Answer:
[tex]\omega = 49.86*10^{-3}rad/s[/tex]
Explanation:
We start converting to SI units,
A mile = 1609m
[tex]L=17mi=27000m[/tex]
[tex]D=4.99mi=7884m[/tex]
We know that the expression, which can relate linear acceleration and angular velocity is given by,
[tex]a_c = r\omega^2[/tex]
Where [tex]\omega[/tex] is the angular velocity
r=radius
[tex]a_c =[/tex] linear acceleration,
Re-arrange for \omega,
[tex]\omega = \sqrt{\frac{a_c}{r}}[/tex]
Our acceleration is equal to the gravity force, so replacing,
[tex]\omega = \sqrt{\frac{9.8}{(7884/2)}}[/tex]
[tex]\omega = 49.86*10^{-3}rad/s[/tex]
