Question

A space station in the form of a large wheel, 283 m in diameter, rotates to provide an "artif icial gravity" of 9.5 m/s 2 for people located at the outer rim. What is the frequency of the rotational motion for the wheel to produce this effect? Answer in units of rev/min.

Answer 1

Answer:

The frequency of the rotational motion for the wheel to produce this effect is 2.473 rev/min.

Explanation:

Given that,

Acceleration = 9.5 m/s²

Diameter = 283 m

We need to calculate the frequency of the rotational motion for the wheel to produce this effect

Using formula of rotational frequency

$a= r\omega^2$

$\omega=\sqrt{\dfrac{a}{r}}$

Where, r = radius

a = acceleration

$\omega$ = rotational frequency

Put the value into the formula

$\omega=\sqrt{\dfrac{9.5\times2}{283}}$

$\omega=0.259\ rad/s$

The frequency in rev/min

$\omega=0.259\times\dfrac{60}{2\pi}$

$\omega=2.473\ rev/min$

Hence, The frequency of the rotational motion for the wheel to produce this effect is 2.473 rev/min.