Question

14. The design for a rotating spacecraft below consists of two rings. The outer ring with a radius of 30 m holds the living quarters and mimics the surface gravity of Earth, approximately 9.80 m/s'. The inner ring is designed to help the astronauts become accustom to the surface gravity of a new planet: 5.35 m/s. Calculate the spacecraft's period of rotation for the outer ring.​

Answer 1

Answer:

$T= 11.0003$s

Explanation:

From the question we are told that

The outer ring with a radius of 30 m

inner Gravity Approximately 9.80 m/s'

Outer Gravity Approximately 5.35 m/s.

Generally  the equation for centripetal force is given mathematically as

Centripetal acceleration enables Rotation therefore?

     $\omega ^2 r =Angular\ acc$

Considering the outer ring,

 $\omega ^2 r = 9.8$

  $\omega ^2= \frac{9.8}{30}$

 $\omega = \sqrt{\frac{9.8}{30}}$

 $\omega= 0.571 rad/s$

Therefore solving for  Period T

Generally the equation for solving Period T is mathematically given as

 $T= \frac{2\pi}{\omega}$

 $T= \frac{2\pi}{0.571 rad/s}$

 $T= 11.0003$s