Artificial Gravity - Answer Key

TIP:
Some students may prefer to calculate the answers using the equation for centripetal acceleration (since this gives a more precise result).

1. The period of rotation for 1.0g, if the radius of rotation is 50m.
   approximately 14.5 +/-0.5 seconds (from the graph) [or 14.2 seconds if you have calculated the centripetal force].

2. The period of rotation for 0.5g if the radius of rotation of 50m.
   approximately 20.0+/-0.2 seconds (from the graph) [or 20.1 seconds if you have calculated the centripetal force].

3. The maximum rotational period for a structure whose rotational radius is 100m.
   approximately 16.0+/-.5 seconds (from the graph). Note that if the rockets which control the "spin-up" rate should malfunction, and rotation rate begin to increase at an uncontrolled rate, there is a danger that the spacecraft will disintegrate through structural failure.

4. The change in rotational period to increase from 0.5g to 1.0g if the rotational radius is 150m.
   The rotation period for 0.5g is about 34.7s and for 1.0g it is about 24.6 seconds. To increase the centripetal force from 0.5g to 1.0g means that the rotational period must decrease by 10.1 seconds.

5. The decrease in the period of rotation from 1g to structural failure for spacecraft having a 60m rotational radius.
   at 1g the period is approximately 16.0+/-0.5 seconds (from the graph), the period required for structural failure is about 12.5+/-0.5 seconds (from the graph). Therefore, a decrease in the rotational period of approximately 4 seconds will lead to structural failure.