Question

The fact that the Earth rotates gives people in New York a linear speed of about \(335 \mathrm{~m} / \mathrm{s}(750 \mathrm{mi} / \mathrm{h})\). Where should you stand on the Earth to have the smallest possible linear speed? The greatest possible linear speed?

Short answer

Maximum speed at the equator; minimum speed at the poles.

Step-by-step solution

Understand Linear Speed on Earth

Linear speed on Earth due to its rotation depends on the distance from the axis of rotation, i.e., how far you are from the poles. The linear speed reaches its maximum at the equator and is zero at the poles.

Determine Maximum Linear Speed Location

The maximum linear speed is experienced at the equator, where the rotational speed of the Earth is directly translated into the maximum linear displacement per unit time.

Determine Minimum Linear Speed Location

The minimum linear speed, which is actually zero, is experienced at the poles. At these points, the rotational movement does not result in any linear displacement.

Key concepts

Linear Speed

Linear speed refers to how fast an object is moving along a path due to the Earth's rotation. It's important to consider that linear speed on Earth varies depending on your geographical location. This happens because Earth is a sphere that rotates once every 24 hours. People located on different parts of the Earth will travel different distances within that time. Those further from the axis of rotation will cover more ground and hence have a greater linear speed.

Imagine standing on a merry-go-round. If you're close to the center, you aren't moving much even as the ride spins. However, if you're standing at the edge, you're swooping around quickly. It's the similar idea—areas on Earth that are further from the axis, like the equator, have higher speeds compared to regions that are closer, like the poles.

Axis of Rotation

The axis of rotation is an imaginary line around which the Earth spins. It runs from the North Pole to the South Pole, passing through the Earth's center. Understanding this concept is crucial to grasp how the Earth's rotation influences linear speed. The Earth completes one full rotation around this axis every 24 hours, leading to the changes in linear speed at various locations on Earth.

The closer you are to the axis of rotation, the shorter the circular path you traverse in a given time, and hence your linear speed is also less.

• At the equator, you're the furthest from the axis, leading to greater speeds.
• Near the poles, you're almost on the axis, so there's minimal movement.

This is why your linear speed decreases as you move from the equator towards the poles.

Equator

The equator is an imaginary line that circles the Earth, dividing it into the Northern and Southern Hemispheres. Positioned equidistant from the poles, it marks the midway line of the Earth's latitudinal lines. This location has a unique significance concerning linear speed.

At the equator, the linear speed is at its maximum due to the maximum possible distance from the axis of rotation. Every complete revolution of the Earth means covering the largest possible circumference. Or in other words, the equator stretches the longest path around the Earth.
People standing on the equator experience the fastest speeds—about 1,670 km/h or 460 m/s—since they are moving along the widest possible circle as Earth rotates.

Poles

The North and South Poles are the locations at the very ends of the Earth's axis of rotation. They are positioned such that any movement due solely to the Earth's rotation results in essentially no linear speed. This is due to their position on the axis of rotation.

At these points, Earth’s rotational motion affects linear displacement minimally. This means that if you were standing directly on the North or South Pole, you would literally just spin in place as the Earth rotates, without traveling any distance around the surface of the globe.

• Your linear speed at the poles is zero.
• The poles are fixed points regarding Earth's surface rotation, creating no path circulation.

This lack of movement at the poles starkly contrasts with the rapid spinning experienced by those on the equator.