For the planetary gear train shown:

$N_2=20t,N_4=40t,N_5=18t,N_6=36t,N_7=154t.$

$3$ is the arm $($carrier$)$ connecting planet gears $N_4$ and $N_5.$

Inputs are the ring gear with an angular velocity of $100$ rpm ccw and the arm with an angular velocity of $50$ rpm cw $,$

Gears $5$ and $6$ are on the same shaft.

Gears $5$ and $4$ are meshed. Gears $4$ and $2$ are meshed.

$3$ denotes the carrier $($arm$).$

a$.$ Determine the angular velocity of planet gear $5.$ What are the gear sets and gear ratio for this question?

b$.$ Determine the angular velocity of the sun gear. What are the gear sets and gear ratio for this question?