Chapter 14

At the conclusion of this chapter, the student should be able to:

• 1. Define the term center of gravity, and explain the basis for its location in the human body.
• 2. Estimate the location of the center of gravity of individuals in any position.
• 3. State the principles of equilibrium, and explain and demonstrate applications of each.
• 4. Locate the center of gravity of an individual using either the reaction board or the segmental method.

### Definition of Center of Gravity

The center of gravity of a body is sometimes described as its balance point or that point about which a body would balance without a tendency to rotate. For this reason, the center of gravity is often identified as the point where all the weight of the body or object is concentrated. More accurately, it is the point where the weight of the body may be said to act.

The ability to locate the center of gravity of a body is based on the knowledge of what it takes for a system to be balanced, or in equilibrium. Two conditions must be met:

• 1. All the linear forces acting on the body must be balanced.
• 2. All the rotary forces (torques) must be balanced.

Another way of expressing these necessary conditions for equilibrium is to say that the sum of all the forces acting on the body must equal zero. If there is a downward-directed linear force, there must be an equal upward force so that the vector sum of these forces equals zero. If there is a negative clockwise torque, it must be canceled out by a positive counterclockwise torque of equal magnitude (Figure 14.1).

###### Figure 14.1

The center of gravity of a body is the point where all forces acting on the body equal zero. In this illustration it is represented as the intersection of the x, y, and z axes. It may be located by application of the principle of torques.

A simple experiment to locate the center of gravity, or balance point, consists of suspending an irregularly shaped object by a string and letting it hang until it ceases to move (Figure 14.2). A vertical line is drawn on the object from the point of suspension in a line that is a continuation of the string. The object is then suspended from another point, and the vertical string continuation line is drawn again. This procedure is repeated one more time. The point at which the three drawn lines intersect is the center of gravity. If the object is suspended from this point, it will hang in whatever position it is placed because the weight of the object is equally distributed about this point and no unbalanced forces (torques) exist.

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