Write an expression for the resultant acceleration of a particle having non uniform circular motion.

Explanation

Consider a particle moving with variable speed v in a circular path of radius r. As speed of particle is variable, it has tangential component ofacceleration `a _(T)` and centripetal acceleration ` a _(c)` due to change in direction of motion.
`a _(T) = ( dv)/(dt) = r alpha and a _(c) = (v ^(2))/( r ).`
The resultant acceleration of paticle is
`a = sqrt (a _(T) ^(2) + a _(c) ^(2))= sqrt (( r alpha ) ^(2) + ((v ^(2))/( r )) ^(2))= sqrt (r ^(2) alpha ^(2) + (v ^(4))/( r ^(2)))`