Apply the Equations of motion (rotational)
#omega=omega_0+alphat#..........#(1)#
#Deltatheta=omega_0+1/2alphat^2#..............#(2)#
The initial angular velocity is #omega_0=?#
The time is #t=4s#
The angle is #Deltatheta=162rad#
The final angular velocity is #omega=108rads^-1#
Substituting those values in equations #(1)# and #(2)# and solving for #omega_0#
#Deltatheta=omega_0+1/2*(omega-omega_0)/2*t^2#
#162=omega_0+1/4*(108-omega_0)*16#
#162=omega_0+432-16omega_0#
#15omega_0=432-162=270#
#omega_0=270/15=18rads^-1#
The angular acceleration is
#alpha=(omega-omega_0)/t=(108-18)/4=22.5rads^-2#
The tangential acceleration is
#a_("tangential")=r*alpha=0.12*22.5=2.7ms^-2#
The velocity is tangential #v=omegar# and the angle is #=0^@#
The total acceleration is
#a=sqrt(a_T^2+a_C^2)#
The centripetal acceleration is #=a_C#
And
#tanphi=a_T/a_C#
