Physics question: I would expect the left fielder to catch the ball....

[Steven G]

I have a question that has been bothering me for awhile. I know that the Earth rotates ~1000mph at the equator.



My concern is the following. Consider playing baseball (say at the equator) where a ball leaves the baseball bat heading toward right field. I would expect the left fielder to catch the ball. But this does not happen as the right fielder will be the player fielding the ball. What am I missing? And yes, I know that the instant the ball leaves the bat it is moving at 1000 mph in the direction the earth is moving and am assuming slows down in that direction according to the laws of Physics, ie Calculus. 1000 mph is .277777 miles/second which is HUGE. Very strange to me!


After some more thinking..... I think that you can consider the ball is attached to a string and swung in a circle and while it is rotating in a circle someone hits the ball with a bat. Does this collision affect the rotation? Even if the rotation is nullified by the collision between the bat and ball, the Earth is STILL rotating making my argument even stronger(?) Argh!

An alternate problem would be if I shot a bullet from a gun that is Vertical would the bullet come back down and enter into the barrel of the gun. I am assuming no air resistant.

 

[Deleted member 4993]

I have a question that has been bothering me for awhile. I know that the Earth rotates ~1000mph at the equator.



My concern is the following. Consider playing baseball (say at the equator) where a ball leaves the baseball bat heading toward right field. I would expect the left fielder to catch the ball. But this does not happen as the right fielder will be the player fielding the ball. What am I missing? And yes, I know that the instant the ball leaves the bat it is moving at 1000 mph in the direction the earth is moving and am assuming slows down in that direction according to the laws of Physics, ie Calculus. 1000 mph is .277777 miles/second which is HUGE. Very strange to me!


After some more thinking..... I think that you can consider the ball is attached to a string and swung in a circle and while it is rotating in a circle someone hits the ball with a bat. Does this collision affect the rotation? Even if the rotation is nullified by the collision between the bat and ball, the Earth is STILL rotating making my argument even stronger(?) Argh!

An alternate problem would be if I shot a bullet from a gun that is Vertical would the bullet come back down and enter into the barrel of the gun. I am assuming no air resistant.

Remember the relative velocity of the ball and the fielders ~0 mph (right before the ball leaves the bat). The effect of rotation of earth is more or less same on everybody (everything) on the field - so we do not see any "relative" effect (one of the basic tenets of Galilean relative motion - pre-Lorentz equations).

 

[Steven G]

Remember the relative velocity of the ball and the fielders ~0 mph (right before the ball leaves the bat). The effect of rotation of earth is more or less same on everybody (everything) on the field - so we do not see any "relative" effect (one of the basic tenets of Galilean relative motion - pre-Lorentz equations).

I'm sure you are right but I am still confused.

You say the effect of rotation of earth is more or less same on everybody (everything) on the field which I agree with. But I am confused because the ball is NOT on the field, but rather in the air. So why does the rotation of the earth have an effect on the ball in the air? Is it as simple as the air is rotating ~ the same speed as the earth is rotating?

 

[JeffM]

I'm sure you are right but I am still confused.

You say the effect of rotation of earth is more or less same on everybody (everything) on the field which I agree with. But I am confused because the ball is NOT on the field, but rather in the air. So why does the rotation of the earth have an effect on the ball in the air? Is it as simple as the air is rotating ~ the same speed as the earth is rotating?

Do YOU ever notice a wind of 1000 miles an hour?

 

[Steven G]

Do YOU ever notice a wind of 1000 miles an hour?

I was thinking about that. So the wind can't be still, it is moving about 1000mph.
Thanks

 

[Deleted member 4993]

I'm sure you are right but I am still confused.

You say the effect of rotation of earth is more or less same on everybody (everything) on the field which I agree with. But I am confused because the ball is NOT on the field, but rather in the air. So why does the rotation of the earth have an effect on the ball in the air? Is it as simple as the air is rotating ~ the same speed as the earth is rotating?

When the ball is leaving the pitchers hand - it has that velocity (it is a vector and added to it will be the velocity imparted by the pitcher) - and it continues to have that till it reaches the bat. In the meantime, the bat and the slugger was also moving with the earth. If you imagine yourself watching the game from a spaceship .....

 

[Dale10101]

A point of view

I have a question that has been bothering me for awhile. I know that the Earth rotates ~1000mph at the equator.



My concern is the following. Consider playing baseball (say at the equator) where a ball leaves the baseball bat heading toward right field. I would expect the left fielder to catch the ball. But this does not happen as the right fielder will be the player fielding the ball. What am I missing? And yes, I know that the instant the ball leaves the bat it is moving at 1000 mph in the direction the earth is moving and am assuming slows down in that direction according to the laws of Physics, ie Calculus. 1000 mph is .277777 miles/second which is HUGE. Very strange to me!


After some more thinking..... I think that you can consider the ball is attached to a string and swung in a circle and while it is rotating in a circle someone hits the ball with a bat. Does this collision affect the rotation? Even if the rotation is nullified by the collision between the bat and ball, the Earth is STILL rotating making my argument even stronger(?) Argh!

An alternate problem would be if I shot a bullet from a gun that is Vertical would the bullet come back down and enter into the barrel of the gun. I am assuming no air resistant.

We are talking about Newtonian physics here. Nobody seems to be talking about momentum.

Essentially you are asking why things fall straight down when you release them. For example, since the earth is rotating beneath an object as it falls “Why doesn’t a baseball dropped over your left toe land on your right toe if you are properly oriented … so to speak.

Consider an object heading towards earth on what would be a near miss trajectory if the earth had no gravitational field. As the object approaches the earth the earth’s gravitational pull on it increases. One of three things can happen. If the objects momentum is great enough its trajectory is bent towards earth but the object passes by and away as the earth’s gravitational pull on it decreases. If the object’s momentum is less, just right, the object will be continuously pulled towards earth as it attempts to pass by. The object’s trajectory will continuously be bent toward the center of the earth’s gravitational field albeit in this case just sufficiently to prevent the object from escaping to a further distance where the gravitational pull would be less. This continuous instant by instant altering of the objects trajectory, when traced, becomes a description of an object orbiting the earth (usually an ellipse but think of the special case of a circle to keeps things simple).

Finally, if the object’s momentum is even less, then, in this last case, the object‘s trajectory will be continuously bent towards the earth’s center of gravity in the pattern of a spiral of decreasing radius. That is, until it’s spiraling trajectory encounters the earth crust.

But what happens then?

Assume for the moment that the “remains” skid to a halt and turn out to be single sphere of baseball dimensions that has come to rest on a near frictionless plane, perhaps a Formica table top sitting on the equator.

If you NOW trace the “baseballs” path through space from, say, a coordinate system whose origin is the sun, and if you eliminated all other details except the point location of the earth’s center of gravity and the baseball, what you see is that the baseball is now orbiting the earth’s center of gravity at the distance of the earth’s radius (assuming the simple case of a circular orbit).

Now, an interesting and germane question, suppose the baseball rolls off of the table, what is the trajectory of the baseball? If you were standing nearby you would report that the ball fell directly off the table and straight down towards the earth’s center of gravity and landed on the floor. However, if you were plotting the trajectory in the sun origin coordinate system you would report that the baseball suddenly commenced spiraling towards the earth’s center of gravity for a very short distance and then stopped and resumed a constant speed orbit around earth but at a slightly reduced radius and at a slightly increased velocity. The important point is that while the nearby spectator viewed the ball as dropping straight towards the earth’s center of gravity, the sun spectator (so to speak) would report that the ball did not fall directly towards the earth’s center of gravity but rather spiraled toward it. Sounds strange, but …

To go a step farther, if the table supporting the ball and the earth supporting the table were to suddenly disappear, but the gravitational field persisted emanating from an invisible point source, the ball would still not drop directly towards the center of gravity, but would spiral around the point source of gravity at an increasing smaller radius, the so called “death spiral” of a satellite.

But why?

The fact is, that operating from the center of gravity you could not force the orbiting ball to drop perfectly straight towards you no matter how you try (according to Newtonian mechanics). You could increase the gravitational force to a degree that gives the appearance of a drop that was straight towards the center of gravity but upon closer examination you would find the path curved. If only you could get a component of force applied to the ball along its instantaneous direction of travel, then you could slow the ball and bring it to a stop from the perspective of the sun spectator. Once the balls was so stopped, then it would fall directly toward the gravitational center since it would no longer have a component of linear momentum that was not directed towards the center of gravity. Alas, you cannot apply such a force since the only force that you have available is the gravitational force and it is acting at a right angle to the trajectory of the ball and hence no component of that force can be applied along the direction of the instantaneous path of the orbiting ball.

This tells you why a baseball dropped over your left toe does not hit your right toe, both you and the baseball are orbiting together around the earth’s center of gravity, merely dropping the baseball does not abate its tangential momentum and hence the baseball must carry along its orbiting path with and over your left toe even as the radius of its orbit is slightly decreased.

The same physics applies to the baseball hit to right field, the ball, the baseball field and its players carry on together in their orbit around Earth, the ball travels towards the outfield within their mutual context of motion. The same applies to each air molecule, to a first degree they are each orbiting together around the earth with their own momentum, the path of each, instant by instant bent around the earth's gravitational center.

At the risk of torturing what is probably overkill but which some might find useful, I revisit the usual illustration of radial motion, that is, the ball on a string that is swung in a circle over your head. The point I make here is that you cannot stop the ball from circling around your head as you reel it in smoothly or with acceleration. Kinesthetically you can feel that the only way to stop the ball from circling is to put your hand in front of it.

Well, that is my understanding, hope it helps.