Since a soccer ball on the surface of the earth is changing direction as the earth rotates, the velocity is changing, which means it’s accelerating. I think. Acceleration requires a force. I figured the acceleration must be due to gravity as with a satellite in orbit but when i went to check online about why the earth continues to rotate the answer was simple inertia. Nowhere could i find gravity mentioned as a contributor. Where is the error in my thinking? I thought i generally understood conservation of angular momentum as well but perhaps not. Thanks in advance.
An object moving in a straight line at constant speed is being subjected to a net force of zero.
If an object is traveling along a curve at constant speed, there is a force acting on it in a direction perpendicular to its path of travel.
a soccer ball parked on the surface of the earth is traveling along a circular path due to the rotation of the earth (to keep this simple, let’s ignore the orbiting of the earth around the sun and the orbiting of the solar system around the galactic center). The force that makes that circular movement happen is gravity - or more precisely, the sum of the following two forces:
-the downward gravitational force pulling the ball toward the center of the earth
-the upward force of the surface of the earth pushing the ball away from the center of the earth
at the north or south pole, these forces are equal and opposite: the soccer ball is not accelerating at all, and not moving in a circular path. At the equator, the ball is moving about 25,000 miles in 24 hours (1042 MPH) due to the earth’s rotation. The upward force from the surface of the earth against the ball will be slightly less than the downward force due to gravity; the differential between these two forces is the amount of force that causes the ball to hew to its circular path as the earth rotates. If gravity pulls the ball with a pound of force, then on the equator the ground is only pushing upward with 0.9965 pounds of force; the net difference, 0.00346 pounds, is what it takes to keep that ball moving at 1042 MPH on a curved path with a radius of 4000 miles.
The earth does indeed continue to rotate because of inertia. This (the fact that inertia is what maintains the earth’s rotation) has nothing to do with the behavior of the soccer ball or satellites. Not sure why you’re comingling these phenomena in your mind.
Is your question why Earth rotates or why the soccer ball rotates with it?
The former: https://astronomy.com/magazine/ask-astro/2015/04/spinning-universe
I guess part of the question is why does Earth spin?
If so, gravity really did set the ball rolling 
After it did start spinning, there was nothing to stop it from spinning, so it has continued to do so through inertia.
There’s no reason spinning objects should stop on their own and, in fact, they don’t. For objects on earth, usually simple frictional losses are sufficient. In the case of planets, that spin can slow due to gravitational effects from other bodies.
For example, the moon is almost tidally locked to earth, i.e. the same side faces the earth all the time.
The same would happen to Earth one day (same side facing the sun all the time), except the slowing of Earth’s rotation would take so long that the sun would go red giant and envelop the Earth well before that point.
Both are correct. As the Earth is rotating, every part of it (except for the points right at the axis) is continually accelerating due to a combination of gravity and other forces. If somehow gravity were suddenly turned off for the rotating Earth, each part of the Earth would stop accelerating, and from that moment continue moving in a straight line in whatever direction it was going at the moment, and the Earth would cease to be an almost-sphere and become an ever-expanding disk. But gravity doesn’t turn off, so that doesn’t happen, and it continues to be an almost-sphere.
I’m commingling them because i see them as equivalent. What is the difference between a soccer ball on the surface of the earth and any rock or atom of molten iron in the earth? They are all rotating about the axis of the earth and therefore require a force, no? If everything that is moving via circular motion requires a force and all the “objects” that compose the planet are moving in a circular motion, then doesn’t the earth require a force to rotate?
If the Earth were ever to become tidally locked to anything, it’d be to the Moon, not the Sun. But even that would take longer than the Sun’s lifespan.
EDIT: The Earth does not require a force to continue rotating. It requires a force to hold it all in one piece while it rotates. In the “gravity turns off” scenario I mentioned, the expanding disk would still have the same amount of rotation (in strict terms, the same amount of angular momentum) as it always had.
A rigid object* rotating in space, considered as a whole, will continue to rotate due to conservation of angular momentum, unless acted on by some external torque.
If instead you consider individual pieces of the object, then you can say that each of them follows a curved path around the axis of rotation. This shows that they experience some centripetal force. Without this force, Newton’s first law of motion tells us that each of these pieces would fly off in a straight line, and thus the object would fall apart. The centripetal force is just whatever forces hold the object together. (For large enough objects, gravity would be the dominant contribution, but for a small solid object it’d just be the forces between its molecules that make it solid in the first place.)
Both of these are legitimate ways to think about a rotating object, and are ultimately equivalent. But in cases where you’re certain that the rotation isn’t enough to make the object fall apart, it’s simpler to treat the body as a whole and just appeal to conservation of angular momentum, rather than having to compute internal forces between pieces of the body.
- The Earth is not exactly a rigid object, but I’m simplifying. Spherical cows and all that.
Ok so that makes sense. Gravity is required for the earth to rotate about it’s axis because it’s required to have an earth in the first place (which i knew of course but wasn’t looking at it from that perspective.)
The difference between a spinning object the size of the Earth and a spinning object the size of a soccer ball (and indeed the size of any object at the human scale) is that to hold together in one piece the Earth needs gravity, while the soccer ball can get by with other forces (interatomic and intermolecular forces that ultimately are basically electromagnetic).
If you suddenly turned gravity off, the bits of earth would no longer clump together - but considered in the aggregate, they would all continue to rotate around the original axis as they moved apart from each other. Conservation of angular momentum demands this.
For a visual example, check out this video of a CD being spun so rapidly that it shatters. The breakup happens at 6:09; the moment of breakup is analogous to suddenly turning off the earth’s gravity. You can see that the pieces don’t fly straight away from the axis of rotation, they fly away along a tangent path.
Some things you may already know, but worth mentioning :
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The earth’s atmosphere rotates with it not just the solid part. If the atmosphere did not rotate, you’d have huge winds. If you use a balloon to rise above the earth, you will still rotate with the earth (barring small winds).
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There is a force (centripetal ) needed to keep a body revolving around a point. The force is perpendicular to the motion at every point and the work done by the force is 0. So for the ball case, the centripetal force is the gravity.
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Global warming redistributes water from the poles to the oceans. This will result in earth slowing down by a few milliseconds (a day will get longer but not noticeable by humans)
Just so I’m clear, is the differential due to friction?
No, it’s due to the acceleration from going in a circular path. Normal force (the sort of pushing force you get between two objects in contact, like the force of the ground on the soccer ball) is always just as big as it needs to be (I think that engineers refer to forces like this as “reactive forces”). On a non-spinning Earth, the normal force due to the ground would be equal to the gravitational force. On a spinning Earth, slightly less normal force is needed.
The difference is due to the inertia of the soccer ball, which makes the ball want to move in a straight line. The surface of the earth is trying to move away from the ball (because the surface of the earth is moving on a circular path around the earth’s axis), and for the ball to follow the same path, the surface of the earth can’t push up on the ball quite as hard.
If the earth’s rotational period were only 90 minutes (and the earth somehow maintained its current shape), your speed at the equator would be about 17,400 MPH. If you go through the math for this situation, you find that gravity is pulling your one-pound soccer ball down with a force of one pound, and the earth is pushing upward on it with a force of zero pounds: it takes the entire one pound of gravitational force to keep that one-pound mass moving in a circle of 4000-mile radius at 17,400 MPH. This is basically what satellites in low earth orbit experience.