The linear velocity of rotation of the Earth varies depending on the latitude of a location. In general, the linear velocity is greatest at the equator and decreases as you move towards the poles. The correct answer, option 1, Kampala, Uganda, is located very close to the equator, which means it experiences the greatest linear velocity of rotation compared to the other cities mentioned in the options.

Option 2, St. Petersburg, Russia, is positioned at a higher latitude than Kampala, so it would have a lower linear velocity of rotation. Option 3, Madrid, Spain, is even further from the equator, so its linear velocity of rotation would be less than that of St. Petersburg. Option 4, Stockholm, Sweden, is the northernmost city among the options, and as such, it would have the lowest linear velocity of rotation.

In summary, the closer a city is to the equator, the greater its linear velocity of rotation. Therefore, Kampala, Uganda, which is located near the equator, represents the greatest linear velocity of rotation of the Earth among the given options.