# Circular Motion and Radius of Curvature

1. ### ThatMathGuy

1
1. The problem statement, all variables and given/known data
Oh boy... Here we go...

At what minimum speed must a roller coaster be traveling when upside down at the top of a circle so that the passengers will not fall out? Assume a radius of curvature of 7.4 m.

I honestly have nothing. To begin with, I drew a free-body diagram but got nowhere considering the teacher never explained 'radius of curvature'. I've tried searching on the Internet but all I get are a bunch of formulas in geodesy and aren't applicable to the problem. It's not in the book either (Giancoli PHYSICS Updated Edition 2009).

2. Relevant equations
Ac=v^2/R
$$\SigmaF$$=mv^2/R

3. The attempt at a solution
Tried setting up a free-body diagram and got nowhere.

2. ### Delphi51

3,410
At the top of the circular motion, gravity must provide no more than the centripetal force needed to hold the car in circular motion. If Fg exceeds Fc, the car will fall off the track. So start with Fc = Fg, fill in the detailed formulas and solve for v.