# Overturning torque on a car navigating a curve The car shown above with mass M is turning to the left with an uniform angular speed W on a circular path with radius R. When the angular speed is increased to a critical value C, one of the normal forces vanishes. If W is increased beyond C, the car will roll over, explain why.

I did some calculations and found C = sqrt(gl/hR). However I ran into some troubles explaining why it will roll over. By the free body diagram shown below When N1 =0, Fs1 =0 and taking moment about center of mass, the only forces are Fs2 and N2, however unless l is significantly smaller than h, by the free body diagram, the car will actually lean in since N2 > Fs2?

As you point out, once $$N_{1}=0$$ and $$F_{S1}=0$$ the only forces remaining which can produce a torque about the center of mass are $$N_{2}$$ and $$F_{S2}$$.
However, since we assume the car is still in uniform circular motion around the curve, $$F_{S2}$$ must adjust as needed in order to maintain the uniform circular motion condition: $$\frac{m v^{2}}{R}$$. I believe this is exactly balancing the torque by $$N_{2}$$ at the critical velocity, so any further increase in speed will produce a larger torque than that produced by $$N_{2}$$ and cause a roll towards the outside of the curve.