The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the earth is a sphere with a radius of 6.38 106 m, determine the speed and centripetal acceleration of a person situated

Question

(a) at the equator and
m/s
m/s2
(b) at a latitude of 40.0° north of the equator.
m/s
m/s2

Answer 1

(a) First of all, there are
T = 86,400 seconds
in a day. The distance travelled by a person at the equator in a day is

X = 2 pi R = 4.01*10^7 m
For the speed, use
speed V = X/T
acceleration a = V^2/R

(b) T is the same, but the radiis of the circle travelled at latitude 40 N as the earth turns once is
R' = R cos 40
use the same formulas as on (a), but with
X' = 2 pi R'
V = X'/T, and
V' = X'/T
and a = V'2/R'