This might be hard to understand but:  Let’s say you measure a partical and it has a spin of clockwise. If you stop measuring it then remeasure it, would it have a 50/50 random chance at changing its spin? Or would it continue to have the clockwise spin?
121521
Yeah, I haven't quite understood, or been told, what happens to, for example an electron and its wavefunction, when you stop to measure it.  I mean, an electron has a wave function describing its position and so on in the region of space it is confined. When I measure it, I get an output, and the wavefunction collapses - as far as I understand. But then, when I stop measuring, the electron has not been "destroyed" has it? So does it resume its original wavefunction, and continue as nothing has happened, or have I totally misunderstood something? :)
56110
One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't believe that they provide as much insight as a mechanical explanation would.  The  Cedric provided looks similar to a diagram that I saw in my physics textbook. This diagram illustrates precession nicely, but doesn't explain why the top doesn't fall. Since the angular acceleration is always tangential, I would expect that the top should spiral outwards until it falls to the ground. However, the diagram seems to indicate that the top should be precessing in a circle, not a spiral. Another reason I am not satisfied with this explanation is that the calculation is apparently limited to situations where: "the spin angular velocity $\omega$ is much greater than the precession angular velocity $\omega_P$". The calculation gives no explanation of why this is not the case.
115404
I am having trouble understanding how centripetal force works intuitively.  This is my claim.  When I have a mass strapped on a string and spin it around, I feel the mass pulling my hand. So, I want to say that the mass is trying to move away from the center of the circle, and yet centripetal force makes it move in a circle, i.e, centripetal acceleration towards the center.  Similarly, when I am driving a car and making a curve, I feel being pushed away from the center of the curvature rather than towards it.  I am having so much trouble with these types of problems because of this counter intuitive concept.  Can someone help me out?
43266
I thought of this question lately, but I'm not satisfied with the answer I got:  If I flip a coin 100 times, what is the probability that I will get a streak of at least ten of the same side?  The way I thought of solving it was just: $\left(90 \times 0.5 ^ 9\right) = 0.0879$, but this has to be wrong because, for the probability of getting a streak of at least 4 in the same scenario, it yields: $\left(96 \times 0.5 ^ 3\right) = 12$, which obviously doesn't make sense.
103136
I have $3$ coins, $1$ coin has $2$ heads (HH), 1 coin has $2$ tails (TT), $1$ coin has $1$ head and $1$ tail (HT). I toss the coin, it fells on my hand, and the side i see is a tail. What's the chance that the other side is also a tail?  I got this as a teaser from a friend, possible from , as you can see he is insisting on 1/2 as not being the correct answer, I got 1/3 as my answer, am I right?
67921
I gave my friend  as a brainteaser; while her attempted solution didn't work, it raised an interesting question.  I flip a fair coin repeatedly and record the results.  I stop as soon as the number of heads is equal to twice the number of tails (for example, I will stop after seeing HHT or THTHHH or TTTHHHHHH).  What's the probability that I never stop?  I've tried to just compute the answer directly, but the terms got ugly pretty quickly.  I'm hoping for a hint towards a slick solution, but I will keep trying to brute force an answer in the meantime.
99022
Griffiths says that you can have only 1 well defined component of the angular momentum because of the uncertainty principle. From the uncertainty principle, we get that  $$ \sigma_{L_x}\sigma_{L_y} \geq \frac{\hbar}{2}|\langle L_z\rangle | $$  If we know $L_z$, can't we make $\sigma_{L_x}$ as small as possible while letting the deviation in the $y$ component get bigger, essentially making it so that we know 2 components?  Also from the uncertainty principle,  $$ \sigma_{L_y}\sigma_{L_z} \geq \frac{\hbar}{2}|\langle L_x\rangle | $$  So if we know the $z$ component, that means its deviation is zero, making the right hand side $\langle L_x \rangle$ zero as well?
39036
"An event less frequent in the long run is likely to happen before a more frequent event!"  How can I show that THTH is more likely to turn up before HTHH with a probability of  9/14, even though waiting time of THTH is 20 and HTHH, 18!  I would be very thankful if you could show me the way of  calculating the probability of turning up earlier,   and the waiting time. Thank you!
59055
Suppose y>x.   What is the probability that the smaller segment of the piece initially split into length y is bigger than the bigger segment initially split into length x?  I ran a simulation and got roughly 47.7% chance but cannot show this analytically.
28324
A two-sided coin has just been minted with two different sides (heads and tails). It has never been flipped before. Basic understanding of probability suggests that the probability of flipping heads is .5 and tails is .5. Unexpectedly, you flip the coin a very large number of times and it always lands on heads. Is the probability of flipping heads/tails still .5 each? Or has it changed in favor of tails because the probability should tend to .5 heads and .5 tails as you approach an infinite number of trials?  I understand that flipping coins is generally a stochastic process, but does that change at all if you see a large number of trials bias to one side?
36835
I have a d20 that seems to be, well, remarkably lucky.*  How can I determine whether it's really just luck, or whether the die is in fact unfairly biased?  *) Well, I don't, really.  This is actually a spin-off from , which is specifically about determining whether a die is loaded.  This one is intended as a more general question about how to detect any kind of bias in dice, since we apparently don't have one yet.  I've posted my own answer below, but feel free to add more.
89301
I have little knowledge of probability and have recently been thinking of a math problem I am sure you guys could answer  If for example I tossed a coin ten times and got all heads, would the odds of the next coin toss beeing heads be 50 50 or s very low as the odds of getting 11 in a row is tiny?   Thanks
79779
Suppose I'm on a non rotating planet. I have two identical, perfect watches. I synchronize them. Then I throw one of them into the air and catch it. Does the one I throw into the air gain or lose time with respect to the one I was holding?
116307
Two discs mounted on different thin, lightweight rods oriented through their centres are made to rotate about their axes seperately such that the angular momentum of the two about their respective axes is same in both magnitude and direction. When both are brought in contact, they stop due to force of friction. Why is the angular momentum not conserved about their axes in this case?(Was positive before contact, but zero after the process completes, no external force present either)
122047
Is there anything that can be said about how many attempts it will take to correctly guess a random number out of 1000 numbers? If the number wouldn't change the probability would just increase every guess, giving in the end a probability of 1.  If the number changes every guess tough, you just have a 1/1000th chance everytime. Can it be calculated how many attempts it would probably take, on average?  (I'm sorry, i'm not very skilled in probability maths)
10667
In general relativity, we assume that the connection is torsion-free. In some alternate theories, like Einstein-Cartan theory, we consider connections with torsion.   According to , torsion can be measured through the precession of spins, but this requires understanding spinors in GR. Is there a way to directly measure torsion without using spin, ideally through a simple mechanical system? (I don't care if this is an impractical experimental test, I just want intuition for what the torsion tensor means physically.)
115460
Suppose a beam of particles is prepared with spin in the $+z$ direction (e.g. by a Stern-Gerlach apparatus).  Suppose this beam then enters a Stern-Gerlach apparatus with orientation $\theta$ relative to $+z$.  Quantum Mechanics predicts that with probability $\cos^2(\theta/2)$ a particle will be deflected in the $+\theta$ direction, and with probability $\sin^2(\theta/2)$ a particle will be deflected in the $-\theta$ direction.    I have not been able to find any published experimental tests of this prediction for arbitrary values of $\theta$.  If you know of any, please provide the appropriate citation.