writer is not likely following any strict writing convention, as the symbol is avoided when possible in many settings (and apparently is against ISO standards for use in mathematical expressions, as I just learned).
This is just what it comes down to, is poor communication because it is ambiguous or not clearly written. Maybe there is a specific context where it is more clear, with specific conventions, but not when presented like this.
To me at least and the conventions I've seen used in papers, the use of no symbol for multiplication is odd when done with numbers, and usually a small, middle dot is used to make it clearer when using numbers and just parentheses. And the use of an obelus doesn't help, when inline text seems to use slashes typically. Then with the slash, the convention and how it kind of looks is to work out the numerator and denominator first, then divide (in physics and math papers at least... as opposed to say most programming languages) . But when you need to make it clear, you use a solidus or vinculum.
Although of course professionals get it wrong sometimes. At least if it looks wrong or unclear in a paper, you can work out what they intended from context. But I've had to contact a paper's author before because they didn't make division clear once, and context wasn't enough. Not to mention use of footnotes on inline equations, which I've seen in actual use before the recent xkcd comic covered that. In the end, you just have to be really careful when you choose to use inline equations to avoid confusion or difficulty reading.
If things haven't changed much and I remember correctly, a lot of portable drills use universal motors. These are motors that are called universal because they can run off of both AC and DC power, but are still used in DC only setups like portable tools because they are cheap to make and have some other nice properties. The unfortunate problem is that the field coils require power for it to function as an efficient motor/generator.
A generator is basically a spinning coil in a magnetic field, so that the amount of the magnetic field going through the coil changes with time, ultimately driving a current. A motor does the opposite, using the a current to force the loop to change its position in the magnetic field. Hence, in either case an external magnetic field is needed. For motors, you have the added option of using the incoming electric current to make an electromagnet to create that field. So when the current goes away, there is no field. If you try turning the rotor, without a field, it won't do anything and can't make a generator out of it...
However, in the real world, usually turning the current off leaves a residual magnetic field because of the iron used. This is enough to jump start the process in some generators (others use a battery to help provide an initial field, or use permanent magnets). So you can get it to act like a generator a bit, but depending on how it is wired, and what is connected to, it may produce far less power than a purpose built generator. Universal motors for example, could be particular bad depending on what you hook it up to, as field coils are in series connection, so whatever current is flowing out would be the current to run that needed electromagnet. If the output draws not much current, then the generator would be rather inefficient compared so something that uses the same amount of current as the drill does when running.
tl; dr: That kind of motor makes a really inefficient generator. I would almost be curious if it would be easier to assemble a more efficient one yourself from wire, scraps of metal and permanent magnets for the same amount of effort used here.
I didn't know those things had an actual name. I had seen examples of them in science catalogs for years, although they are expensive enough to typically be found only in university demo collections. And at that level, someone in the department might end up making their own custom one.
In particular, I had come across this page which shows a range of motions possible if you had a giant version of one of those tubes. I've used one of the images near the end in talks before as an example of a magnetic mirror motion, a topic important to some fusion plasmas and to behavior of plasmas near the Earth too. Unfortunately that seems to be another topic that could use a better intro level explanation somewhere on the web (assuming there isn't one I haven't found yet), although one could easily spend a whole hour long lecture trying to explain all of the motions seen in just the second to last image on that one page.
Unfortunately, to throw a one pound brick hard enough, so that you have enough time to deal with two other one pound bricks in the same way, takes at least three pounds of force.
The most relevant force in such cases is Lorentz force. In particular, it is mainly the second half dealing with the magnetic field's effect on charged particles, as typically the electric fields within the plasma are small because the plasma is mostly neutral and a good conductor. The plasma consist of a soup of both positive and negative charges all intermixed, so over any macroscopic distance it looks neutral. In fact, if you attempt to create an electric field by adding charge, the plasma will tend to rearrange to block that out (e.g. if you add a positive charge, it will pull a bunch of electrons closer to it, and at a distance, beyond a few millimeters for the solar corona, there will be no net charge seen). So Coulomb's law isn't typically useful over large distances in that particular kind of plasma, although does still get used over very short distances, e.g. working out how collisions between the particles influence things. And gravity would still be relevant here too, even if the magnetic fields strongly constrain the motion. The Wikipedia article on guiding center talks a bit about what happens when you have both a magnetic field and other forces, although I realize neither article I linked has a particularly simple introduction and I don't know of a better site at the moment.
And the real fun starts with more macroscopic effects that can change the magnetic fields and flows together. E.g. too much current in the plasma gives the Kink instability or too much flow causes the firehose instability, and you get wiggles and structure forming along the flows down the field lines.
Magnetic fields cause loose charge particles to go in circles perpendicular to the field while not applying any forces along the field. The result it is very difficult for them to cross field lines, but very easy to go along the field lines. Although positive and negative particles will go in circles in the opposite direction, the movement along the field lines works the same for both, where they both easily spread out from just pressure.
So if you have heating in the center of the loop, you can keep pushing plasma out of both ends. Although loops on the surface of the sun also have a lot of structure you can't easily see in such videos, due to some of the plasma around them being too cold to light up as much or to the same colors that are being looked at in such videos, so that is another source of material and flow.
So while it is not in the spirit of such brain teasers and it is already known clowns violate the laws of physics with their little cars, I found thinking about the answer to the clown juggling the bricks a bit amusing:
Assuming you have a bridge that fails at exactly 150 pounds of force, and that we can ignore that when walking you create forces on the ground greater than your weight (maybe the clown is riding an ultra-light weight unicycle), you still need a force to throw a brick in the air. If you have 2 pounds of force to work with, you can fling a one pound brick upward with the same acceleration as it would normally fall down with, which means no matter how high you throw, it would spend as much time in your hands as in the air (and would require long, long arms to throw really high). So with perfect coordination and timing, you could juggle two such bricks, but would not have any spare time or force to throw a third.
Now this ignores air resistance, as for a dense gold brick, it would be pretty small effect, and symmetry of the brick means it would be about the same on both the way up and down. Although if one were to hammer it into a flat sheet (stopping before reaching gold leaf... as for 1 lb that would be a square 40 ft to a side), you could fold it into something like a paper airplane though that can be thrown up quickly, but takes a long time to fall. But if you are going to do that, you can easily just make the gold into a wire long enough such that less than half of it is on the bridge at any given time while dragging behind you, assuming it doesn't just fly like a kite in a breeze.
My preferred solution though: Rip the sign off the bridge and hope that the sign weighed more than a pound.
There were a bunch of "could"s and "may"s in there though, because in the end, the pattern may become too messy to be seen due to the thickness of the water (e.g. take one of the linked graphs and imagine the lines becoming really thick), it starting to break up into droplets, or issues with consistency. And for the lower frequencies and ratios that produce a cycling of frames, the brain will pretty quickly interpret cycling more than 2 or 3 frames as smooth motion.
I would do this myself some weekend to double check I am thinking clearly about it... but my old camera does only maybe 0.2 FPS depending on how fast I can push the button and wait for it to focus.
To me at least and the conventions I've seen used in papers, the use of no symbol for multiplication is odd when done with numbers, and usually a small, middle dot is used to make it clearer when using numbers and just parentheses. And the use of an obelus doesn't help, when inline text seems to use slashes typically. Then with the slash, the convention and how it kind of looks is to work out the numerator and denominator first, then divide (in physics and math papers at least... as opposed to say most programming languages) . But when you need to make it clear, you use a solidus or vinculum.
Although of course professionals get it wrong sometimes. At least if it looks wrong or unclear in a paper, you can work out what they intended from context. But I've had to contact a paper's author before because they didn't make division clear once, and context wasn't enough. Not to mention use of footnotes on inline equations, which I've seen in actual use before the recent xkcd comic covered that. In the end, you just have to be really careful when you choose to use inline equations to avoid confusion or difficulty reading.
A generator is basically a spinning coil in a magnetic field, so that the amount of the magnetic field going through the coil changes with time, ultimately driving a current. A motor does the opposite, using the a current to force the loop to change its position in the magnetic field. Hence, in either case an external magnetic field is needed. For motors, you have the added option of using the incoming electric current to make an electromagnet to create that field. So when the current goes away, there is no field. If you try turning the rotor, without a field, it won't do anything and can't make a generator out of it...
However, in the real world, usually turning the current off leaves a residual magnetic field because of the iron used. This is enough to jump start the process in some generators (others use a battery to help provide an initial field, or use permanent magnets). So you can get it to act like a generator a bit, but depending on how it is wired, and what is connected to, it may produce far less power than a purpose built generator. Universal motors for example, could be particular bad depending on what you hook it up to, as field coils are in series connection, so whatever current is flowing out would be the current to run that needed electromagnet. If the output draws not much current, then the generator would be rather inefficient compared so something that uses the same amount of current as the drill does when running.
tl; dr: That kind of motor makes a really inefficient generator. I would almost be curious if it would be easier to assemble a more efficient one yourself from wire, scraps of metal and permanent magnets for the same amount of effort used here.
In particular, I had come across this page which shows a range of motions possible if you had a giant version of one of those tubes. I've used one of the images near the end in talks before as an example of a magnetic mirror motion, a topic important to some fusion plasmas and to behavior of plasmas near the Earth too. Unfortunately that seems to be another topic that could use a better intro level explanation somewhere on the web (assuming there isn't one I haven't found yet), although one could easily spend a whole hour long lecture trying to explain all of the motions seen in just the second to last image on that one page.
And the real fun starts with more macroscopic effects that can change the magnetic fields and flows together. E.g. too much current in the plasma gives the Kink instability or too much flow causes the firehose instability, and you get wiggles and structure forming along the flows down the field lines.
So if you have heating in the center of the loop, you can keep pushing plasma out of both ends. Although loops on the surface of the sun also have a lot of structure you can't easily see in such videos, due to some of the plasma around them being too cold to light up as much or to the same colors that are being looked at in such videos, so that is another source of material and flow.
Assuming you have a bridge that fails at exactly 150 pounds of force, and that we can ignore that when walking you create forces on the ground greater than your weight (maybe the clown is riding an ultra-light weight unicycle), you still need a force to throw a brick in the air. If you have 2 pounds of force to work with, you can fling a one pound brick upward with the same acceleration as it would normally fall down with, which means no matter how high you throw, it would spend as much time in your hands as in the air (and would require long, long arms to throw really high). So with perfect coordination and timing, you could juggle two such bricks, but would not have any spare time or force to throw a third.
Now this ignores air resistance, as for a dense gold brick, it would be pretty small effect, and symmetry of the brick means it would be about the same on both the way up and down. Although if one were to hammer it into a flat sheet (stopping before reaching gold leaf... as for 1 lb that would be a square 40 ft to a side), you could fold it into something like a paper airplane though that can be thrown up quickly, but takes a long time to fall. But if you are going to do that, you can easily just make the gold into a wire long enough such that less than half of it is on the bridge at any given time while dragging behind you, assuming it doesn't just fly like a kite in a breeze.
My preferred solution though: Rip the sign off the bridge and hope that the sign weighed more than a pound.