The length of one revolution is equal to the perimeter of the orbit. Since the radius is r=6 m, the perimeter is
[tex]L=2 \pi r = 2 \pi (6 m)=37.7 m[/tex]
The object completes one revolution every 8 seconds, so its frequency of revolution is
[tex]f= \frac{1}{8 s}=0.125 Hz [/tex]
and the angular frequency is
[tex]\omega = 2 \pi f=2 \pi (0.125 Hz)=0.785 rad/s[/tex]
So now we can find the centripetal force acting on the body, which is equal to
[tex]F=m \omega^2 r = (2 kg)(0.785 rad/s)^2(6 m)=7.4 N[/tex]
