Artificial gravity rotating on two axes

[DaveC426913]

"What would the occupants experience as gravity?"

The [inverse of the] acceleration of the floor under their feet.

"Would it change over time?"

Yes. As has been described, the instantaneous axis of rotation will not remain fixed relative to the body. Points at the instantaneous axis have zero g. Points away from the axis have non-zero g. It follows that the g for body-fixed points can change over time.

Cool. That's half the answer.
Magnitude would change over time. Would direction?

 

[jbriggs444]

Cool. That's half the answer.
Magnitude would change over time. Would direction?

Yes. A little bit of reasoning shows that it must be so.

Consider two points on the body with the instantaneous axis somewhere between them. "Gravity" at both points is away from the direction of the other.

Now let the rotational axis move so that gravity stays in the same direction at both points. That means [some point on] the rotational axis moves along a line between the two points.

Now consider a third point not located on the line connecting the first two. "Gravity" there also points away from the rotation axis. But the direction will be changing over time. This is not quite bulletproof, as it stands, but the basic idea holds -- if the rotational axis wanders around and gravity points away from the rotational axis, gravity cannot point in the same direction forever for everyone.

Edit: Had to swap "away from" for "toward" due to brain error.

 

[vanhees71]

I think that this implication still needs a detailed explanation



Perhaps this is understandable. But I think an angular velocity of a rigid body is nowhere included to the curriculum of a high school. By my own experience I see that this is not a simple topic for university students.

I didn't say, it's simple, I only said it's understandable by a motivated enough high school student.

 

[vanhees71]

Reporting to have this thread closed, as it seems to be unanswerable at the education level specified.

I have answered it at the education level specified. You only have to think hard enough about it!

 

[DaveC426913]

You only have to think hard enough about it!

'Think hard enough...' I can't even decipher it. I didn't learn this in HS.

 

[OmCheeto]

View attachment 301959'Think hard enough...' I can't even decipher it. I didn't learn this in HS.

It's possible you did but are just too old, like me. I've just finished going through my college level first year math textbooks* and much of the vector notation used by vanhees71 is nowhere to be found.

*
ISBN 0-87150-283-6 Functions and Graphs 3rd Edition Stokowski circa 1980
ISBN 0-15-505731-6 Calculus With Analytic Geometry 2nd Edition Ellis and Gulick circa 1982

 

[berkeman]

Thanks for an entertaining and interesting thread folks.