Let us consider a point mass - for reasons of simplicity - on a string
swinging around in a circle (e.g. in vacuum, with constant speed). This
mass experiences the centripetal force Fp which
is directed inward, towards the center of the circle.
However the hand, holding the string "feels" an outward directed force
- according to Newton´s third law (actio=reactio). This "reactive" forceFR
has the same magnitude as the centripetal force - but opposite direction
- and applies at the hand holding the string. This reactive force is not
the centrifugal force, because the centrifugal force applies at the center
of mass of the body.
The necessity to consider a centrifugal force can best be understood
from the following:
Assume a mass on a spring that swings around in a circle with constant
velocity. This spring will show some tension.
From the position of an observer in a reference system which rotates
with the mass one finds:
The necessity to consider the centrifugal force simply arises from the fact, that the reference system fixed to the earth, within which we consider bullet motion is rotating.