Question

Chilling with a bunch of space equipment you spot a spaceship. Starting up the wheel shaped spaceship that is 1km in diameter and designed to reach angular speed over 2 min as a cubic function of time that would generate a radial acceleration on the rim equal to Earth's gravity (9.81) after the 2 min start up.

Answer 1

The radial acceleration will be given by:

$a = \omega^2 r$

here, $\omega = \gamma t^3$

where $\gamma$ is a proportionality constant.

$a = \gamma^2 t^6r$

r = d/2 = 500 m

so,

a 500-2to

now, it is given that when t = 2 min = 2 x 60 = 120 seconds, a = 9.81 m/s²

=>

500%2(120) 9.81

=>

8.106 x 10-8rads

therefore, the expression for radial acceleration is:

.

a = 3.285 × 10-12