Answer to Question #80549 in Mechanics | Relativity for Ankit

Question

What should be the angular velocity of the earth such that a person of mass 80 kg
standing on the earth at the equator would actually fly off the earth?

Answer 1

A person will fly off the earth if centripetal force will be equal to the force of gravity.
Centripetal force is F_c=mω^2 r, where m – is mass of a person,  - is angular velocity, and r – is Earth’s radius.
Gravity force is F_g=mg, where m – is mass of a person, g is acceleration of gravity.
F_c=F_g
mω^2 r=mg
ω=√(g/r)=√(9.8/6378245)=0.0012 rad/s
Answer
If the angular velocity of the Earth will be 0.0012 rad/s , a person of mass 80 kg standing on the Earth at the equator would actually fly off the Earth.