Simple Physics request

[Wyrmshadow]

It's been more than a decade since I've used any sort of physics equations, I've forgotten everything.

I have a simple request: I have a space station (2001 movie) that is only 914.7 ft. in diameter. How fast should it spin to simulate 1/3 and 1/2 G?

I'm doing an animation project and I want it to be accurate.

 

[TheBladeRoden]

damn, at one point I figured out how big of a ring I needed to rotate once a day and still have normal gravity. But I forgot the equation. It was some impractical size

 

[GoodGame]

Shouldn't it be a simple centripetal accelaration equation?

http://hyperphysics.phy-astr.gsu.edu/HBASE/cf.html

Use 9.81 m/s^2 for the Force (F, and take appropriate fraction: 1/3 or 2/3 your choice), convert 914.7 / 2 from feet to meters and use as the radius (r), and solve for the velocity. You will need an estimate of the mass of the ring and whatever else rotates with it. The velocity you find will be for an object sitting on the edge of the ring so you'll have to convert that speed into a speed of revolutions per time (using the length of the perimeter of the ring to do the conversion).

 

[anhu]

Shouldn't it be a simple centripetal accelaration equation?

http://hyperphysics.phy-astr.gsu.edu/HBASE/cf.html

Use 9.81 m/s^2 for the Force (F, and take appropriate fraction: 1/3 or 2/3 your choice), convert 914.7 / 2 from feet to meters and use as the radius (r), and solve for the velocity. You will need an estimate of the mass of the ring and whatever else rotates with it. The velocity you find will be for an object sitting on the edge of the ring so you'll have to convert that speed into a speed of revolutions per time (using the length of the perimeter of the ring to do the conversion).

A small problem... "9.81 m/s^2" is not force; it is acceleration. There is an error here...you would not need any type of mass to calculate the angular velocity.

To simulate G/3 or G/2, set G/3 or G/2 as the acceleration. Centripetal acceleration is related to the tangential velocity and radius by:

A= v^2 / r

Your r (radius) is 914.7/2 ft. Your A is your acceleration, which is either G/2 or G/3. G is 9.8 m/s^2.

Calculate v after converting everything to whatever unit you want to use and you'll have your tangential velocity.

To convert your v to angular velocity (in radians/sec), simply divide it by r. To make it degrees/sec, multiply it by 180/pi. As you'd guess, the acceleration would only be maintained at only this specific radius, all else being the same.

 

[TheBladeRoden]

Cripes, my ring would need to have a radius of over 2 million km.

 

[Perfection]

What angular velocity are you using?!

 

[uppi]

Centripetal force = gravitational force

g: gravitational acceleration (~9.8 m/s^2)
w: angular velocity
r: radius
x: desired fraction of gravity (1/2 or 1/3)
f: frequency

-> m*w^2*r = m*x*g

-> w^2*r = x*g

with w=2*Pi*f:

4*Pi^2*f^2 = x*g/r

-> f = 1/(2*Pi) * sqrt(x*g/r)

Now you only have to put in the radius in meters and the desired gravity and you get your frequency (in revolutions per second).

 

[Wyrmshadow]

Thank you uppi. That saved me a lot of work.

.333G 1.4618 rev/min
.5G 1.7903 Rev/min
1G 2.5319 Rev/min

Anyone want to check my math?

 

[Gigaz]

Cripes, my ring would need to have a radius of over 2 million km.

And it would need a big asteorid thats made of antimatter to create the rotational energy. They rotational speed would be so high that the inhabitants need the theory of relativity to calculate their time

 

[anhu]

Thank you uppi. That saved me a lot of work.

.333G 1.4618 rev/min
.5G 1.7903 Rev/min
1G 2.5319 Rev/min

Anyone want to check my math?

That's correct, I think (your 1G is, at least).

Just on pure curiosity, what movie is this? I have never seen such a space station...

 

[Wyrmshadow]

That's correct, I think (your 1G is, at least).

Just on pure curiosity, what movie is this? I have never seen such a space station...

Stanley Kubric's 2001? The space station from it? I'm using a model of it for my habitat ring in the center of the ship

 

[Perfection]

well, it's not from 2001

The Space Station:

Discovery: