Question

You have designed a space station that rotates on its axis in order to produce " artificial gravity." The space station has tree levels consisting of rings connected to spokes that rotate about a single axis as shown in the figure. The outer ring has a radius of 245 m.

a. what must the angular velocity of the space station be to simulate the acceleration due to gravity on Earth's surface on the outer ring of the space station?

b. What must be the radius of the middle ring of the space station if the centripetal acceleration equals the acceleration due to gravity on the surface of Mars( one-third that a Earth's surface)?

c. What must should be the radius of the inner ring of the space station if the centripetal acceleration equals the acceleration due to gravity on the surface of the Moon(one-sixth that at Earth's surface)?

d. Initially after construction, the space station will not be rotating. To spin up the station small, constant thrust rockets are attached to the rim of the outer ring of the station and provide thrust in a direction perpendicular to the spokes of the station. If the rockets operate constantly for 10 hours, what is the angular acceleration of the space station?

e. What is the tangential acceleration of the a point on the rim of the under ring?

245 m

Answer 1

g = 9.81 m/s² - R= 245 metre w²R = 9.81 - w * 0.200 rad[sec J 2.45 b) Now w?r= 9.81 R = 9.81 x 245 3 x 9-81 E 81.67 metre c) wära 9.91 6 8 : 9-81 x 245 6x9-81 2 40.83 metre D) 0-20-0 x= wf-Wi time TOX3600 = 5.56 x10-6 rad /secz E) tangential acceleration =Ra = 245 x 5.56 X10-6 = 1-36 x 10-3 m/s2