Calculate rpm with circular motion

[Workout]

Homework Statement

Imagine that NASA plans to builds a large donut-shaped space station. The station will rotate in outer space in order to simulate gravity. If the station has a radius of 200m, what must be its rotation speed in revolutions per minute, to produce an artificial gravity of 0.8 g?

Homework Equations

ac=v^2/r
rev/min = 60v/2pi*r

The Attempt at a Solution

Okay, so I have somewhere in my notes that if ac = g then T = 0. So I replaced ac with 0.8. So my equation went 0.8 = v^2/(200m).

So I got my v = 12.65 m/s.

Then I plugged my v into rev/min at 60(v)/2pi*r and I got my answer to be 0.604 rev/min.


I was just wondering if I did this right?

 

[Simon Bridge]

Okay, so I have somewhere in my notes that if ac = g then T = 0.

What does T refer to here? Is that relevant to the space station?

So I replaced ac with 0.8.

0.8 what?

So my equation went 0.8 = v^2/(200m).

So I got my v = 12.65 m/s.

Then I plugged my v into rev/min at 60(v)/2pi*r and I got my answer to be 0.604 rev/min.

I was just wondering if I did this right?

... well, if you look at your calculation, checking the units, v=12.65m/s means a=0.8m/s².
Is that the correct acceleration?

 

[Workout]

How do I solve for rpm? I think my v is correct.

 

[Simon Bridge]

Well, since you are sure you have the correct v...
You can either convert your v into angular velocity or work out the circumference of your circle and how many times you'd travel that distance at speed v in one minute.

However, if you don't answer questions I cannot help you.
i.e. is 0.8g, the acceleration you are asked to get, the same as 0.8m/s² - which is the acceleration you used to get v?

 

[Nickie]

Your approach and calculations are correct. To summarize, you have correctly used the equation for centripetal acceleration (ac = v^2/r) and equated it to the desired artificial gravity (0.8 g). From there, you solved for the velocity (v) and then plugged it into the equation for revolutions per minute (rev/min = 60v/2pi*r) to get your final answer. Great job!