In the system shown in Figure $1,$ link OB has a constant angular velocity of $200$ rad$/$s clockwise. For the position shown if $=270,$ determine:

OB$=5$

AB$=14$

$$

a$)$ The angular velocity of rod AB$.[25$ Marks$]$

b$)$ The velocity of piston A$.[25$ Marks$]$

c$)$ The angular acceleration of rod AB$.[25$ Marks$]$

d$)$ The acceleration of piston A$.[25$ Marks$]$