I need the angular speed and radial speed. You must show all of your work to rec

Question

I need the angular speed and radial speed.  You must show all of your work to recieve points.  Must have both answers.  Thanks in advance.  

EML 3217

Consider a collar with mass m that is free to slide with no friction along a rotating arm, which has negligible mass. The system is initially rotating with an angular velocity omega 0 while the collar is kept a distance r0 away from the z axis. At some point, the restraint keeping the collar in place is removed so that the collar is allowed to slide. If no external forces and moments are applied to the system, what are the radial speed and the total speed of the collar when it reaches the end of the arm? Use m = 2.6 kg, omega 0 = 1.2 rad/s, r0 = 0.6 m, and d = 1.9 m.

Explanation / Answer

W = angular speed = wo =1.2 rad/s

let Vr = radial velocity

ar = radial acceleration = r*Wo^2 = 1.44*r

dVr/dt   =1.44*r

Vr*dVr   = 1.44*r*dr

integrating on both side ::

integration[Vr*dVr ] = integration[1.44*r*dr] , where r =0.6 to 1.9

Vr^2/2   = 1.44*[1.9^2-0.6^2]/2

     Vr   = 2.16 m/s

Vt = tangentail speed= 1.9*Wo =2.28 m/s

total speed = [vr^2+Vt^2]^0.5 =3.14 m/s

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