Question

A space station is designed in the shape of a large, hollow donut that is uniformly rotating. The outer radius of the station is 350 m.
1. With what period must the station rotate so that a person sitting on the outer wall experiences "artificial gravity," i.e. an acceleration of 9.8 m/s^2.
2. What is the total outer circumference of the space station?
3. What is the time period of the rotation needed to create, "artificial gravity"?

Answer 1

Answer:

37.5492141859 seconds

2199.11485751 m

37.5492141859 seconds

Explanation:

$\omega$ = Angular speed

r = Radius = 350 m

Acceleration is given by

$a=\omega^2r\\\Rightarrow \omega=\sqrt{\dfrac{a}{r}}\\\Rightarrow \omega=\sqrt{\dfrac{9.8}{350}}\\\Rightarrow \omega=0.167332005307\ rad/s$

Circumference is given by

$C=2\pi r\\\Rightarrow C=2\pi \times 350\\\Rightarrow C=2199.11485751\ m$

The outer circumference is 2199.11485751 m

Velocity is given by

$v=\omega r\\\Rightarrow v=0.16733200530\times 350\\\Rightarrow v=58.566201855\ m/s$

Time period is given by

$T=\dfrac{C}{v}\\\Rightarrow T=\dfrac{2199.11485751}{58.566201855}\\\Rightarrow T=37.5492141859\ s$

The time period of rotation is 37.5492141859 seconds