# Search results

1. ### Review article on astrophysical collapse to a black hole?

@bcrowell - I cannot say anything about the WP conformal diagram (it looks flat out wrong at first glance, but I'll get back to you). As for the diagram in #3, it is common practice to draw the center as a vertical line (since the center is supposed to be timelike). But if you actually perform a...
2. ### Volume of a segment of a sphere

I'm not sure what is part of Calculus II (Non-US bachelors, sorry). But in any case, if using Cartesian coordinates, having your origin at the top of the spherical cap (the north pole of the sphere) gives the bounds as x = 0 to r, y = 0 to r and z = 0 to -h, with the constraint that x2 + y2 + z2...
3. ### Volume of a segment of a sphere

The integration (whose bounds you are speaking of, presumably) would be considerably simpler if done in spherical polar coordinates.
4. ### Inclined plane and velocity

Magnitude is the absolute value, so, yes, it will always be increasing. If your answer was "it depends on relativity, being as its a vector quantity (i.e. up can be negative or down can be negative)", it's absolutely right. But if instead your answer was "it depends on relativity, being as its...
5. ### Inclined plane and velocity

Yes, that is correct. It's possible that your teacher was thinking about the magnitude of the velocity (also known as speed) which does increase as the object starts falling downwards.
6. ### ReIndexing a Series(non-infinite)

Define a new variable, say, j. How should j and k be related so that j goes from 1 to 6 when k goes from 3 to 8?
7. ### Velocity, Speed, and Time question

The boldface part is not right. What you have in the first line is V_{1} = \frac{1}{T_{1}-10} - 4.5 and the second line doesn't agree with this. It should read \frac{1}{T_{1}} = \frac{1}{T_{1}-10} - 4.5
8. ### Velocity, Speed, and Time question

Yes, that is correct. I think instead of ft/s, you should stick with miles per hour. Then, you will have two equations in two variables! Do you see it?
9. ### Velocity, Speed, and Time question

Yes, here you can use velocity and speed interchangeably. Notice how the question says "When you increase your speed by 4.5 mi/h" ... it means V2 = V1 + 4.5. How do the equations look now?
10. ### Velocity, Speed, and Time question

Look at the line I have boldfaced. The question says the speed increases by 4.5 mph, but you're increasing your distance D by 4.5 :eek:
11. ### Back and forward orbit [around gravitating objects]

Ah! That's enlightening. Can you draw the forces on the "object" and the "tube", possibly in two separate figures (to avoid confusion)?
12. ### Back and forward orbit [around gravitating objects]

Trying to understand the point you're making - are you suggesting a levitating mechanism using magnetic fields?
13. ### Black Hole Firewalls

It seems a popular assumption -- "Consider a black hole that forms from collapse of some pure state" (quoted from the AMPS paper). I don't see an obvious reason for this though. Can someone explain this or direct me to one?
14. ### Gravitational force problem: finding r

Step 0: G\frac{m_{earth}m_{spacecraft}}{r^2} = G\frac{m_{moon}m_{spacecraft}}{(r_{earth-moon}-r)^2} Step 1: \frac{(r_{earth-moon}-r)^2}{r^2} = G\frac{m_{moon}m_{spacecraft}}{Gm_{earth}m_{spacecraft}} Step 2: \frac{(r_{earth-moon}-r)}{r} =...
15. ### Gravitational force problem: finding r

Exchange LHS numerator and RHS denominator. Take square root. Do you see it now?
16. ### Spin expectation value of singlet state from two axes

I believe they are trying to tell you to have both S_1 and S_2 in the same basis, i.e, either choose S_1 to lie along z-axis and S_2 to lie theta away from it, or choose S_2 to lie along z-axis and S_1 to lie -theta away from it. Since they already chose the first of these options, the hint is...
17. ### Spin expectation value of singlet state from two axes

Yes, but you need to be careful about the sign, whether it is cos(θ) or -cos(θ), since the question says -"makes an angle θ down with the z axis".
18. ### Probability of picking a ball randomly from a group of balls

Since the order (in which balls are picked) matters, should instead be 10P2.
19. ### Spin expectation value of singlet state from two axes

Start by writing S1 and S2 in terms of the pauli matrices.

That's why.
21. ### Charge distribution

I think E should be -1000 <some units>?
22. ### Charge distribution

That's what you have find. You know the other two quantities in the equation.
23. ### Charge distribution

Your intuition(?) is correct here. One of the ways to produce a constant electric field is to have two very long charged plates (or, sitting in the middle of two charged plates placed very close to each other). The charge density on each plate to produce such an electric field is given by your...
24. ### Charge distribution

Yes! I'm not sure what you're saying. solve for potential? q value?
25. ### Charge distribution

Yes! If you were to draw the electric field lines, they would be equally spaced parallel lines, parallel to the z axis, pointing from negative to positive direction (or positive to negative, I'm not very sure). And no problem!
26. ### Charge distribution

Which equation are you referring to? For this question, the answer is independent of the values of x and y, so should be fine at x=0=y.
27. ### Charge distribution

Near wherever you found that expression of radial electric field, should be an expression for electric field in cartesian coordinates. If not, Wikipedia goes in detail about gradients in different coordinates system. If that article is too loud, here is gradient in the three-dimensional...
28. ### Charge distribution

Yes, with a slight modification. Your electric potential is written in cartesian coordinates, so it'll be easier to have the gradient (and the electric field) in cartesian coordinates also.
29. ### Charge distribution

How are electric field (the thing you want) related to electric potential (the thing you have)? Before I give details, I'll give a short answer: Electric field is the negative gradient of electric potential. You can find the definition of gradient in case you don't know it, in your...
30. ### Blocks, Pulley, Ropes, and Tension

Your confusion is justified. I was not doing the calculation correctly. But the idea is right. Your professor has explained it mathematically already, my earlier post (below) explained it in English. I will try to explain it more clearly later tonight (unless you figure out that 4a_{10} =...