# Fast spinning earth

1. Aug 20, 2010

### boffinwannabe

what would the affects of a faster and faster spinning earth be gravitationally? Mass increases with rotation i believe? If rotation neared the speed of light how much would the mass and gravity change?

I am wondering what is more significant, the gravitional affects or the centifugal affects? Would a hugely faster spin keep us firmer on the ground or fling us off into space?

Last edited: Aug 20, 2010
2. Aug 20, 2010

### AJ Bentley

If you fasten a heavy weight on the end of a string and whirl it round your head, you would easily be able to break the string.
You can probably generate the equivalent of several kilograms of weight that way without having to get up a speed of more than 100mph.

On the other hand, the mass increase due to Kinetic Energy is probably in the order of the weight of a single atom.

So, which is stronger, centrifugal or relativistic gravitation?

{Edit}PS Having had my curiosity tickled, I did the calculation - the correct figure for a 1kg mass at 100mph is rather more than my off-the-cuff guess. It doesn't significantly affect this answer - but it's surprising how big it actually is.

Last edited: Aug 20, 2010
3. Aug 20, 2010

### cshum00

So from your calculations AJ Bentley, is the velocity provided by the centrifugal force higher than the escape velocity?

4. Aug 20, 2010

### AJ Bentley

I should say so - work it out yourself.
Even using a classical calculation of centrifugal force F=mv^2/r you get F=mc^2/r

c is 300,000,000 and the earth is about 6,000,000 metres radius so the upward force on a 1kg mass would be 15,000,000,000 Newtons.

5. Aug 20, 2010

### pallidin

Whoa, hold on a sec...
Are you trying to fling something out into space using centrifugal force?

Well, it is theoretically possible, and the US government has explored it many years ago. Sorry, don't have a source.
Anyway, the main problem is the strength of the centrifugal containment prior to release. Be it a steel cable, carbon nano-tube, etc... the "cable" will snap well before escape velocity.
But, the theory itself is quite sound. That's why it was actually experimented.

6. Aug 20, 2010

### boffinwannabe

im a non-phsycis non-maths guy who just finds the subject interesting but frustratingly dotn understand the maths to work things out. So im really trying to envisage what happens to the earth if its rotation were to approach the speed of light. I trying to understand what forces become dominant. So i understand that at those speeds the increase in mass is significant but my mind is asking what would this make the net gravity on earth given the increase in the centrifugal force. If the earth stopped spinning i understand gravity would still be the dominant force keeping us on the ground. Now im trying to understand the other extreme. Keeping it simple and just working on the basis that the rotation is near the speed of light and no worrying if the increase in rotation from was sudden or slow.

7. Aug 20, 2010

### Dr Lots-o'watts

Centrifugal force would make the earth unrecognizable long before relativistic mass increase becomes relevant.

Are there actually any cosmic bodies having relativistic rotational velocities? This is certainly very exotic.

8. Aug 20, 2010

### cjl

Well, some of the fastest millisecond pulsars can have surface velocities in excess of 10% of the speed of light, if I didn't screw up the calculation (12km radius object, rotating at 500-800 rev/sec).