Question

PART 1: You're out in space, on a rotating wheel-shaped space station of radius 688 m. You feel planted firmly on the floor, due to artificial gravity. The gravity you experience is Earth-normal, that is, g = 9.81 m/s^2. How fast is the space station rotating in order to produce this much artificial gravity? Express your answer in revolutions per minute (rpm).

A) 1.140 rpm

B) 0.119 rpm

C) 82.2 rpm

D) 0.684 rpm

PART 2: This time, the space station as a radius of 1279 m. And this time, the amount of artificial gravity you experience is 18.2 m/s^2. How fast is the space station rotating in order to produce this much artificial gravity? Express your answer in revolutions per minute (rpm).

A) 1.139 rpm

B) 0.119 rpm

C) 152.6 rpm

D) 0.570 rpm

Answer 1

Solution:

1. (A)

radius r=688m

gravity

The velocity at any point on the wheel is given by,

  

The angular velocity is given by,

  

Therefore, number of revolution is given by,

2)(A)

radius r =1279m

acceleration

The velocity at any point on the wheel is

  

The angular velocity is given by,

The number of revolutions per minute is