2) In this situation, is there any way of determining whether you are in such a spacestation or on Earth?
Anyway, Einstein notwithstanding, there actually is a way to differentiate between gravitational acceleration and things such as fake centrifugal gravity and linear acceleration due to a rocket, or some such. Namely, the gravitational field around a massive body follows a gradient, which can be measured with precise enough instruments. Linear acceleration has no such gradient, while fake centrifugal gravity has a different gradient. (This doesn't actually contradict relativity since we're cheating by making certain assumptions and measuring at multiple points.)
1) Assume that there's no physical limit (imposed by material strength, etc) to the size of the space station. To make the problem more difficult, let's build a space station which makes one full rotation in 24 hours, like Earth, and produces the same perceived gravity like that. Question: What would the radius of the space station have to be in order to achieve this (iow. it makes a full rotation in 24 hours and the perceived gravity at the outer edge is the same as on the surface of the Earth)?
2) In this situation, is there any way of determining whether you are in such a spacestation or on Earth?
Contrary to what you have said, a pendulum will NOT show rotation on a rotating space station, just as it will not show rotation at the earth's equator.
A wheel mounted vertically will rotate once per day on the space station and at earth's equator, but will not rotate at all at the north pole.
And a bonus one that some of you already know the answer to: You are a rude warrior that needs to pass two men. One always tells the truth and the other always lies. They wont let you pass until you have figured out who is the lying one. What is the fastest way to do so?
And a bonus one that some of you already know the answer to: You are a rude warrior that needs to pass two men. One always tells the truth and the other always lies. They wont let you pass until you have figured out who is the lying one. What is the fastest way to do so?
If you are in a small room, that gradient is probably so small that it would probably not be measurable (probably even physical limits come into play, such as the Planck length; although I'm not a physicist, so don't quote me on that).
I'm looking for a general expression for a combinatorics problem, it would be great if someone could provide an expression and a motivation for it. The problem is: You have n integers a(1), a(2), ..., a(n) where a(i)>=1 for all i, a(i)>=a(i-1) (i.e. they are sorted in descending order) and a(1)<=b where b is a positive integer. How many possible combinations of a(1),...,a(n) can you create? If possible, express it as an explicit function of n and b.
I'm looking for a general expression for a combinatorics problem, it would be great if someone could provide an expression and a motivation for it. The problem is: You have n integers a(1), a(2), ..., a(n) where a(i)>=1 for all i, a(i)>=a(i-1) (i.e. they are sorted in descending order) and a(1)<=b where b is a positive integer. How many possible combinations of a(1),...,a(n) can you create? If possible, express it as an explicit function of n and b.
Actually, it's not clear for me that there are other factors. :P I think you should continue ^^
