Question

People in the future may well live inside a rotating space structure that is more than 2 km in diameter. Inside the structure, people on the inside of the outer edge will experience 1 g while people halfway to the axis will experience ______________.

a) 0 g
b) 1/2 g
c) 1/4 g

Answer 1

In a rotating space structure, artificial gravity decreases with the square of the distance from the center. At half the radius from the outer edge, occupants would experience 1/4 of the artificial gravity, or 1/4 g.

Step-by-step explanation:

The concept of artificial gravity in a rotating space station is an intriguing aspect of physics that relates to the centripetal force experienced by occupants of the station. Artificial gravity is generated by the rotation of the station, with the centripetal acceleration acting as a substitute for gravitational pull. This acceleration is dependent on both the angular velocity of the space station and the radius at which the person is located from the center of rotation. Following the inverse-square law, at half the distance to the center, the centripetal force—and thus the experienced artificial gravity—would be one-fourth, or 0.25 g. Therefore, people located halfway to the axis from the outer edge would experience an acceleration of 1/4 g. Option C is correct .

For example, if the rotating space structure is designed such that at the outer edge (assuming a radius R) the occupants experience 1 g, the centripetal force experienced would correspond to the normal gravitational force felt on Earth. If someone moves to a point halfway towards the center of the structure (at a radius of R/2), the centripetal force they experience at this new radius would be (R/2)²/R², which is 1/4 of the original force, hence experiencing 1/4 g.

Answer 2

option B

Step-by-step explanation:

given,

diameter of the rotating space = 2 Km

Force exerted at the edge of the space = 1 g

force experienced at the half way = ?

As the object is rotating in the circular part

Force is equal to centripetal acceleration.

at the edge

g = ω² r

ω is the angular velocity of the particle

r is the radius.

now, acceleration at the half way

g' = ω² r'

`g' = \omega^2 ((r)/(2))`

`g' =(1)/(2)(\omega^2 r)`

`g'=(g)/(2)`

People at the halfway experience g/2

hence, the correct answer is option B