Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.
Then, one day, the captain fires rockets which accelerate the station at alpha = 0.02 rad/s^2 for t = 10 sec.
What is the centripetal acceleration at the outer rim after the engines have fired?
Answer: The original centripetal acceleration is
a(centripetal) = 9.8 m/s^2 = R * omega^2
Therefore, the initial angular velocity is
9.8 m/s^2
omega = sqrt(---------) = 0.443 rad/s
50 m
When the captain fires the engines, he increases the angular
velocity to
omega = 0.443 rad/s + (0.02 rad/s^2) * (10 s)
= 0.443 rad/s + 0.20 rad/s
= 0.643 rad/s
So the centripetal acceleration on the rim is now
a(centripetal) = R * omega^2
= (50 m) * (0.643 rad/s)^2
= 20.7 m/s^2
Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.