Please show all work neatly as well as showing all the work

Please show all work neatly as well as showing all the work, thanks.

The cylinder rolls without slipping between two moving plates E and D. What is the angular velocity of the cylinder? What is the velocity of the center of the drum, point C?

Solution

since no slipping occur the contact points A and B on the cylinder have the same velocities as plate E and D respectively ,VA and VB are parallel so the IC is located at a point on line AB

distance from B to IC is x and distance from AB is .25

VB=wx,0.5=wx

VA=w(.25-x),2=w(0.25-x)

from above two equations

x=0,05

so w=VB/x=0.5/0.05=10rad/s

velocity pf point c

VC=10*(0.05-.125)

=0.75m/s