Problem $2(40$ points$)$

At a given instant the roller $\backslash ($ A $\backslash )$ on the bar has the velocity and acceleration shown.

a$)$ Determine the angular velocity of the bar. Specify direction$/$orientation$.(5$ points$)$

b$)$ Determine the velocity $($magnitude$)$ of the roller $\backslash ($ B $\backslash ).$ Specify direction$/$orientation$.(5$ points$)$

c$)$ Determine the acceleration of the roller $\backslash ($ B $\backslash )$ in vector form, and the bar's angular acceleration. Specify direction$/$orientation for both. $(20$ points$)$

$-$ On the given figure, draw the instaneous center of zero velocity. Make sure to show all dimensions and angles. $(10$ points$)$