Why do pendulums swing more slowly at the equator?

In summary, the longer period at the equator than at other latitudes is due to the Earth's oblateness and the difference in R would account for the difference in the period. The period of a pendulum is 2\pi\sqrt{l/g} so if g is less the period (time for a swing) becomes longer. g varies by a few percent around the world dependign on the density of local rocks. The direct and indirect effect of Earth's rotation and altitude are the leading factors in variations in gravitational acceleration.
  • #1
Blue_Jaunte
21
0
I was asked this recently and the only explanation I could come up with was that the Earth is oblate and the difference in R would account for the difference in the period. Is this wrong? Is this even a real phenomenon (the longer period at the equator than at other latitudes)?
 
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  • #2
The period of a pendulum is [tex]2\pi\sqrt{l/g}[/tex] so if g is less the period (time for a swing) becomes longer. g varies by a few percent around the world dependign on the density of local rocks.
Tt also depends on latititude because, as you said, the Earth bulges at the equator and so you are futrther from the centre of the Earth and the force of gravity is slightly lower.
 
  • #3
A pendulum swings slower at the equator because the Earth is rotating. The rotation acts to make the pendulum swing slower directly and indirectly. The direct effect is easiest to envision from the perspective of the rotating Earth-fixed frame. In this frame, a centrifugal force of [itex]r\omega^2[/itex] arises directly from the Earth's rotation. At the equator, this direct effect alone amounts to 0.034 m/s2. There is of course no centrifugal force at the poles.

For those who insist there is of course no such thing as centrifugal force anywhere, you will be forced to look at things from the perspective of an inertial frame. I leave this as an exercise to you curmudgeons. Keep in mind that the answer you get will be the same.

I also cited an indirect effect that results from rotation. The Earth's rotation makes the Earth bulge at the equator. As mgb_phs noted, this makes things at the equator further from the center of the Earth. Together, the direct and indirect effect act to make Earth's gravitational acceleration 9.780 m/s2 at the equator. This is about 0.052 m/s2 less than it is at the poles, or a 0.53% reduction in the gravitational acceleration. The direct effect accounts for about 65% of the difference.

The next leading factor in variations in gravitational acceleration after Earth rotation and the J2 non-spherical harmonic term is altitude above the spheroid. Things weigh 0.28% less at the top of Everest than they do at sea level at the same latitude. Local variation in density is a distant fourth.
 

1. Why do pendulums swing more slowly at the equator?

Pendulums swing more slowly at the equator due to the Coriolis effect. This is caused by the rotation of the Earth, which creates a force that affects the pendulum's motion.

2. How does the Coriolis effect affect pendulum swing at the equator?

The Coriolis effect causes the pendulum's path to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This deflection results in a slower overall swing at the equator.

3. Does pendulum length affect its swing at the equator?

Yes, the length of the pendulum does affect its swing at the equator. The longer the pendulum, the slower it will swing due to the increased force of the Coriolis effect.

4. Are there any other factors that contribute to slower pendulum swing at the equator?

In addition to the Coriolis effect, the Earth's shape and its gravitational pull at the equator also play a role in slowing down the pendulum's swing. The equator is the widest part of the Earth, so there is more distance for the pendulum to cover in one swing.

5. Can pendulums swing at the same speed at the equator as they do at other latitudes?

No, pendulums cannot swing at the same speed at the equator as they do at other latitudes. The Coriolis effect and other factors, such as the Earth's shape and gravitational pull, make the pendulum swing slower at the equator compared to other latitudes.

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