$$a_c = \frac{v^2}{r}$$
where:
- \(a_c\) is the centripetal acceleration
- \(v\) is the tangential velocity
- \(r\) is the radius of rotation
Setting the centripetal acceleration equal to 9.8 m/s² and solving for the tangential velocity, we get:
$$v = \sqrt{a_c \cdot r} = \sqrt{9.8 \text{ m/s}^2 \cdot 110 \text{ m}} = 33.20 \text{ m/s}$$
The frequency of rotation is then given by:
$$f = \frac{v}{2\pi r} = \frac{33.20 \text{ m/s}}{2\pi \cdot 110 \text{ m}} = 0.1514 \text{ Hz}$$
Therefore, the space station must rotate at a frequency of approximately 0.1514 Hz to simulate gravity.
