Dynamics of Circular Motion (Centripetal Force and Centrifugal Force)

Whenever a body performs circular motion, SOME resultant real force must be acting on it, directed towards the centre of the circle -- this resultant force is called the centripetal force (CPF), and its magnitude is $CPF=mr\omega^2=\frac{mv^2}{r}$. It is important to understand that 'centripetal' is not the NAME of a distinct kind of force (unlike, say, gravitational or electromagnetic force); it is simply an ADJECTIVE describing the direction (towards the centre, 'centre-seeking') of whatever real force or combination of real forces happens to be providing that particular instance of circular motion -- string tension for a whirled stone, gravity for an orbiting satellite, friction for a car turning on a flat road, and so on. The resultant of all real forces on a body in circular motion is ALWAYS centripetal (this can be written as $\sum \vec{F}_{real} = -mr\omega^2\hat{r}$), but the converse is not automatically true: a resultant force directed towards a fixed point does not by itself guarantee circular motion unless the body's velocity is also correctly matched to be tangential to a circular track (a simple harmonic oscillator, for instance, also always has its restoring force directed towards a fixed centre, yet moves back and forth along a straight line, not a circle). …