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    Wood Angle Falls Faster Than Rubber Ball
    By Sascha Vongehr | January 10th 2011 12:15 AM | 35 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    The following is a neat little experiment whose result may be counterintuitive to some of those who embrace the “all bodies fall the same way inside earth’s gravity” ‘doctrine’ without quite understanding it.

    Remember, in old ages long ago people thought that a feather does not fall as fast to the ground as a cannon ball. Nowadays, people are so much smarter, well, at least they feel so much smarter, and they know that the feather only falls slower due to the air resistance. This has become somewhat of a 'doctrine' in the sense that many who 'know' it do actually not really understand the underlying reasons. In result, they are surprised by the nifty little experiment in the linked video: The wooden angle reaches the table long before the ball does not only because they start out a little different but also because the tip of the plank accelerates faster than the freely falling ball (See the golf tee? It Immediately separates from the ball and speeds downwards, leaving the ball behind.).

    It is a very simple set-up and a good idea for a project that can involve small children. Older ones may be able to calculate the required lengths of the wooden angle's arms and so on. If the video should not be embedded correctly, you may have to surf to it on the MIT website.

    And afterward: Who comes up with the shortest and most philosophical reason for why the ball ends up in the cup?

    CLARIFICATION: I am not interested in why the ball is in the cup but in the fact that the end of the arm accelerates more than the free falling ball although much of the force onto the wooden plank just presses on the joint (hinge). (This is necessary for the ball to land in the cup, so I formulated the question above that way, which has misled some readers. Sorry about that. This is really about that the tip accelerates faster, as is proven by the tee separating from the ball at once without dragging it to the side. Moreover, at larger starting angles, all this would not happen!)

    Comments

    socrates
    The center of mass of the plank is much closer to the table than the ball and so reaches the table much faster than the ball with the same acceleration, 9.81 m/s2. The plank, in addition to falling, is also rotating. The velocity of the edge of the plank (as opposed to the velocity of the center of mass of the plank) is greater because it is the sum of the velocity due to falling plus the velocity due to rotation.

    Nice demonstration, Sascha.
    Citizen Philosopher / Science Tutor
    Ladislav Kocbach
    Steve Donaldson has naturally explained the whole "paradox". The "philosophical one" could be: it is in fact the plank which is falling slower (because it falls shorter time), but because of extending the motions to rotations its end with the cup is moving faster. For us others - have you noticed the rope below which allows the plank to be rotated only so high that the ball is dropped exactly over the final position of the cup? Very nice MIT News Office!
    Is this thing perhaps made at  the MIT Toy Lab http://web.mit.edu/newsoffice/component/mitmultimedia/?&videoid=218 ?

    By the way, Sascha's link to the video above is broken now about 16:00 CET, it worked first time I looked, in the morning CET.
    socrates
    Ladislav, you are entirely correct to point out the further paradox that the center of mass of the plank is, on average, actually traveling even slower than the ball. The average velocity of the ball is 21/2 (i.e. the square root of 2, approximately 1.4) times the average velocity of the plank center of mass.

    However, as we both observed, the distance that the plank center of mass has to travel is just 1/2 the distance the ball has to travel and so the plank reaches the table sooner. (above I said it gets there "faster", but, it indeed, better to say it gets there "sooner". In everyday English we often say faster, when we mean sooner.)

    The actual difference in time is that the time the ball travels, Tb, is 21/2 times longer than the time the plank travels, Tp.
    Citizen Philosopher / Science Tutor
    Ladislav Kocbach
    Nearly ten days ago I asked about this video:
    Is this thing perhaps made at  the MIT Toy Lab http://web.mit.edu/newsoffice/component/mitmultimedia/?&videoid=169 ? - it means I wanted to ask that, but the link was to the original video. This link is correct. The error was caused by the MIT webserver keeping things sort of secret (it happily shows video 169 while showing in the address bar the number of the previous video (218 in our case)
    Look at the angle, if it is almost 90degree: Most of the force sits on the joint at the table and presses down. Because of this, the ball falls much faster than the end point of the wooden plank. Whatever teh angle, 80, 70, 60, there is always part of the force that just presses down on the joint and the plank can never fall as fast as the ball. The video is a fake!

    socrates
    Oh gosh, Mr. Strawman, why did you have to ruin my nice simple explanation! You are right that the angle makes a difference. You are not right to say the video is a fake. So you make me go through the more complicated analysis. Here goes:

    The problem with my original analysis was that I was assuming the center of mass of the plank could fall straight down. Of course this is not possible. It will in fact fall along the path of an arc since the plank is fixed at the hinge. Therefore, we need to analyze its motion in terms of rotational dynamics instead of linear equations of motion. So lets see what the torque on the plank is. Well it changes as it falls.

    Initially the torque is mgrsin(pi/4), where m is the mass of the plank, g acceleration due to gravity, and r the distance from the hinge to the center of mass. The final torque is simply mgr.

    The time required for the plank to "fall" through the angle, pi/4, will be given by the following equation:
                        theta = (1/2)(alpha)t2
    where theta is the angular displacement and alpha is the average angular acceleration. In our case theta is pi/4 (45 degrees). If we could determine the average acceleration, we could then find the time it took the plank to fall and compare that to the time it took the ball to fall.

    Well alpha equals the torque divided by the moment of inertia. The moment of inertia for a rotating rod is (1/3)mL2, where L is the length of the rod.  So the initial alpha is:
                    alpha1 = [mgrsin(pi/4)]/[(1/3)mL2]
    Note that L = 2r and m also appears in the numerator and denominator so we can simplify:
                    alpha1 = 3gsin(pi/4)/4r
    The final angular acceleration is given by:
                    alpha2 = mgr/(1/3)mL2 = 3g/4r

    We should probably use calculus here to find the average angular acceleration, but I will be lazy and use the approximation that the average is about half way between the initial and final accelerations (in truth the average acceleration will be closer to the faster final acceleration).
    So let's approximate the average angular acceleration as:
                    alpha = (alpha1 + alpha2)/2 = 3g[1 + sin(pi/4)]/8r

    Now let's find Tp, the time for the plank to rotate through an angle of pi/4:
                    theta = (1/2)(alpha)t2
    Therefore:        Tp = [2(pi/4)/alpha]1/2 = [2(pi/4)/(3g[1 + sin(pi/4)]/8r)]1/2
                                    = [16r(pi/4)/(3g[1+sin(pi/4)])]1/2

    Everything here is known except for r which depends of the length of the plank. That makes sense. The length of the plank will affect the time of fall for both the ball and the plank. The longer the plank the longer the fall.

    Now we just need to compare the plank's time to the ball's time. The ball is easier, because it falls straight down. The time for the ball to fall is given by:
                            Tb = [2h/g]1/2
    where h is the initial distance from the ball to the table. Of course, h depends on the initial angle and the length of the plank:
                            h = Lsin(pi/4) = 2rsin(pi/4)
    So let's see how long it takes the ball to fall:
                            Tb = [2(2rsin(pi/4))/g]1/2 = [4sin(pi/4)/g]1/2
    Now lets compare Tp to Tb by taking their ratio:
                            Tp/Tb = [16r(pi/4)/(3g[1 + sin(pi/4)])]1/2/[4rsin(pi/4)/g]1/2

    Simplifying we get:
                            Tp/Tb = [4(pi/4)/(3[1 + sin(pi/4)]sin(pi/4)]1/2
    If this ratio is less than one, then the time it takes for the plank to fall through the angle, pi/4, is less than the time for the ball to fall to the table. Putting in numbers we get:
                            Tp/Tb = .8675
    The plank does indeed reach the table before the ball.
    Citizen Philosopher / Science Tutor
    vongehr
    "Strawman, why did you have to ruin my nice simple explanation!"
    Because that is what Strawman is there for to begin with, muahahaha.

    Yours truly, Sascha (this time logged in properly)

    PS: The challenge was to come up with a SHORT, PHILOSOPHICAL explanation! Not sure whether your new comment is a promising entry. ;-)
    socrates
    Ha, ha, Sascha, you are toying with us, and I can tell that you are enjoying it. :-)

    Well in my own defense, I am reminded of what Niels Bohr once said about his own long-winded explanations. He said it was a simple consequence of the principle of complementarity that he could give either a simple, understandable explanation or one that was true, but not both at the same time. The simpler his explanation, the less true it would be and the truer his explanation the more difficult he would be to understand. Well, I can certainly sympathize with that.

    However, as I have said elsewhere, I do not completely agree with Niels Bohr on this. I have always thought that his obsession with complementarity was just an excuse to stop looking for deeper understanding. And so, I feel I must take up Sascha's challenge again and see if I can provide a SHORT, CLEAR AND TRUE explanation for the video. It will be similar to my first explanation, but will include the role of the angle. Here goes:

    The short and true explanation (without mathematical detail):
    The ball falls with a constant acceleration, g. The center of mass of the plank has a vertical acceleration that is a fraction of g, that depends on the angle, theta. When theta equals 45o, the vertical acceleration of the center of mass is in fact (1/2)g. The motion of the edge of the plank will always be twice as great as the motion of the center of mass, because it is twice the distance from the hinge. Therefore the edge of the plank will have an initial vertical acceleration of g, when the initial angle is 45o. As the angle approaches zero, the vertical acceleration of the center of mass approaches g, and the vertical acceleration of the edge of the plank approaches 2g. So we see that the acceleration of the edge of the plank is always greater than or equal to g and therefore the plank will reach the table sooner than the ball which has a constant acceleration of g.

    Bonus philosophical observations:
    When the initial angle is greater than 45o, the initial acceleration at the edge is less than g. We see this as a pole starts to fall over. At first the falling is very slow. However, when the pole reaches 45o, then all points past the center of mass will start to accelerate faster than g. Where does the extra force come from to give the mass beyond the center this greater acceleration? It comes from the intermolecular forces that hold the sold pole together. In fact, if the pole is made of weak material, you will see the pole break upwards once the pole passes the 45o angle. You may have seen this in films showing tall structures, such a old factory chimneys, falling over and breaking up when they pass the 45o angle.

    Bonus mathematical detail:
    How does the acceleration of the center of mass depend on theta? First let's find the tangential acceleration, at which also depends of theta. This is the component of g that is perpendicular to the plane of the plank.
                                at = g[cos(theta)]
    Now let's find the y component of the tangential acceleration. This will be the vertical acceleration of the center of mass at angle theta:
                                ay = at[cos(theta)] = g[cos2(theta)]
    If we now set theta to pi/4 (that is, 45o) we see
                                ay = g[(1/(21/2)]2 = g(1/2)
    If theta is greater that pi/4, then the acceleration of the center of mass will be less that g(1/2) and the acceleration at the edge will be less that g. That is why we must start with the plank at 45o.
    Citizen Philosopher / Science Tutor
    vongehr
    The short and true explanation (without mathematical detail):
    ... a fraction of g, that depends on the angle, theta. When theta equals 45o, the vertical
    acceleration of the center of mass is in fact (1/2)g. ...

    For a short and true explanation without mathematical detail it is again surprisingly long, not quite true, and has a lot of maths (especially implicit - not writing down the derivation does not make the core of the argument less mathematical). About the truth of the argument: did you check whether your method gives the correct difference between a homogeneous plank and one where all the mass is inside its COM? You hope that the energy that feeds into the rotation of the plank works out fine if you do it like this - what if your student is not equally optimistic? (There is a good reason the angle starts even lower than 45 degrees.)

    socrates
    Oh boy, isn't this a wonderful example of how science works - as an iterative process of making errors, submitting to reviews, discovering errors, correcting errors, doing more work, making more errors, more review, and so on, but in the long run, learning from mistakes and converging ever closer to "truth". Let's hope.

    Okay, I did leave out the rotational inertia (moment of inertia) in my third, "simpler", explanation. (It was included in my second long-winded explanation.) The initial vertical acceleration of the edge of the plank should be:
                        ay = (1.5)g[cos2(theta)] .....(not ay = (2)g[cos2(theta)] as I suggested above)

    So if we need the edge of the plank to accelerate faster than the ball from the very start, we need cos2(theta) to be 2/3, which means theta must be about 35 degrees, not 45 degrees.

    I hope that corrects my mathematical errors. Nevertheless, I take it you are looking for something much simpler than all this mathematical analysis.

    I think Helen is on the right track. The ball does start higher than the cup. The additional requirement is just that the tee and the cup both move to the left so the ball lands in the cup instead of landing on the tee. The tee and cup move to the left because they must travel in an arc and not straight down.

    Is that it, or is that now too simple?
    Citizen Philosopher / Science Tutor
    vongehr
    Nevertheless, I take it you are looking for something much simpler than all this mathematical analysis.
    I am looking for something convincing. What you provide is the very reason people do not trust scientists: Because they really cannot be trusted! They just believe they are correct and throw equations and titles or citations at us, but most of it turns out wrong after closer inspection. Are you sure you are right this time? What makes you so sure? Same sure-feeling as the first time ("true explanation")? Why should anybody believe you this time with that track record? Because you know how to write equations? You should know one thing and ponder its implications for your own philosophy and how you approach tutoring [as you claim you are philosopher and science tutor]: I never bothered to look at any of your equations! In fact, I do not care whether they are right or wrong. Maybe they are right, I don't have time to check, but you are still wrong.
    I think Helen is on the right track. The ball does start higher than the cup
    Sorry, I should have not mentioned the cup in the last question in the post (see my answer to Helen's comment above). The tee separates from the ball and arrives much earlier. The cup is a gimmick much like the white lab coat.
    socrates
    You should know one thing and ponder its implications for your own philosophy and how you approach tutoring [as you claim you are philosopher and science tutor]: I never bothered to look at any of your equations! In fact, I do not care whether they are right or wrong. Maybe they are right, I don't have time to check, but you are still wrong.
    You are starting to sound like a creationist (just teasing). I teach my students that when it comes to science, they should never trust philosophy alone. You need to do the math to check your thinking. Aristotle was one of the greatest philosophers that ever lived, but he was wrong about how and why things fall. How could he be so smart and so wrong? Because he did not do the math. We had to wait for Galileo for that.

    I agree with you that many people do not trust science, and that bothers me too. Most people are not as comfortable with math as scientists. Most people prefer a simple philosophical solution. That is why it is so easy to get so many to believe in creationism. It is easier to "understand" than some inflationary big bang theory with all that general relativity stuff.

    You are also right that it does not help win trust when people learn how science makes so many mistakes. People think science should not make mistakes. But science is supposed to make mistakes. That is an important part of the process. One should expect mistakes when one attempts to solve difficult problems. We should not be so afraid for our reputation that we stop attempting to solve difficult problems for fear of making a mistake. (I teach that to my students as well)

    So back to the plank. I already gave my simplest explanation in my first answer. The plank as a whole has a shorter distance to fall than the ball, as measured from the center of mass. The end of the plank moves faster than the center. It is true, as you point out, that some of the weight of the plank is initially held up by the hinge. However, at a certain angle (which I computed to be about 35 degrees) the shorter distance between the COM and the table will more than make up for the smaller initial downward force.

    [All of this assumes an honest experiment. There are many ways to "cheat". For instance, you could use a plank that had its center of mass closer to one end of the board than the other. You could also make the string elastic so that it would give the plank added acceleration when you let go. I am trusting that the video is not fake. It shouldn't be necessary to cheat. It is a more interesting problem when it is real.]
    Citizen Philosopher / Science Tutor
    vongehr
    I teach my students that when it comes to science, they should never trust philosophy alone. You need to do the math to check your thinking.
    But you trust the math without doing the philosophy, and that is much worse, as you have proven here in the comments. I teach my students to first think and do the maths after they know the solution.
    Most people prefer a simple philosophical solution. That is why it is so easy to get so many to believe in creationism. It is easier to "understand" than some inflationary big bang theory with all that general relativity stuff.
    Simple philosophical solution? If it is so simple, why have you not come up with a convincing one? You are completely wrong here. If I had to trust the mathematical treatment as it is developed today, I would neither trust evolution nor inflation. I know evolution is true and inflation extremely likely because of the philosophical underpinnings.

    You are also right that it does not help win trust when people learn how science makes so many mistakes. People think science should not make mistakes. But science is supposed to make mistakes.

    Science is not supposed to go ahead and hype preliminary results every time as "the true explanation" only to somewhat later go ahead and hype the now really true explanation. That is something you have done here with your math-before-thinking style and I am thankful for you to have done so, because it showcases the problem with science today very well indeed. Technicians that have learned some sort of method (maths, genetic sequencing, whatever) and go through the moves, some getting successful via publish-or-perish culture, nowhere in the whole procedure is scientific insight involved anymore. The result is rubbish that nobody can trust anymore.
    I already gave my simplest explanation in my first answer. The plank as a whole has a shorter distance to fall than the ball, ...
    If you stick with this, it is plainly a bad explanation. It is wrong at any angle if the mass of the plank should be all at the very end of it. If you have no argument but some maths that the layman cannot follow for that this turns around before all the mass is considered to be at the hinge instead, your explanation is not convincing in the way science should convince: By insight rather than by authority ('I can do math and you don't'). You do not yourself actually understand why the end of the plank falls down faster than free fall, and because of this, your maths cannot be trusted. Maths is just a language - it cannot make a wrong message true!
    socrates
    Science is not supposed to go ahead and hype preliminary results every time as "the true explanation" only to somewhat later go ahead and hype the now really true explanation. That is something you have done here with your math-before-thinking style and I am thankful for you to have done so, because it showcases the problem with science today very well indeed. Technicians that have learned some sort of method (maths, genetic sequencing, whatever) and go through the moves, some getting successful via publish-or-perish culture, nowhere in the whole procedure is scientific insight involved anymore. The result is rubbish that nobody can trust anymore.
    Ha, ha, Sascha, you are so funny. You seem to want to blame me for why people don't trust science. Well let's be clear. You are the scientist here, not I. It is your behavior that will reflect on science, for better or worse. I am just one of your readers who accepted your invitation to help solve this riddle. And after making an honest effort, all I get from you are insults. If you are concerned about the reputation of science, perhaps you should consider how it looks to your readers when you treat our honest efforts with disrespect.

    What is so hard for you to understand about my explanation? I don't think it is so hard to understand that a falling object, which is also rotating, will have different parts moving at different velocities relative to the ground. The leading edge will be moving downward faster than the center of mass and the trailing edge will move downward at a slower speed (in this case zero) than the center of mass. This is all very logical. I don't see why you have a problem with that.
    Citizen Philosopher / Science Tutor
    vongehr
    I am science but you are not??? You are the 'Science Tutor'!
    Sorry, but science is not about being friendly to each other to the extend to bury the truth, it is about the scientific method. Sorry if you may have lost your face along the way, but you did claim truth by putting up math in exactly such a way as it is done in many fields today and in exactly such a way as it should not be done. And I have thanked you for this. It does not make you a bad man, and I am afraid, given the state of science and who gets successful inside that structure, you are the scientist more than I.
    I don't blame you - I blame the wrong methods being used! People don't trust science. Because I insult a few readers once in a while or because people have found out too many times that scientists and their fake statistics cannot be trusted?
    What is so hard for you to understand about my explanation? I don't think it is so hard to understand that a falling object, which is also rotating, will have different parts moving at different velocities relative to the ground. The leading edge will be moving downward faster than the center of mass and the trailing edge will move downward at a slower speed (in this case zero) than the center of mass. This is all very logical. I don't see why you have a problem with that.
    Simple: no layman can grasp this as making clear that the edge is faster than the free falling ball. You could write the exact same for if the ball hit the ground first. You still have no explanation!

    [UPDATE: I just got an email ripping on me for being bad to Steve and Siju. Hey - I am sincerely sorry, OK. People like me on the Aspergers scale kind of have a problem seeing where people get pissed off. I was sincerely assuming they enjoy our playful forth and back ripping at each other, like blokes normally do (Siju: "Ok, I guess I'm a sucker for punishment"), so I am really surprised that it is 'snap' all of a sudden. Hey, if I try to destroy somebody in a discussion, that first of all means I take her seriously. If I did not like Steve, I would not give a moist rat's behind about whether he reconsiders his philosophy!]
    socrates
    Hey - I am sincerely sorry
    Apology accepted. Looking forward to hearing your answer to the riddle.
    Citizen Philosopher / Science Tutor
    Samshive
    Not really sure if an apology is necessary. 
    i dont know how i ended up here but this is cool. i dont know much about the math but the ball ends up the same distance from the bottom of the cup as it was at the start, so maybe the location of the cup is the center of mass? they both traveled the same distance in the same time. the end hit first because its out at the end of the arc and moves faster because it has to bottom at the same time as the center of mass? i dont know

    Errrm... the rubber ball will always hit the surface second because there's a golf tee and a big bit of wood in its way as it falls. :-)

    But yes, the video proves conclusively that if you combine the plank's lower centre of gravity with the low-ish angle and the well-oiled hinge, the integral of cos(theta) times F is always going to be the right jockey to back. Having said that, the height added by the golf tee seems to account for about 20% of the effect shown in the video making it perhaps not an entirely fair race, but what the hey. :-)

    Congratulations for the interesting problem! So interesting that I will give it a try:

    I will provide an explanation but first I would like to some considerations:

    The air resistance may play a role in here. If I could do the experiment I would detach the plank, put it on horizontal position with the rubber ball on the tee and let it fall to see if it arrives on the floor sooner than the rubber ball. If true it would suggest the rubber ball is facing more air resistance than the plank and explain at least part of the effect. A careful analysis of the video could show it too using a measure of velocities accelerations and a model of air resistance. Here I will suppose that air resistance although might playing a role here is legible for the explanation.

    Now I will focus on the plank. I the tip of the plank is really falling faster than the ball the energy to this increase is coming from somewhere. From where?? The plank being rotating must an important factor here.

    Lets conduct a thought experiment:

    1) All parts of the plank are being attracted by the same g force
    2) The plank is connected to the right and rotating
    3) Lets choose 2 points of the plank:
    Point A 50 centimeter to the left of its connection
    Point B 2 centimeter to the left of its connection
    4) As the plank is falling and rotating its angular velocity is equal over all points (Im ignoring that the plank is bending during the fall !!) but the linear speed is different and the tip of the plank is falling faster! (Greater arc due to a greater radius)
    5) Now lets consider the point B 2 cm from the connection. Suppose that plank is lifted and it is now 1 cm from the table. When it is released it should hit the table considerably faster than the point A that is 25 cm from the table! (same force acting and less distance to travel) But it is impossible because the plank is rotating and point A AND B MUST hit the table at the SAME TIME! It might mean that the kinetic energy from the points near the connection are transferring kinetic energy to the points near the tip! It may explain why it arrives faster than the ball.

    Using this I can construct a mathematical model showing how this transference occurs and the expected speed at the tip. I will not do that because such a model is only useful against real measurement and it is very easy build a model and claim it works if you don’t test it :)

    Thanks for reading my humble opinion!

    vongehr
    point A AND B MUST hit the table at the SAME TIME! It might mean that the kinetic energy from the points near the connection are transferring kinetic energy to the points near the tip!
    Yo - The best answer yet. You are on the right track!
    Using this I can construct a mathematical model showing
    No No No, pleeease not. Do not enter any maths. Maths messes up good physics. Just add one or two more considerations about having all the mass in the tip versus having it close to the hinge. No more maths allowed anymore in this thread. You are on the right track because you did not use any maths.
    I will Try :)

    1) The plank is connected to the right and rotating
    2) Lets choose 2 points of the plank:
    Point A 50 centimeter to the left of its connection
    Point B 2 centimeter to the left of its connection

    First supposing all mass is on Point B 2 centimeter to the left of its connection and 1 cm above the table. In this case the only force acting will be on this point and the plank will take time proportional to that of an object in free fall would take to travel that 1 cm (will travel on the circumference rather than a straight line).But as point A AND B MUST hit the table at the SAME TIME the Point A (50 centimeters to the left 25 above the table) must travel 25 times faster on average speed (same time 25 times more distance to travel).

    So, necessarily the tip of the plank (and therefore the whole plank)arrives on the table sooner than the ball because it has more kinetic energy than it would have without the hinge. This can be seen on the movie that the tee arrives sooner than the ball.

    The position of the cup will be the point on the plank that the ball arrives in free fall. Its position is a function of the angle the plank is left. An angle too acute the ball would not enter the cup (because the cup's height). The angle (and cup position) are chosen to give the effect of the ball entering the cup.

    If there is a point near the hinge that is slowed e the tip that is speeded up then there is a point in the midle that travel at the same average speed that a free falling body. This point will keep a constant distance from the ball during the fall.

    If this point is the middle of the plank it means that for a 45 degrees angle
    the average speed of the tip would be the double of the free falling body (double of the height traveled in the same time).This not appears to be the case on the video (air resistance or else?). So, the point that has the same average speed must be on the left of the middle(otherwise the tip would be much faster). Maybe it is a good point to put the cup :)

    trying to put simple:

    The hinge makes the whole plank touch the table at the same time. It slows down the points near the hinge and speeds up the points near the tip (otherwise a point almost on the hinge would make the tip of the plank fall almost instantaneously). It makes the plank hit the table faster than the ball. The angle and cups position are chosen to give the effect
    of the ball entering the cup.

    ok, so where looking for the laymans explanation. the center of mass of the plank is somewhere around the mid point. the midpoint of the plank will fall at the same rate as the ball. since the end of the plank is travelling a larger radius it is moving faster than the midpoint. the distance between the balls elevation in relation to some point along the board is the same at the top as it is when the plank hits bottom. This is somehow important because it doesnt appear to be the midpoint, so maybe being hinged moves the center of mass outward. i give up

    Hi Confused!
    Aren't you Sascha Vongehr are you?
    If you dont reveal yourself I will claim to have a true and final explanation! :)

    vongehr
    No, I only do such sock-puppetry either as "Straw-man" or as "Sock-puppet", afterward making clear I did so. No cover to bust.
    im just an electrician with an interest in physics, and i stumbled into this. Mike

    Here is a simple explanation:

    There is a vertical distance between the rubber ball and the cup. The cup was positioned in the plank to match the point when the ball will hit the table. When falling the vertical distance between the ball and the cup is constant so when the plank hit the table it has the same vertical distance from the ball that is in the begining. This happens because the ball and the cup fall with the same vertical speed although the cups total path is larger because the rotation of the plank.

    Ladislav Kocbach
    One picture is worth thousand words, and I have about 20 animated. They show snapshots of a simulation of this fascinating little problem. It looks like a video, but there are about 16 different snapshots taken of a running PHUN toy simulator (the engine of it is no toy, though, it is very efficient toy, based on a PhD in computer science / numerical mathematics).

    My little contribution (worth about 16 000 words, but much much shorter) is at our department local webserver (do not be afraid to click here, uib.no means University i Bergen, Norway) -
    http://web.ift.uib.no/AMOS/faster_fall/
    Picture no. 209 (you can stop and type it into the text field) shows clearly that your statements, dear
    Simple Mind (not verified) are not confirmed by computer simulations. The end of the plank arrives before the ball, and is ahead a much longer distance than the original length of the golf tee.

    The above addres contains links to the original MIT video, PHUN, and ALGODOO. I strongly recommend all the participants, as well as Sascha, to get PHUN for fun and understanding
    vongehr
    Fun, but I reject the idea that a simulation is better than the real thing. We can just pause or slow down the video and all that your simulation shows can be much better seen in the video without fearing somebody has introduced laws of nature of a parallel universe via 'too clever' coding.
    Especially, I reject your last statement about that these tools is what I need for understanding. I got the solution to the question by using my head, not video or simulation. If video/simulation do not confirm what logic tells me, they will be wrong. This is the attitude to take in the age of photoshop and video manipulation software.
    Ladislav Kocbach
    Dear Sascha, thank you for sharing this deep insight with us. Why do not we close all the supercomputers and ask you about the weekend weather? Your logical analysis will surely give us all the answers we really need.
    vongehr
    Ladislav, simulating complex systems is one thing, stupefying people by telling them effectively that they better do not think and just let a computer do the thinking is dangerous. There is absolutely no reason to use computers for this problem except if you want to ensure that your students do not develop critical thinking. If you look at my discussion, you will see that the maths fetishism made people get going into completely wrong directions although the problem is a trivial, linear system. The computer does something similar. So what do you charge me with? Is my criticism to be understood as doing science entirely without maths? Surely not.
    Ladislav Kocbach
    This is a sort of "complex system". Your "logical analysis" at the other post is not even wrong (just to keep the same level of discussion you practice both here and other places - I hope that Hank is not going to flood his keyboard this time).
    vongehr
    "not even wrong"

    You are welcome to contribute in a constructive manner and free to argue that your solution is wrong instead of not even wrong and thus constitutes superior didactic. Just screaming "bully" and giving me these troll comments won't cut it. In case you are not able to "keep the same level of discussion" I "practice both here and other places", maybe spending some time to understand the deeper issues that motivate the author can help.

    How a scientist can call a watertight proof using symmetries and extremal considerations "not even wrong" is beyond me. Not sure how you do your science, but at the cutting edge where I sometimes work, these are vital.

    BTW:

    By the end of sophomore year, 45 percent of students show no significant improvement in critical thinking, writing and complex reasoning, the Associated Press reports.
    Ladislav Kocbach
    Yes, I am really a bad man. I am even trying to steal your audience, I have put up this:
    Falling Faster Than Freefall - No, rotating faster than a free fall - and if it attracts discussion I will try to be nicer.

    When I talked about bullying the audience, I definitely did not refer to myself, as you preferred to understand. I referred for example to this ...  ... This is not philosophy - this is stuff teenagers come up with after smoking a bong. Technically that is not at your blog, but your tone at your blog resembles this very often. Critical thinking is not about criticizing people, as you definitely know.

    I was just trying to show you how people feel when you write as you write. I would not do it again on purpose.  Sorry, but my "attack" on you was purely "pedagogical".  But, with your permission, I will still claim that your "critical - logical - analysis" does not really cover the problem, I hope to clarify this later. It is simply not possible to discuss it fully without thinking about the rotation.

    Keep writing exciting articles, but please, less  "rose candies" in the future!  Thanks for exciting ideas!
    vongehr
    I do not see where your attack was pedagogical - they surely are not close to how I 'attack' as I out of principle use arguments that are on topic. I am still missing this from you. Now you say that somehow your explanation is better than my proof because it is about rotation. So I went to see with anticipation, but I could not find any explanation in your post at all.
    I will still claim that your "critical - logical - analysis" does not really cover the problem, I hope to clarify this later. It is simply not possible to discuss it fully without thinking about the rotation.
    Well maybe this means that you want to post an actual explanation later in another post, which is fine, but if you want to argue that my analysis does not really cover the problem (are you entirely sure you understand the problem my post is after???), I encourage you to go to the post where I presented the solution and tell us where (which step in the short proof exactly) is wrong. You will not find one.