The figure below shows a bar AB rotating clockwise about pin A with a constant angular velocity $\backslash (\backslash$omega$\_\{$A B$\}=4\backslash )$ rad$/$s$.$ The block C is constrained to move along a horizontal channel.

A$.$ Draw a free$-$body diagram for bar AB and bar BC including labels for the different position and velocity vectors.

B$.$ What is the absolute velocity of the point $\backslash (\backslash$mathrm$\{$B$\},\backslash$mathrm$\{$v$\}\_\{\backslash$mathrm$\{$G$\}\}\backslash ),$ at the instance shown? Write it as a Cartesian vector.

C$.$ Determine the absolute velocity of the block $\backslash (\backslash$mathrm$\{$C$\},\backslash$mathrm$\{$v$\}\_\{\backslash$mathrm$\{$C$\}\}\backslash ),$ and the angular velocity of the bar $\backslash (\backslash$mathrm$\{$BC$\},\backslash$omega$\_\{$B C$\}\backslash ),$ at the instance shown.

D$.$ Reflection: Start with the diagram provided below or redraw the links AB and BC$.$ Show visually the motion of the system by adding a sketch on top of your starting image with the arrangement of AB and BC a short time later. Describe in words what is physically happening to the bar AB $,$ bar BC and block C in terms or translation$/$rotation and the direction. Do your calculations above match the directions you expect for the rotations and velocities based on the physical motion occurring? Remember that we consider positive $\backslash ($ x $\backslash )$ as to the right, positive y as upwards, and positive rotation as counterclockwise.

C$.$ Velocity of C and angular velocity of BC :

List out the relevant variables as Cartesian vectors before solving:

Applying the relative velocity equation gives the following results:

The velocity of block $\backslash ($ C $\backslash )$ is $\backslash (\backslash$mathbf$\{$v$\}\_\{$C$\}=\backslash )$

$\backslash (-8\backslash )$

in$+$

$0\backslash (\backslash$hat$\{$j$\}\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Block C is moving to the