Simple question

[between3and26characterslon]

Having a conversation the other day about the speed at which space stations are depictded to be rotating in movies and whether or not the size of the craft is taken into account. Obviously angular speed will vary depending on radius but having watched people in human sized hamster wheels I would guess that the speed needed to effect 1g would be something like 10 to 12mph

 

just to be clear I'm thinking if the circumference was 12 miles and it rotated once every hour that would be 12mph.

 

I can't do the maths but I would appreciate it if someone could tell me at what speed a station would have to rotate to effect 1g

 

Thanks in advance

[AndresKiani]

Inertia, it all depends on how much force is applied, how much inertia a massive object has, ect.

[swansont]

Missed this when it was first posted.

 

The situation is centripetal acceleration, and the solution is well-known. The acceleration of something moving in a circle is v²/r so v = sqrt(rg). If you have a 3 meter radius human "hamster wheel" then you need to be moving at 5.4 m/s at the surface of the wheel (12 mph). That's 1g where the feet meet the mat.

 

Going bigger means you have to go faster; four times as big requires you to go twice as fast.

[between3and26characterslon]

Thanks for the reply

 

So as the radius increases the speed increases but the RPM decreases?

[swansont]

Thanks for the reply

 

So as the radius increases the speed increases but the RPM decreases?

 

Yes, that's correct. v = wr and in keeping centripetal acceleration constant, r increases faster than v does. (w is angular speed)