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 x 106 m, determine the speed and centripetal acceleration of a person situated (a) at the equator and (b) at a latitude of 76.0 ° north of the equator.

Answer 1

ω=2π/T= 2π/24•3600= 7.27•10⁻⁵rad/s
1) equator
v= ω•R=7.27•10⁻⁵•6.38•10⁶ = … m/s
a=ω²•R= … m/s²
2) at a latitude of 76.0 ° north of the equator
r=Rcos76.6⁰=6.378•10⁶•cos76.6⁰=1.48•10⁶ m
v= ω•r= … m/s
a=ω²•r= … m/s²