Why does the speed of earth’s rotation not affect us?
February 20th, 2023
Because the rotation speed isn’t fast enough.
The centrifugal force is the fictitious force seen in a rotating reference frame.
It has a magnitude of
##F_C=momega^2r##
The angular speed has a value of
##omega=(2pi)/(24h)=pi/(12*60*60sec)=7.27*10^(-5)(rad)/s##
Earth’s radius is
##r=6,37*10^6m##
So
##F_C=m(7.27*10^(-5)(rad)/s)^2 6,37*10^6m=m*0,034m/s^2##
Compared to gravitational force
##F_C/(mg)=(0,034)/(9,81)=0,0034~~10^-3##
The centripetal force is one thousand weaker than the gravitational force, so we don’t see its effect in the most situation. For a situation in which this effect was important look for the first Falkland’s Battle.