On planet Earth, at which location is the centrifugal force due to Earth rotation effectively zero?

Introduction / Context:
This question deals with basic physics applied to Earth rotation. As the Earth rotates, points on its surface experience a centrifugal effect that reduces the effective weight of objects compared with a non rotating planet. However, this effect is not the same everywhere. The question asks where on Earth the centrifugal force is zero.

Given Data / Assumptions:

• The Earth spins around its axis once in approximately twenty four hours.
• The options list the equator, the two tropics, the poles and the Arctic Circle.
• We want the location where the centrifugal force caused by rotation vanishes.
• We assume a basic understanding that centrifugal force depends on distance from the axis of rotation.

Concept / Approach:
Centrifugal force associated with circular motion can be expressed in simple form as proportional to radius times angular velocity squared. On a rotating sphere like Earth, the effective radius for this motion is the distance from the point to the axis of rotation. This distance is maximum at the equator and decreases toward the poles. At the poles, a point lies on the axis itself, so its radius for circular motion is zero and the centrifugal force becomes zero.

Step-by-Step Solution:
Step 1: Recall that centrifugal force depends on the distance from the axis of rotation. The greater the distance, the stronger the effect.Step 2: At the equator, the distance from the axis is maximum because points there move in the largest circle around the axis, so centrifugal force is greatest at the equator, not zero.Step 3: As we move toward the tropics and mid latitudes, the distance from the axis decreases but is still greater than zero, so there is still some centrifugal effect.Step 4: At the North Pole and South Pole, a point lies exactly on the axis of rotation, so the radius of rotation is effectively zero.Step 5: With radius equal to zero, centrifugal force goes to zero. Therefore, centrifugal force is zero at the poles.

Verification / Alternative check:
A simple way to verify is to imagine drawing circles of latitude on a globe. The equator is the largest circle and has the longest circumference, so points there travel the greatest distance in one day and feel the strongest centrifugal effect. Circles shrink in size as you approach the poles until they collapse to a point at each pole. A point that does not trace a circle but remains at one spot on the axis has no circular motion and therefore no centrifugal force.

Why Other Options Are Wrong:
The equator has maximum centrifugal force, so option A is the exact opposite of what the question asks. The Tropic of Cancer and Tropic of Capricorn are at mid latitudes where the distance from the axis is reduced but still significant, so centrifugal force is present but not zero. The Arctic Circle also lies at a high latitude but still describes a small circle around the axis, which means some centrifugal effect remains. Only the poles lie directly on the axis.

Common Pitfalls:
A common misunderstanding is to assume that extreme conditions, such as maximum rotational speed or maximum distance from the centre of Earth, must occur together at one place. Some learners incorrectly choose the equator because it has greatest linear speed due to rotation. The key is to focus on the distance from the axis of rotation rather than just thinking about speed. Once this is clear, it becomes easy to see that the poles are special points where rotational motion vanishes for a person standing there.

Final Answer:
On planet Earth, the centrifugal force due to rotation is zero at the poles.