An object of mass 5 kg moves at a constant speed of 6 m/s in a circular path of radius 2m. Find the magnitude of the object's acceleration and the net force responsible for its motion.

Explanation

By definition, an object moving at constant speed in a circular path is undergoing uniform circular motion. Therefore, it experiences a centripetal acceleration of magnitude `v^(2)//r`. Which is always directed toward the center of the circle.
`a_(c)=(v^(2))/(r)=((6m//s)^(2))/(2m)=18m//s^(2)`
Newton's second Law, coupled with the equation for centripetal acceleration, gives:
`F_(c)=ma_(c)=m(v^(2))/(r)`
This equation gives the magnitude of the force. as for its direction, remember that because F=ma, the directions of F and a are always the same. since centripetal acceleration points towards the center of the circular path, so does the force that produces it. therefore, it's called centripetal force. the centripetal force acting on this object has a magnitude of `F_(c)=ma_(c)(5kg)(18m//s^(2))=90N`.