Question

A body of mass 2 kilograms moves on a circle of radius 6 meters, making one revolution every 8 seconds. find the centripetal force acting on the body.

Answer 1

The length of one revolution is equal to the perimeter of the orbit. Since the radius is r=6 m, the perimeter is

`L=2 \pi r = 2 \pi (6 m)=37.7 m`
The object completes one revolution every 8 seconds, so its frequency of revolution is

`f= (1)/(8 s)=0.125 Hz`
and the angular frequency is

`\omega = 2 \pi f=2 \pi (0.125 Hz)=0.785 rad/s`

So now we can find the centripetal force acting on the body, which is equal to

`F=m \omega^2 r = (2 kg)(0.785 rad/s)^2(6 m)=7.4 N`