# Net force on a brick sitting on an accelerating merry-go-round

everyone. I'm doing some exam prep (not a homework question), and I'm not sure how to parse the total force acting on the brick. Here's the question:

"A friend and I are bored. So we visit the local park, which has a merry-go-round. It’s a smooth metal disk 2m in radius (50 kg in mass). We hook it up to his motorcycle engine so that we can accelerate it to spin REALLY FAST. Then I place a brick on it at radius r = 2.0m at the edge. The brick has mass m = 0.8kg, and the coefficient of static friction between the brick and the surface is µ = 0.7. Starting from rest (at t = 0), we accelerate the disk with angular acceleration α = 0.2s^-1. I want to predict how much time it will take before the brick goes FLYING OFF!

At what time will surface of the merry-go-round slip from under the bottom of the brick?"

So friction is providing the force to keep this brick on the surface of the merry-go-round, right? But to find when it goes flying off do I have to use Pythagoras theorem to add the tangential and centripetal forces together to find when it's equal to the maximum static frictional force between the brick and the merry-go-round? Thanks for any help.