Problem$-1$

Consider Bar AB as shown in the diagram. The bar is $5$ m in length and has a mass of $40$ kg $.$ Each end of the bar is connected to rollers of negligible mass, which move smoothly within the slots as indicated. At the given position, a counterclockwise couple $C=150N*m$ is applied to the bar, and point A has a velocity of $3\mathrm{.}5\frac{m}{s}$ directed downward along the slot.

Determine the following quantities:

Angular Velocity of Bar AB $($magnitude and Direction$)$

Velocity of Point B $($magnitude and Direction$)$

Angular Acceleration of Bar AB $($magnitude and Direction$)$

Acceleration of Point B $($magnitude and Direction$)$

Acceleration of Point A $($magnitude and Direction$)$

Acceleration of the center of mass of the bar AB

Reactions on the Bar at Points A and B