Question #e6799

1 Answer
Feb 22, 2018

Answer:

See the explanation below

Explanation:

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#