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.
What is your centripetal acceleration m/s?
To determine the centripetal acceleration at the equator, we need to consider the circular motion of the point on the Earth's surface due to its rotation.
The centripetal acceleration (a) is given by the formula:
a = (v^2)/r
Where:
v is the linear velocity of the point on the Earth's surface
r is the radius of the Earth
To find the linear velocity (v), we need to calculate the distance traveled by a point on the Earth's surface within one day (24 hours). The distance traveled is equal to the circumference of the Earth:
C = 2πr
Substituting the values:
C = 2π * 6371 km = 40075.99 km
To find the linear velocity (v), we divide the distance traveled by the time taken (24 hours), making sure to convert the distance from kilometers to meters and the time from hours to seconds:
v = (40075.99 km * 1000 m/km) / (24 hours * 60 min/hour * 60 s/min)
v = 463.04 m/s
Next, we can calculate the centripetal acceleration using the formula mentioned earlier:
a = (v^2) / r
a = (463.04 m/s)^2 / 6371000 m
a = 0.034 m/s²
Therefore, the centripetal acceleration at the equator of the Earth is 0.034 m/s².