Spinning Planet Physics Question?

Question

My wife has taken more physics classes than I and is better at math than I, but still we have a bet. Help if you can.

I say that if the Earth started spinning faster and faster eventually the centrifical force tangent to the surface would overcome gravity and everything (people, cars, bodies of water) would be thrown off the planet like a giant Merry Go Round.

She says (I don't understand this) that if the Earth started spinning faster it's gravity would somehow become stronger and we'd all be stuck to the surface, unable to move.

I don't know the math in this but I'm sure I'm right. Could someone give me the equation to prove to her? Thanks a mil.

Answer 1

It's a moot point, because the Earth's rotation is slowing down, not speeding up. But let's assume it somehow happened. Then the Earth would become more oblate, that is, it would bulge out at the equator and become squashed at the poles. Gravity would certainly not increase, since it depends only on mass and radius, not rotational characteristics.

As for objects not structurally bound to the Earth, it is possible that the Earth could speed up so much that it could no longer hold them. Calculating it out, centripetal (not "centrifugal") force is m*v^2 / r, and the force of gravity is mg. Canceling out m and solving for v using g = 9.8 m/s^2 and r = 6378137 m at the equator, I get v = 7906 m/s. The Earth's actual equatorial surface velocity is 465 m/s, so the earth could be going a whopping seventeen times faster than it is now, and we'd still be fine. Gravity may be the weakest of the fundamental interactions, but it gets the job done.

The rocky parts of Earth itself would not fly apart just yet, because material strength holds it together in addition to gravity.

Answer 2

You are right. Gravity has nothing to do with spinning. She may be confusing ideas to simulate gravity by spinning a wheel shaped space station with the real gravity of the Earth. In the space station, centrifugal force would make people stick to the INSIDE surface of the wheel, but the Earth is like the OUTSIDE surface of the wheel.

Gravity force is GMm/R^2
Where:
G is the universal gravitational constant
and m are the masses of the objects attracting each other, like the Earth and a person.
R is the distance between the centers of the two masses.

Centrifugal force is mV^2.R
Where:
m is the mass of the moving object, say a person.
V is the speed of the moving object
R is the distance from the axis of rotation to the moving object.

So gravity depends on the mass of the Earth but not on any kind of speed, and centrifugal force depends on speed but not the mass of the Earth. Confusion may arise since both depend on the mass of the person, but just keep in mind that gravity depends on BOTH masses and not the speed while centrifugal force depends on speed and only ONE of the masses, and that mass is not the mass of the Earth, it is the mass of the object, like a person, feeling the force.

Answer 3

the spinning of the planet has nothing to do with gravity, so if the Earth were to spin faster the gravity would not increase. Gravity is determined by mass, not speed.

You are correct, but not entirely. If the Earth were to spin faster, it would eventually get to a point where the Earth itself would break apart, long before people started flying away due to centrifical force.

Answer 4

The formula for the revolution ot the earth in an orbit with the Sun is as follows:
V^2 = G x Mass of the earth divide by the earth orbit radius to the sun
Where v is velocity of the earth in its orbit and it varies slightly per the changing radius. And G is Newton"s Universal gravitational constant.

If the velocity of the earth was to Increase by a larger factor lets say a number "n"; than the earth in order to maintain its rotational energy in equilibrium there would be a decrease in Earth's mass by the same factor of ' n '.

However the mass of the Earth never really decreases it always increase because it gets tons and tons of mass per year from the sun. This mass increase cause the earth's orbit to increase each year.
However this increase is so slight and is observed by a change of the Earth's spin which is resulting in a very minute slow down of the spin.

Therefore the day's lenght dilates as a function of mass increase.

Therefore in terms of Physics the orbital velocity is a function of mass increase.
In conclusion the mass increase is inversely proportional to the orbital velocity squared. and a increase of velocity is a decrease in mass.

As far as life on earth being affected by gravity the changes are so slow that according to the Relativity Principle it is not noticable to how Humans would feel gravity.

Answer 5

Your wife is the sense that the Gravity of a spinning body would go up slightly, but definitely not enough to compensate for the centripetal acceleration. In theory you are right, if the Earth rotated fast enough, gravity would not be enough to hold objects to the surface. Keep in mind though that even though this might be true near the equator, near the north and south poles this effect would not be nearly as strong.

Answer 6

Hm - could be that her hypothesis is that the only way the earth could start spinning faster was if it collapsed towards the centre. Then, to keep the angular momentum constant it would just naturally spin up faster but having the same mass and you now being on a much smaller planet the surface g would also be a lot higher.

Answer 7

First, the Force that determines your weight - can be described by two terms:

F = mg + mv^2/ r

The second term has to do with the centripetal acceleration on a mass m (your mass) - undergoing rotational motion because of the Earth's rotation, where v is the velocity of Earth's rotation at a particular latitude and r the distance to the center of Earth.

As you can see, the terms are additive. If the Earth started spinning faster you would have more force holding you down.

Answer 8

attraction force of objects due to gravity is F=G*m1m2/Rsqr. I think what she is referring to is the Einsteinium fact that mass increases with the speed of an object, but, since light travels at 671 million miles per hour,, you really gotta be going pretty fast for it to add mass to the planet. In the equation there is no symbol for speed,, so it isn't a issue in Newtonian physics. the earth is spinning at about 1,160 mph,, which is way less than 670 million miles per hour. the mass builds exponentially with speed, so the centrifical force would tear it apart long before it's mass and there for it's gravity would increase to the level nec to hold it together. best I can do,, C.

PS DougK is an idiot who couldn't engineer his way out of a paper bag. The forces aren't additive,, they are opposing. David K93 seems right,, you would fly off at about 17x or speed,, or about 18,000 mph.

Answer 9

I'm far to lazy to formulate an equation....but I agree with your opinion. I can't think of any reason why gravity should increase with an increase in rotational velocity. Gravitational attraction is dependent on the mass of objects,so should be unaffected by velocity. Here's a twist on your question... How much more would you weigh if the Earth were to stop spinning on its axis...? (Note - that's weight...not mass!)

Oh..before I go... what was yours wife's explanation of an increase in gravity if rotation increases?

Answer 10

This end would desire to be precise in case you have been discussing the moments purely after the large Bang. at contemporary after the explosion, each and all the debris would have been spinning interior the comparable relative direction, whether, we are actually billions of years down the line. All you're able to alter the path of an merchandise, its velocity, or its spin, is an exterior rigidity, including gravity, or perchance a collision. Even collisions between molecules can impact spin; it would not could be 2 large products bumping into one yet another.