One problem for humans living in outer space is that they are apparently weightless. One way around this problem is to design a space station that spins about its center at a constant rate. This creates 'artificial gravity' at the outside rim of the station. (a) If the diameter of the space station is 800 m, how many revolutions per minute are needed for the 'artificial gravity' acceleration to be 9.80 m/s2?

Video transcript

Welcome back everybody. We are taking a look at the International Space station. Now, International space Station, which I'm gonna put right here is connected to this giant ring and this giant ring actually rotates in order to simulate Earth's gravity. Now we are told that the diameter of this ring is 109 m and we are tasked with finding the frequency of revolutions, revolutions per minute that the International space station must rotate in order to achieve that simulated gravity. So essentially saying that our centripetal acceleration will be equal to the acceleration of Earth's gravity, which is 9.8 m per second squared. What we know. A formula for centripetal acceleration is for I squared are over its period squared, rearranging some things here we get that T is equal to the square root of four pi squared are over our centripetal acceleration which we want to be 9.8, but we're looking for the frequency not the period. So the relation between these two is that the period is just the uh sorry, the reciprocal of frequency given by this equation right here. This gives us that our frequency is equal to the square root of our desired acceleration divided by four pi squared times r radius. So our radius is just gonna be one half of 109 is 54.5. Plugging this into our calculator. That our frequency is 1/ 0.675 seconds. And we need to convert this two revolutions per minute. So we are going to have that 1.1 divided by 0.675 seconds. I'm going to The second is on bottom. Sorry, I'm gonna multiply this by 60 seconds. Over one minute. These units cancel out. And we find our final answer that the ISS must rotate at a speed of . rpm corresponding to our final answer choice of C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.