How Do You Calculate the Rotation Rate of a Space Station Wheel?

[Ninjaku]

Homework Statement

Basically the problem is asking me to find the rate of rotation of a space station that is in the shape of a wheel 120m in diameter, and rotates to provide an "artificial gravity" of 3.00 m/s.

And it has to be in rev/min.

Homework Equations

The only equation so far I that has to deal with this is the one

a_c = $$v^2/r$$

The Attempt at a Solution

it seemed pretty simple and straightforward. So first i took the gravity which is of course the acceleration in this case. And then set it equal to v^2/60.

Then i solved for v.

After solving for v I used that to see how long one revolution is by using the equation, v=d/t. Substituting in the 120 m for d.

So I send up with a time in sec for every 120m revolution.
Then I converted from sec to min by divinding by 60.

I still can't get the answer in the book.

 

[tiny-tim]

Hi Ninjaku!

(have an omega: ω and a pi: π and try using the X² tag just above the Reply box )

So I send up with a time in sec for every 120m revolution.
Then I converted from sec to min by divinding by 60.

I still can't get the answer in the book.

Did you use the 2π factor to convert radius to circumference?

(and btw it would have been easier to start with the alternative formula a_c = ω²r instead of v²/r)

 

[Ninjaku]

Hey thanks for the reply.

I retried the the computation with the 2π conversion factor that I forgot on my first try. And my answer is a little closer but still no cigar.

The answer in the book is 2.14rev/min

I got .084388.

Oh and I'm not reallly familiar with that other formula, what does omega represent in that equation.

 

[tiny-tim]

Well, I make it 2.14 also.

Show us how you got .084388.

(ω is the angular velocity in radians per second: v = ωr, ω = v/r )