Kevin S. Huang

2014: Problem 20

Topic: Rigid Bodies
Concepts: Angular kinematics, Artificial gravity, Rotational Newton’s 2nd law

Solution:

Setting the centripetal acceleration equal to $g$ , we have

a_c=\omega^2R=g

so the space station needs to be rotating at angular velocity

\omega=\sqrt{\frac{g}{R}}

By Newton’s 2nd law,

\tau=2TR=I\alpha

Since we have a ring, $I=MR^2$ so

2TR=MR^2\alpha

\alpha=\frac{2T}{MR}

From kinematics,

\omega=\alpha t

The rockets need to fired for time

t=\frac{\omega}{\alpha}=\frac{MR}{2T}\sqrt{\frac{g}{R}}=\frac{M}{2T}\sqrt{gR}

so the answer is B.