A body  moves on  a horizontal  circular  road  of radius r, with a tangential acceleration ${\alpha }_t$ The coefficient   of friction between  the body  and the road surface is $\mu$ It  begins to slip  when  its speed is v 

The tangential acceleration$a_r$  and the radial acceleration $a_r=v^2/r$being mutually  perpendicular, have  a resultant  acceleration  $a={[a_t^2+{(v^2/r)}^2]}^{1/2}$The only  horizontal force on the body  is the  force of  friction $F=\mu mg$= ma, acting  in the direction  of  a