Question #$7$: Kinematics of Rigid Bodies $($Angular Velocities and accelerations$)$

$(20$ points$)$

Link AB rotates with a constant angular velocity of $=7ra\frac{d}{s}$ in the counter$-$clockwise direction, as indicated. Point $C$ is guided to move vertically by a roller. Determine:

A$.$ The location of the instantaneous center of rotation of the link BC

B$.$ The velocity of point $C$

C$.$ The angular velocity of link BC

D$.$ The acceleration of point $C$

E$.$ The angular acceleration of link BC