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a) What is ther maximum linear speed the bug can have and stay on the disk?

b) How many seconds until the bug falls of the disk assuming the string is long enough to keep applying the force?

I know the solution, but I'm confused as to why my teacher did it. He said:

"Because there is a constant tangential acceleration and an increasing centripetal acceleration, so the acceleration is the resultant of those two perpendicular components.

For part a, He set potential energy equal to net force and solved for v (umg= ma). Why didn't he take into account centripetal force? Why is centripetal accel. increasing, but tangential acceleration constant?

For part b, he said v= a tangential * t. Why did he just use tangential acceleration to determine how long the bug stays on the disk?

Thanks in advance for any help.