problem $4(40$ points$)$

Bar $\backslash ($ A B $\backslash )$ has a constant counterclockwise angular velocity of $\backslash (2\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The $\backslash (1-\backslash$mathrm$\{$kg$\}\backslash )$ collar $\backslash ($ C $\backslash )$ slides on the smooth horizontal bar.

At the instant shown in the figure, in vector form, determine the following:

a$)$ position of $\backslash ($ B $\backslash )$

b$)$ velocity of point $\backslash ($ B $\backslash ),(5$ points$)$

c$)$ acceleration of point $\backslash ($ B$,(5\backslash )$ points$)$

d$)$ position of $\backslash ($ C $\backslash )$ with respect to $\backslash ($ B $\backslash )$

e$)$ angular velocity of $\backslash ($ B C $\backslash )$ and velocity of point $\backslash ($ C $\backslash ),(5$ points each$)$

f$)$ angular acceleration of $\backslash ($ B C $\backslash )$ and acceleration of point $\backslash ($ C $\backslash ).(5$ points each$)$

Draw the free body diagram of the collar at the instant shown. $(10$ points$)$

BONUS

g$)$ Determine the tension in the cable $\backslash ($ B C $\backslash )(5$ noints $\backslash ()\backslash )$