the rotation of earth is a period of 86164 seconds. the earth has a radius of 6380 km. how fast would you be moving due to earths rotation at the equator? also how fast would you be moving at a latitude of 27 degrees north of the equator? also calculate the centripetal acceleration that youre experiencing as a result of the rotation of the earth
To calculate the speed at the equator due to the rotation of the Earth, you need to use the formula:
Speed = Distance / Time
Given that the rotation period of the Earth is 86164 seconds, which represents the time taken for the Earth to complete one full rotation on its axis, you can calculate the speed at the equator as follows:
Speed = 2 * π * Radius / Time
Where:
- π is the mathematical constant Pi, approximately equal to 3.14159
- Radius is the radius of the Earth, given as 6380 km
- Time is the rotation period of the Earth, given as 86164 seconds
Substituting the values, we have:
Speed = 2 * 3.14159 * 6380 km / 86164 s
Calculating this expression gives us the speed at the equator due to Earth's rotation.
To calculate the speed at a latitude of 27 degrees north of the equator, you can use a similar formula, but you also need to consider the change in circumference at that latitude. The formula becomes:
Speed = 2 * π * (Radius * cos(Latitude)) / Time
Where:
- Latitude is the angle of the latitude, given as 27 degrees
- The rest of the variables have the same meaning as before
Substituting the values, we have:
Speed = 2 * 3.14159 * (6380 km * cos(27°)) / 86164 s
Calculating this expression gives us the speed at 27 degrees north of the equator due to Earth's rotation.
To calculate centripetal acceleration resulting from Earth's rotation, you need to use the formula:
Acceleration = (Velocity^2) / Radius
Where:
- Velocity is the speed at which you are moving due to Earth's rotation
- Radius is the radius of the Earth, the same value as before
Substituting the respective velocity values obtained from the previous calculations into this formula will give you the centripetal acceleration you're experiencing.