$(20)$ A $40-cm$ rotating gear rotates on a stationary axis. It is uniformly sped up from rest to a top speed of $900$ rpm in a time of $20$ s $.$

a$.(4)$ Find the angular acceleration, $,$ of the gear.

b$.(4)$ Find the tangential acceleration, at$,$ of a point on the tip of the gear.

c$.(4)$ Find the radial acceleration, $ar,$ of a point on the tip of the gear.

d$.(4)$ Find the angular distance, $,$ the gear travelled during this time.

e$.(4)$ How many revolutions did the gear make during this time?