Is the Earth rotating?

A little physics quiz..

[Go2]

I read about this quiz in the latest issue of a popular science magazine. I couldn't solve it but I think it is an interesting experiment.

We all know that the Earth is rotating on its axis. In order to prove that a stone is dropped from a very high tower. If the earth really is rotating the ground should have rotated to the east while the stone is in a free fall, and the stone should hit the ground a little bit west of the tower.

Is this hypothesis correct? If not, where should the stone land?

[lawman]

WARNING - I Was A History Major. Take That Into Account If I'm Wrong

I assume the tower is attached to the earth. Therefore it is turning with the earth. The tower has the same forward momentum as the earth. Unless acted on by some other force, the stone will drop (or appear to drop) straight down.

Alrighty physics majors, straighten me out.

lawman

[Mardi_Gras]

Since the tower would be rotating at the same rate as the earth, and the two would rotate together as the stone fell, I would expect the hypothesis is not correct.

<<guess we're thinking alike, lawman ;)>>

[locke]

IIRC, that hypothesis is wrong. if the stone fell in a vacuum (ie there was no wind/air resistance to cause it to change its course) it should fall straight down, because it is rotating with the earth.

<edit> i must type too slow </edit>

[Key_Master]

One of the reasons why there is wind is because of the drag the atmosphere has on the rotating earth. Therefore, it's logical to conclude that the stone falling through the air will also be effected (ever so slightly).

[digitalghost]

Similar in theme:

Foucault's Pendulum [stenomuseet.dk...]

[Visi]

Would answer the question, but was walking along the other day downtown, when was hit on the head by a rock. Memories shot and brains not functionibg at full speed yet:):)

[victor]

While we're on the subject and the physics majors are about, can you solve an old problem for me?

I learnt at school that if you drop (in a vaccuum etc) a light object (say an apple) and a heavy object (say a year's worth of AOL CDs) they both fall at the same speed. The weight of the object is irrelevant. The speed is due to the earth's gravity.

Similarly, if I drop my two objects on the moon, they'll fall at the same speed as each other, but a different speed to that on earth. The speed is due to the moon's gravity.

That's okay so far.

But....
Surely it follows that if I dropped an apple and the moon onto the earth they would fall at one speed. And if I dropped an apple and the earth onto the moon they would fall at a different speed.

How can that be?

[Go2]

lawman, you are thinking along the lines I did. However, in order to solve the question of the rotation of the earth you have to consider a few more aspects of rotating motion...

Anyone who solves this quiz will get a prize. Brett, can you donate a membership in the WebmasterWorld Supporters Forum?

[Key_Master]

Coriolis Force [windpower.dk]

[Mardi_Gras]

Brett, can you donate a membership in the WebmasterWorld Supporters Forum?

Not sure Brett wants to give up memberships in return for solving puzzles - especially when the puzzle is not his own. He does have bills to pay:)

[mivox]

Is the Earth rotating?

What a silly question.

Much as pizza dough rotates on the skilled hand of the pizzamaker tossing a fresh crust, so our flat earth spins atop the unseen hand of the Universe.

You spherical-earth people are so behind the times.

[korkus2000]

I agree with mivox. My grandmother always told me the earth may be round like a plate but not like a ball.

[digitalghost]

>>so our flat earth spins atop the unseen hand of the Universe

No, no, no, the earth is round, we just live on the inside of the sphere, the sun is really very tiny. Centrifugal force keeps our feet on the ground...

No arguments about centrifugal force, we know it's not really a force, just inertia. ;)

[mivox]

I like pizza more.

[lorax]

The stone will actually hit the side of the tower. Because the stone has the eastward momentum of the tower at it's furthest point from the earth (think of the speed of an object on the end of 24" string as you spin it in air versus the speed of the same object 20" to your hand) when the stone is released it falls in an arc towards the tower because the lowest part of the tower is moving at a much slower speed than the stone. Hows that!?

[digitalghost]

>>If the earth really is rotating the ground should have rotated to the east while the stone is in a free fall, and the stone should hit the ground a little bit west of the tower.

If that hypothesis proves, I'm buying a helicopter tomorrow. I won't need to actually fly it anywhere, just lift off and wait until the earth spins beneath me...

Unfortunately, the earth and its atmosphere are moving at the same speed.

[brotherhood of LAN]

hey if its a 50 mile tower the stone wont drop anywhere? ;)

Gravity included, lorax sounds bang on t ome

[ggrot]

I'm not sure if Lorax is saying the same thing as me, but on a rotating object (the earth), all parts of the object are accelerating towards the center(centrifugal force). On earth there is also the gravitational force. As soon as the stone is released, the centrifugal force stops applying to it and it's initial velocity is tangential to the earth, while the earths velocity is changing direction due to the centrifugal force(albiet a small change).

Thus the rock and tower have the same initial velocity tangential to the earth, but the tower has both centrifugal force AND gravity pulling it down, whereas the rock has only gravity. Thus the earth does rotate 'under' the rock and the rock will not hit the dead center of the tower. It would be a small difference though unless the tower is very high, so it is unlikely that the rock will hit the tower wall.

[ggrot]

But if you assume that the air acts on the rock as well, then it could provide the same centrifugal force due to the shearing between it and the earth at the crust.

[digitalghost]

[calstatela.edu...]

Scroll down to Day 2.

[Visi]

Finally an explanation of why the rock hit me on the head:)

[mack]

I once saw this theory tsted in practice using a slightly similar method.

A large room with a rope suspended from the center. A large weight is atatched to the end of the rope. The rope is then taken to a point marked with a red dot and released. Because of the size of the weight and the lenghth of the stroke there is enough momentum to keep the pendulim effect going for almost 30 mins. Within about 10 mins there is a notiable effect in the swing and the weight now swings over an area to the side of the red dot but still swings in streight motions back and forth... so in effect the world has turned and the weight has remained in the same place.

[digitalghost]

Yep Mack, that's Foucault's Pendulum, and an excellent book by Umberto Eco, also wrote Name of the Rose. ;)

[Key_Master]

A marble dropped from a tower 328 feet (100 meters) tall at latitude 45 degrees will be deflected a little over half an inch.

The Coriolis Force [216.239.57.100]

[Go2]

..because the lowest part of the tower is moving at a much slower speed than the stone

lorax was, as far as I can tell, closest to solving the quiz. In a rotating motion an object will move at a higher (tangential) speed the longer the distance is from the axis. As a result the stone will travel at a higher speed eastbound when it is dropped, compared to the base of the tower. At the same time gravity pulls the stone down, and hence the stone will actually hit the ground a little bit east of the tower.

Scientific experiments also consistently show that stone lands a little bit east of the center line.

[lawman]

I told ya I was a history major.

[mivox]

S'okay... I was a PoliSci major, which probably explains the pizza thing somehow.

[digitalghost]

Philosophy major, so I just question the fact that the earth, the rock the tower and the observers actually exist... ;)