(Originais Teachy 2023) - Question Very Hard of Physics

An engineer from a roller coaster company is designing a new loop model for an amusement park. The project requires a deep understanding of the forces and accelerations involved in circular movements. Considering a point where a roller coaster car performs a loop of radius R, the engineer wants to calculate the linear velocity necessary for passengers to feel a maximum normal force of 6 times the acceleration due to gravity. Using the concept that at the highest point of the loop, the normal force is given by n = mg - m(v^2)/R, where n is the normal force, m is the mass of the passenger, g is the acceleration due to gravity, and v is the linear velocity of the point. Considering the acceleration due to gravity g = 9.8 m/s^2 and neglecting air resistance, determine the linear velocity necessary for the normal force to be the desired one, and explain how this velocity is related to the angular velocity of the movement.