AI Tutor
Why can a Formula 1 race car corner aggressively without rolling over, while a tall passenger van risks flipping during a sudden swerve at modest speeds?
The answer lies in rotational stability, which is determined by where an object's mass is concentrated relative to its contact points on the ground.
How do the downward pull of gravity and the object's geometry combine to decide whether it snaps back upright or rolls over?

The Base of Support and Restoring Torque

An object's base of support is the entire boundary connecting all points of contact with the ground, such as the rectangular area between four vehicle tires or two feet.
The entire gravitational force acts through the center of mass, which is the average position of all mass in the object.
As long as the vertical line of action from the center of mass stays inside the base of support, gravity produces a restoring torque that pulls the object back down.
Can we derive an exact mathematical formula to predict this critical tipping angle?

Deriving the Critical Tipping Angle

In 1638, Galileo Galilei explored static equilibrium by noting that leaning stone columns topple precisely when their plumb line passes outside the base.
Consider a symmetrical body of total base width ww and center of mass height hcmh_{\text{cm}} resting on a flat surface.