Question

A space station of radius 20 m spins so that a person inside it has a sensation of artificial gravity when afloat in space. The rate of spln is chosen to attain. g= 9.8 ms-2. Calculate the length of the day as seen in the spacecraft through a wlndow.

Answer 1

Answer on Question #69223, Physics / Other

A space station of radius $20\,\mathrm{m}$ spins so that a person inside it has a sensation of artificial gravity when afloat in space. The rate of spin is chosen to attain $\mathrm{g} = 9.8\,\mathrm{ms}^{-2}$. Calculate the length of the day as seen in the spacecraft through a window.

Solution:

Occupants of the station would experience centripetal acceleration according to the following equation,

$$a = \frac{\omega^2}{r}$$

where $\omega$ is the angular velocity of the station, $r$ is its radius, and $a$ is linear acceleration at any point along its perimeter.

Thus,

$$\omega = \sqrt{a r} = \sqrt{9.8 \times 20} = 14\,\frac{\mathrm{rad}}{\mathrm{s}}$$

The length of day will be the period of rotation

$$T = \frac{2\pi}{\omega} = \frac{2\pi}{14} = 0.45\,\mathrm{s}$$

Answer: $0.45\,\mathrm{s}$

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