[yumei]

How many kilometers would you have to go above the surface of the earth for your weight to decrease to half of what it was at the surface?

If a cylindrical space station 300 m in diameter is to spin about its central axis, at how many revolutions per minute rpm must it turn so that the outermost points have an acceleration equal to g?

*mods - you can move it if it's in the wrong section.

[tripperazn]

I'm not sure about the first problem, since I'm in Physics C and we only do mechanics first semester.

The second problem is essentially a circular motion problem. An "outermost point" can be simply thought of as a particle traveling in a circle as the space station spins with it's central axis. Since the problem doesn't involve mass at all. You want to use the equation (V^2)/R. V being velocity in m/s and R being radius in meters for this problem. The nature of circular motion is basically that the sum of the accelerations equals an acceleration vector towards the center of the circular path. In this case, there are no forces on the particle other than the spin, so you don't have to worry about summations. It's a simple equation involving one variable and 2 constants. You have g (9.8 m/s) is equal to (V^2) our variable divided by 150 meters (the radius).

9.8=(V^2)/150

Once you find the velocity, you must convert it into RPM. The RPM of the 300 meter diameter station is 300 pi. RPM is a measure of speed, which is a comparable quantity to velocity which you just solved for. Take the velocity that you solved for and multiply it by (60 sec)/(300 pi meters). That is the velocity needed to achieve such an acceleration in terms of RPM.

Hope that helps!

[yumei]

ooooooooooooooooh ! thank you ! ^^*