Pendulum Predicament

[jordan]

I saw a few minutes of Jeopardy tonight and one of the questions had an answer along the lines of the following: A pendulum takes longer (or was it shorter?) to make a 360^o rotation the nearer it gets to the equator. My question is simple: why?

[bloodhound]

360 degree which way? horizontally or vertically

[jordan]

Horizontaly.

[bloodhound]

i cannot answer this question. but it may have something to do with the Coriolis Force.

The same force that makes the water do down the sink in different directions in north and south

[Freeman]

Oh, a tangent question on pendulems! Is it theoretically possible to have a pendulum move by the force of earth's gravity?

[jordan]

Isn't that how they move now?

[JaKiri]

i cannot answer this question. but it may have something to do with the Coriolis Force.

The same force that makes the water do down the sink in different directions in north and south

 

This is your answer.

[Gant]

Actually its the movement of the earth,,not just the gravity. The Earths rotation exacts a centrifical force onto the pendulum and gravity does the obviouse,,,keeps it here on earth. Anyways,,,the centrifical forces are stronger nearer the poles than on the equator. Kinda like how the center of a record seems faster than the outside of a record. Same kinda thing only grander.

 

Actually,,i dunno,,just thought i'd take a wack at it:)

[Dave]

Doubt that has much (if anything) to do with it. If you were to do it in a stationary gravitational field then the pendulum would swing exactly the same.

[jordan]

This is your answer.

Care to expand or should I just go google it?

[JaKiri]

Care to expand or should I just go google it?

 

Well, it's sort of the answer. It's to do with differing rotation speeds of the earth. Google for Foucault's Pendulum. No, not the book.

[ed84c]

jeopardy, what programme is that?

[ed84c]

an answer could be allthough im almost sure its wrong, that everything is faster at the equator due to the nature of time itself. There is a slight bulge and as a result we are further away from the earths center of gravity resulting in time going faster. That probably would be a difference of <a pico second though.....

[LucidDreamer]

Ok, i have been thinking about this since last night, I didn't want to look it up because I wanted to figure it out myself. I believe I have the answer. To really understand this you must visualize it.

 

If you were at the North Pole and you set a pendulum in motion by pulling back on it as you walked towards the South Pole you would create a motion along an axis from the North Pole to the South Pole (a vertical path). If you drew a line underneath you representing the pendulum path you would be able to detect any change in its pattern. As the day grew later you would notice that the line that the pendulum traced was moving and was no longer tracing the same line but was actually changing. At six hours you would notice that the pendulum was tracing a pattern perpendicular to its original path, at 12 hours it would be vertical, 18 hours perpendicular and at 24 its pattern would be vertical again and would have done a 360 in one day. Basically, since the earth is spinning but the pendulum is not attached to the earth except by a string that does not force it to rotate it, the world spins underneath the pendulum.

 

If you set up the pendulum experiment at the equator and set its motion vertical from the north pole to the south pole the and traced its pattern over the day or even a year the pattern would never change. The earth would be spinning underneath it traveling north to south while the earth is moving east to west.

 

What about if you set up a pendulum somewhere in between the North Pole and the equator. Let’s set up our experiment just 50 miles south of the North Pole. This time it would rotate like it did at the North Pole but it would take just a little bit longer than a day. As you get farther from the north or south poles and approach the equator the amount of time it takes to change its motion 360 would increase until you reach the equator and it would no longer change.

 

Now, the reason for this. The pendulum swings because of the force of gravity. The force of gravity of the earth is centered in the center of the earth. The earth spins along an axis going from the North Pole to the south. When the pendulum is set in motion at the equator the motion of the pendulum going from north to south and the axis of the earth spinning are exactly perpendicular. But if you move the pendulum say half way in between the North Pole and the equator they are no longer perpendicular.

Think of it like this. If I take a globe or and ball and drove a spike through it from the north to the south pole and I had another spike with the restriction that it could only be held perpendicular to the spike and then decided to drive it through the spot where I set up the pendulum it would not go through the center of the globe. Since I set the pendulum halfway in-between the north pole and the equator and I can only drive my second shaft through the globe perpendicular to the north and south pole it would be driven into the globe on the upper hemisphere half way to the pole.

 

But the pendulum is not attracted to the depth of the earth directly below it 1/4 of the way up the world. It’s attracted to the center of the earth 1/2 way between both poles. So the plane that is created when you drove the spike in perpendicular to the poles and the plane created if you went directly to the center of the earth are not the same and they create an angle between them. As the earth spins this angle causes the pendulum to spin around in its path.

 

You can really see this if you take a large ball. Put a dot the top and bottom for the poles and draw a line halfway around to create the equator. Place the pen halfway between the equator and the North Pole. If you hold the pen perpendicular to the poles and spin the ball along the north and south axis you will draw a circle halfway between the North Pole and the equator. But if you hold the pen towards the center of the ball and spin it along the north and South Pole you will create a spiral and you will understand the twisting motion that causes a pendulum to change its path.

 

Sorry about the length of this thread.

[ed84c]

ok time dialation theory out the window then

[swansont]

an answer could be allthough im almost sure its wrong, that everything is faster at the equator due to the nature of time itself. There is a slight bulge and as a result we are further away from the earths center of gravity resulting in time going faster. That probably would be a difference of <a pico second though.....

 

Actually the bulge of the earth and the corresponding reduction in the gravitational redshift is compensated by the time dilation due to the rotation speed. Clocks on the geoid all tick at the same rate.