00:01
In this problem, we want to figure out the revolutions per minute to achieve the desired gravitational pull in space station.
00:07
So to do this, i'm going to write this form for the radial acceleration in terms of the period.
00:13
It's equal to 4 pi squared times r over t squared.
00:18
In this case, 1 over t is equal to the number of revolutions per second.
00:32
And so if i solve this for t, i get that t is equal to 2 .5.
00:38
By ton of square root of r over g.
00:45
And this is really the key equation in this problem.
00:49
We're given r is 800 meters, and in part a, we want the acceleration to be equal to g, which is how i solve for this.
01:00
I said a rad is equal to g, and then i solve for t to get this.
01:05
And so the g in this case, it's 9 .8, because we want to simulate to earth's gravity.
01:12
And so when we plug that in, i get that t is equal to 56 .77 seconds, which means that 1 over t is equal to 0 .076 revolutions per second.
01:27
Remember the interpretation, 1 over t is revolutions per second.
01:31
And so we need to convert this into revolutions per minute because that's what the problem is asking.
01:36
So to do that, i'm going to have seconds on the top to cancel these seconds, and then minutes on the bottom...