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

`T= 11.0003`s

Step-by-step 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= (9.8)/(30)`

`\omega = \sqrt{(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= (2\pi)/(\omega)`

`T= (2\pi)/(0.571 rad/s)`

`T= 11.0003`s