Circular Motion Homework: Finding Period of Rotation for a Space Station

[cheerspens]

Homework Statement

A space station has a radius of 200 meters. An astronaut has a mass of 55 kilograms and the station rotates at 1.5 rev/min. What is the period of rotation for the station?

Homework Equations

$$\tau$$=2$$\pi$$r/v
a=v²/r
Fg=mg
F_NET=ma

The Attempt at a Solution

I think the F_NET equation is F_sp=ma and I'm pretty sure you have to solve for $$\tau$$ but in order to do that I need to solve for a. How do I either find a velocity or acceleration to do this?

 

[kuruman]

Time out. This is not a Newton's Second Law problem. Just think. If the station does 1.5 revolutions in one minute, what is the period, i.e. how long does it take to make one revolution?

 

[cheerspens]

Would you just have to set it up as a proportion and find that it takes 1.5 seconds to make one revolution?

 

[kuruman]

What kind of proportion? If (as you say) it takes 1.5 seconds to make one revolution, then it will make two revolutions in 3 seconds. But you are told that it makes 1.5 revolutions in one minute or 60 seconds. So what you say can't be right. Look at it this way: it makes 1.5 revolutions in 60 seconds. Can you find how many seconds for one revolution? It must be greater than 30 and less than 60.