Understanding Earth's Rotation and Linear Velocity

The Earth rotates on its axis, completing one rotation approximately every 24 hours. All points on the Earth's surface complete a full circle in this same amount of time. However, the size of this circle varies depending on the location's latitude.

Imagine a point on the Earth's surface. As the Earth rotates, this point traces a circular path around the Earth's axis. The radius of this circle is the perpendicular distance from the point to the Earth's axis of rotation.

The speed at which a point moves along this circular path is called its linear velocity of rotation. This linear velocity depends on the angular velocity of rotation (which is the same for all points on Earth) and the radius of the circular path traced by the point.

The formula for linear velocity ($v$) is given by:

\(v = \omega r\)

Where:

• \(v\) is the linear velocity
• \(\omega\) (omega) is the angular velocity
• \(r\) is the radius of the circular path

Since the angular velocity (\(\omega\)) is constant for all points on Earth, the linear velocity ($v$) is directly proportional to the radius ($r$).

Linear Velocity and Latitude Explained

The radius of the circular path traced by a point on the Earth's surface is largest at the equator (where the radius is equal to the Earth's equatorial radius) and decreases as you move towards the poles. At the poles (latitude 90° North or South), the radius is zero, and therefore the linear velocity is also zero.

This means that locations closer to the equator have a larger radius of rotation and thus a greater linear velocity of rotation compared to locations further from the equator (at higher latitudes).

Comparing Linear Velocity for the Given Cities

To find which city represents the greatest linear velocity of rotation, we need to determine which city is closest to the equator (latitude 0°).

Let's look at the approximate latitudes of the given cities:

Comparing the latitudes, Kampala at 0.3° North is very close to the equator (0° latitude). The other cities are located at significantly higher latitudes in the Northern Hemisphere.

• Kampala (0.3° N) is closest to 0°.
• Madrid (40.4° N) is further north.
• Stockholm (59.3° N) and St. Petersburg (59.9° N) are much further north.

Conclusion: City with Greatest Linear Velocity

Since Kampala is the city located closest to the equator among the given options, the radius of the circular path it traces as the Earth rotates is the largest. Consequently, Kampala represents the greatest linear velocity of rotation of the Earth among the given choices.

Revision Table: Earth's Rotation Concepts

Additional Information: Earth's Speed and Velocity

While all points on Earth rotate with the same angular velocity, their linear speed depends on how far they are from the rotation axis. This is similar to how points on a spinning merry-go-round move faster if they are further from the center.

The linear velocity at the equator is approximately 1670 kilometers per hour (about 1038 miles per hour). At a latitude of 45°, the linear velocity is about 70.7% of the equatorial velocity. At the poles, the linear velocity is 0 km/h.

This difference in linear velocity has implications for things like rocket launches, where launching from a location near the equator (like French Guiana) provides a boost from the Earth's rotational speed, requiring less fuel to reach orbit.