What angular speed is necessary to make this cylinder experience the same accelertion as gravity?

Question

A rotating cylinder about 20 km in length and 8.0 km in diameter is designed to be used as a space colony. With what angular speed must it rotate so that the residents on it will experience the same acceleration due to gravity on Earth?

Not sure of the process on how to work this one given just the dimensions of the cylinder...

Here's the answer: 0.0495 rad/s

Not quite sure where to start... any help would be appreciated, thanks a lot in advance!

Answer 1

We want centripetal acceleration = g, or ω^2r = 9.8 m/s^2, so ω = sqrt(g/r) = sqrt(9.8/4000) = 0.049497 rad/s.

Answer 2

Gravity on earth exerts a pull of 16 feet per second every second, expressed as  16'/sec*2

If your colony ship were to have a diameter of 8 kilometres, then its radius would be 4 miles.

4 miles = 4 x 5,280 feet  = 21,120 '

How much  might 0.0495 of 21,120 ' be?

Use your calculator:  1,045.45'

Now, this can be divided by 16 over 5 steps to get 1

I suspect your answer would be16 feet per second raised to the power of seven, 16'/sec*7  (We started off with sec*2.)

That'll get you started, but I don't know how to go any further. It is using calculus, though, isn't it?