centripetal  acceleration  and  centripetal  force   Consider a particle  moving  in  a circular path at a constant speed. The velocity  of  the  particle  is constantly changing in direction, even  though  its  magnitude  remains  the  same. Therefore the particle is constantly accelerating. This acceleration is called centripetal  acceleration. The magnitude of this acceleration is given by

a = v²/ r

where r is the radius of the circular path, and v its velocity.

The  force required to produce this acceleration is directed towards the center, and is called the centripetal force. It is given by,

F_centripetal = m v²/ r

where  m  is  the mass of the particle. The centrifugal force is the reaction force of centripetal force.

F _centrifugal = - F _centripetal

Example  of  systems  under  centripetal  force:  An artificial satellite  of  mass  m orbiting   around earth. The centripetal force is provided by the gravitational pull of the earth.