Why is it that the Coriolis force is maximum at the poles where there is zero rotation and zero at the equator and centrifugal force zero at poles and high at the equator?
The Coriolis Force is not a "force", as such, but an illusion created by the rotation of the Earth. At the Poles, where there is no sideways motion of the ground supporting a pendulum, the force appears to be largest because as the Earth turns around you (because of its rotation) there is nothing to hide that rotation relative to you. But at the Equator, you and your pendulum are being dragged around the Earth at over 1000 miles/hour, which twists the support of the pendulum in a way that hides the rotation of the Earth from your view. The "torque" on the top of the pendulum support is largest at the Equator, but since you can't see any rotation, it appears that the "force" is zero.
In reality, watching a pendulum swing back and forth at the Equator, as it moves northward it twists a smidgen toward the right, while as it moves southward it twists a smidgen to the left (as a result of the torque acting on its support), because the effect is in the opposite direction in the northern and southern hemispheres; and although you could see each of the two small twists with a very high magnification, since they exactly cancel each other, you can't detect any deviation from a straight-line motion with ordinary instruments.
I don't know whether it would help, but my website has a page about "Coriolis Effects" with both a discussion and diagrams I created for my astronomy students, and links to two online videos. Unfortunately, since I wrote the page over 20 years ago, the top one, though it still goes to the linked page, doesn't go directly to the video, so you have to click on the .mpeg link to download the short playground demo (I'll fix that ASAP, but probably not before you read this). However, the link to the outstanding film "Frames of Reference" still goes directly to the Internet Archive's copy. The text I wrote is probably a more useful discussion of the pendulum's demonstration of the Coriolis Effect, but the 1950's movie is well worth watching, even though it only deals with the Effect near the end. (The URL for the page I wrote is https://cseligman.com/text/planets/coriolis.htm )
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