# Rate of roation of a wheel

1. Feb 23, 2010

### Ninjaku

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

ac = $$v^2/r$$

3. 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.

2. Feb 23, 2010

### tiny-tim

Hi Ninjaku!

(have an omega: ω and a pi: π and try using the X2 tag just above the Reply box )
Did you use the 2π factor to convert radius to circumference?

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

3. Feb 23, 2010

### Ninjaku

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.

4. Feb 23, 2010

### 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 )