As denizens of the surface of a spinning planet, we are always in uniform circular motion. Imagine you are in Nairobi (on the Earth's equator) at noon on a Monday. Answer the following questions only considering the rotation of the earth and NOT the Earth's circular motion around the sun. The radius of the earth is 6371 km. A day is 24 hours.
How fast are you travelling in m/s ?
To determine how fast you are traveling at noon on a Monday in Nairobi, considering only the rotation of the Earth, you need to calculate the speed of rotation at the Earth's equator.
- The circumference of a circle (the path traveled by a point on Earth's equator in one rotation) is given by the formula C = 2πr, where r is the radius of the Earth.
- Plugging in the given radius of the Earth (6371 km), the circumference is C = 2π(6371 km).
- However, the speed needs to be calculated in meters per second, so we need to convert the distance from kilometers to meters. Since 1 kilometer equals 1000 meters, the circumference becomes C = 2π(6371 km × 1000 m/km) = 2π(6,371,000 m).
- A day comprises 24 hours, and there are 60 minutes in an hour and 60 seconds in a minute. Therefore, there are 24 hours × 60 minutes × 60 seconds = 86,400 seconds in a day.
- To calculate the speed, we divide the distance traveled (circumference) by the time (duration of a day in seconds): Speed = C / (24 hours × 60 minutes × 60 seconds) = 2π(6,371,000 m) / (86,400 s).
Calculating this expression, the speed at which you are traveling at noon on a Monday in Nairobi considering only Earth's rotation is approximately 465.1 m/s.