Balancing Act

(no alternate text) — The torque from the weight on this bar would cause the bar to swing counterclockwise around the pivot. Since there are no other torques on the bar, the bar will start to fall.

Gravity is able to exert a torque on objects too, causing the object to spin (and often fall over). The point where the weight of an object acts on it is called the center of mass (or c.o.m.) For a symmetrical object, the center of mass lies along the axes of symmetry so long as the mass is evenly distributed.

One way we can determine the location of an object's center of mass is to suspend it from a piece of string. The tension in the string acts at the place that the string attaches to the object. If we think of that spot as the pivot, then the weight of the object is the only force providing torque on the object, and the weight's torque must be zero for the object to be in equilibrium. The only way this happens is if the center of mass lies directly below the pivot, so that the weight points away from the pivot. If we hang the object from two different pivot points, we can find the location of the center of mass as shown in the figure.

We know that a normal force is able to adjust its value to maintain equilibrium, but it can also adjust its location as well. For instance, the center of mass of a right triangle is closer to the leg than to the hypotenuse, and so the normal force from the table will be centered directly below the center of mass. (In fact the normal force will act along the entire base, but we can treat the force as if it were in that one location.) The normal force can't go beyond the base of the object, however; if the center of mass is not above the base, then the object will fall over (unless there is another torque applied somewhere to balance it, of course).