Question

If you have to create artificial gravity equal to that on the earth, how many rotations per minute will be required?
A. $1.49{\text{ rpm}}$
B. ${\text{1.6 rpm}}$
C. ${\text{1.78 rpm}}$
D. none of the above

Answer 1

We need to know the concepts of radial and centripetal acceleration.Artificial gravity is the creation of an artificial inertial force same as that of the earth’s gravitational force usually by rotation.

Complete step by step answer:
The only known way to create artificial gravity is to supply a force on an astronaut that produces the same acceleration as on the surface of the earth. It is believed that on applying such an amount of force the body would experience a rotating motion and it would rotate about its axis and would experience centripetal (radial) acceleration.

To achieve the desired value of $g$ , we have to match the acceleration due to gravity to the earth’s radial acceleration.
$r{\omega ^2} = g$
Where $\omega$ is angular speed and $r$ is the radius of the earth.
Substituting the values, we get
$\Rightarrow \omega = \sqrt {\dfrac{{9.8}}{{400}}} \times \dfrac{{60}}{{2\pi }}$
$\therefore \omega = 1.49{\text{rpm}}$

Hence, the correct option is A.

Additional information: centripetal acceleration is the acceleration that causes a body to move in a circular path or turn. Because of its direction, it is also referred to as radial acceleration. There is no confirmed technique that can simulate gravity other than actual mass or acceleration. Because unlike the electric force, which is generated by positive and negative charges, there's only one type of gravitational "charge," and that is mass-and-energy. The gravitational force is always attractive, and there's simply no other way around that. Instead, we have to do the best we can do with the three types of acceleration: gravitational, linear, and rotational which is available to us.

Note: Centrifugal acceleration is what you feel when your car takes a turn and you are shoved sideways into the car door, or what you feel on a roller coaster as it travels a sharp curve in the tracks. $1\;RPM$ is equal to rotating one full circumference every minute.