Acceleration due to Earth rotation
Physics problem and solution
What is the centripetal acceleration of a person standing on our planet at latitude 30 deg, caused by the rotation of the Earth? Earth’s radius R=6371km. This is a mean value of the Earth’s radius, which is accurate enough for the purpose of our problem.
Given:
R = 6371km – mean radius of Earth at Equator
T = 24 h – period of motion, we assume it is known to us.
Looking for:
a = ? – centripetal acceleration at altitude 30 deg.
To calculate this value we must find the radius of circular motion for the point on Earth at latitude 30 deg, we name it r.
From the formulas describing circular motion we have
(1)
From trigonometry we find see
r = Rcos30 (2)
Substituting the numbers into formula (2) we get
r = 5517.5 km = 5517500 m
Substituting this value and value for period T into formula (1) we get
This centripetal acceleration due to Earth’s rotation is about 327 times smaller than gravitational acceleration g.