If you tilt a box up on one edge by a small amount and let go, it falls back down. If you tilt it too much, it falls over. And if you tilt “just right,” you can get the box to balance on its edge. What determines these three possible outcomes?

FIGURE 12.36 illustrates the idea with a car, but the results are general and apply in many situations. As long as the object’s center of mass remains over the base of support, torque due to gravity will rotate the object back to its equilibrium position.

FIGURE 12.36 Stability depends on the position of the center of mass.

A critical angle ${\theta }_{\text{c}}$ is reached when the center of mass is directly over the pivot point. This is the point of balance, with no net torque. For vehicles, the distance between the tires is called the track width t. If the height of the center of mass is h, you can see from Figure 12.36b that the critical angle is

For passenger cars with $h\approx 0.33t$, the critical angle is ${\theta }_{\text{c}}\approx 57\text{°}$. But for a sport utility vehicle (SUV) with $h\approx 0.47t$, a higher center of mass, the critical angle is only ${\theta }_{\text{c}}\approx 47\text{°}$. Various automobile safety groups have determined that a vehicle with ${\theta }_{\text{c}}>50\text{°}$ is unlikely to roll over in an accident. A rollover becomes increasingly likely when ${\theta }_{\text{c}}$ is reduced below $50\text{°}$. The general rule is that a wider base of support and/or a lower center of mass improve stability.