Answer:
Engular velocity: [tex]w=1,24*10^{-3}/s[/tex]
Linear velocity: [tex]V=7905 m/s[/tex]
The time it takes:
[tex]t=5060s=84min[/tex]
Explanation:
The magnitude of the centripetal acceleration can be related to the angular velocity and radius as:
(1)[tex]a=r*w^{2}[/tex]
Solving for w:
(2)[tex]w=\sqrt{\frac{a}{r} }[/tex]
Replacing a=9,8m/s2 and r=6,375,000m:
(3)[tex]w=\sqrt{\frac{9,8m/s^{2}}{6375000m} }=1,24*10^{-3}/s[/tex]
And the angular velocity relates to the linear velocity:
[tex]V=w*r=1,24*10^{-3}/s*6375000m=7905 m/s[/tex]
The perimeter of the orbit is:
[tex]P=\pi *2*r=\pi *2*6375000m=40.05*10^{6}m[/tex]
The time it takes:
[tex]t=\frac{P}{V} =\frac{40.05*10^{6}m}{7905 m/s}=5060s=84min[/tex]
