Chapter 10-Center of Gravity

10.1 Center of Gravity
Located at the average position of weight, the center of gravity is the geometric center of an object. Irregularly shaped objects that have more weight at one end, such as a bat or wrench, have there center of gravity towards the heavier end. Some objects have there center of gravity far from the geometric center such as objects with varying densities. The center of gravity is the point around with an objects rotates, as seen when sliding a baseball bat across a smooth surface. The bat rotates around its center of gravity and this point always follows a straight line path. No matter how the object rotates it will always rotate around the center of gravity, and similarly if an object is thrown up in the air its center of gravity will follow a smooth parabola no matter how it rotates.
10.2 Center Of Mass
Center of mass is often synonymous with center of gravity and is known as the average position of all the particles of mass that make up and object. The only time in which there is a difference between these two terms is when an objects large enough for gravity to vary from one part to another. This is notable in very large buildings and even the solar system. This shows that the center of mass of an object is not always at the geometric center as other factors can contribute to this position as in the solar system. Although the sun is extremely large and you would expect the geometric center to be at the center of the sun it is not because the other planets contribute to the overall mass, so the center is slightly towards the rest of the planets.
10.3 Locating the Center of Gravity
When locating the center of gravity on uniform objects you would look towards the geometric center and find a balance point, or a point that when supported will support the entire object. Another method used in finding the center of gravity is a plump line. To construct a plumb line you would suspend an object at a single point and then draw a vertical line (called a plumb line) straight down from the point of suspension. The center of gravity lies somewhere along this line. Sometimes however the center of gravity lies where no material exists a phenomena seen rings, boomerangs, and donuts. The center of gravity of a donut is in the middle, but no matter actually exists there, proving me previous statement.
10.4 Toppling
The rule for toppling is: If the Center of Gravity, or CG, of an object is above the area of support, the object will remain upright. If the CG extends outside the area of support, the object will topple. The Leaning Tower of Pisa does not topple because its CG does not extend beyond its base. A good example of toppling is balancing a pole end of a broom or mop on the palm of your hand. It is difficult to do because the support base is very small and far beneath the CG.
10.5 Stability
The difficulty of an object to tip over is its stability. With no net force, an object is either easy or difficult to tip over depending on the size of the supporting base. Unstable Equilibrium is when an objects CG is directly over the edge of its supporting base. Due to a small displacement, an object will lower its CG and tip over. An object with a Stable Equilibrium will return to its initial position because the CG is not on the edge of its supporting base. A small displacement will raise its CG and the object will return to its initial position. Neutral Equilibrium is where the distance from the CG to the outside of an object is the same for any orientation of the object. It means that a small displacement won't raise or lower the CG.
10.6 Center Of Gravity
Your Center of Gravity is usually about 2-3 cm below your navel, halfway between your front and back. Women have a slightly lower CG than men because they have larger pelvis's and smaller shoulders. When you move, your CG also moves with you. Birds have been known to move there head back and forth when walking because they must use their supporting foot over their CG.