Center of Gravity Test Notes

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CENTER OF GRAVITY TEST NOTES

10.1 Center of Gravity

· Throw a baseball into the air, it follows a smooth parabolic path. Throw a baseball bat into the air and its path is not smooth, it seems to wobble all over the place. It wobbles about its center of gravity--- the point located at the object’s average position of weight.

· For a baseball the center of gravity is at the geometric center, for a baseball bat it is toward the heavier end.

· If a wrench were sliding across a smooth horizontal surface, the center of gravity as the wrench moves follows a straight line path. The motion of the wrench is a combination of straight line motion of its center of gravity and rotation around the center of gravity.

10.2 Center of Mass

· Center of gravity is often called center of mass, which is the average position of all the particles of mass that make up an object.

· For almost all objects on and near the surface of the Earth, these terms are interchangeable.

· Example of a difference: center of gravity of the World Trade Center is about 1 millimeter below its center of mass.

· The center of mass of the solar system is not at the geometric center of the Sun. If all planets were lined up on one side of the Sun, the center of mass would be about 2 Solar radii from the Sun’s center.

10.3 Locating the Center of Gravity

· The center of gravity of a uniform object(such as a meter stick) is at the midpoint, its geometric center.

· If you suspend an object(pendulum) at a single point, the center of gravity will hang directly below the point of suspension. A plumb line can be used to construct a line that is exactly vertical. You can locate the center of gravity by suspending the object from a different point and finding where the two lines intersect.

· The center of gravity may be located where no actual material exists. Examples: donut, empty cup, bowl , boomerang.

10.4 Toppling

· The rule for toppling is this: If the center of gravity of an object is above the area of support, the object will remain upright. If the center of gravity extends outside the area of support, the object will topple.

· The Leaning Tower of Pisa does not topple because the center of gravity does not extend beyond its base.

· The support base of an object does not have to be a solid. The four legs of a chair bound a rectangular area that is the support base for the chair.

10.5 Stability

· Unstable equilibrium- an object balanced so that any displacement lowers its center of gravity.

· Stable equilibrium- an object balanced so that any displacement raises its center of gravity( pushing a ping pong ball down into a glass of water.)

· Neutral equilibrium- where displacement occurs with no raising or lowering of the center of gravity( a fish suspended in water)

· The center of gravity is lowered if much of the structure is below ground level. This is important for all tall, narrow structures such as the Space Needle in Seattle, Washington.

10.6 Center of Gravity of People

· When you stand erect with your arms hanging at your sides, your center of gravity is within your body( typically 2 to 3 centimeters below your navel and midway between front and back)

· The center of gravity is slightly lower in women than in men because women tend to be proportionally larger in the pelvis and smaller in the shoulders.

· In children, the center of gravity is approximately 5% higher because of their proportionally larger heads and shorter legs.

· Raise your arms vertically overhead. Your center of gravity rises 5 to 8 cm. Bend your body into a U or C shape and your center of gravity may be located outside your body altogether.

· In unstable situations, as in standing in the aisle of a bumpy-riding bus, you place your feet farther apart to increase this area. Standing on one foot greatly decreases this area.