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# Center of Gravity of Symmetrical and Asymmetrical Objects

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Author: Janice VanCleave

Any object can be balanced if it is supported at the right place. This place is at or in line with a point called the center of gravity.

In this project, you will discover how to locate the center of gravity of a symmetrical (having matching halves) space figure (geometric figure that is three-dimensional) with uniform density (mass per volume) as well as of an irregularly shaped object with an irregular density. You will also find the center of gravity of a plane figure (a geometric figure that lies flat on a surface). You will then investigate how the height of an object's center of gravity and the width of an object's base affect the object's mechanical stability (how easily it falls over).

### Getting Started

Purpose: To find the center of gravity of a symmetrical space figure with uniform density.

### Materials

• 18-inch (45-cm) piece of string
• -by-36-inch (1-by-90-cm) dowel
• transparent tape
• marker
• yardstick (meterstick)

### Procedure

1. Tie one end of the string around the dowel.
2. Tape the free end of the string to the edge of a table. The dowel should hang freely.
3. Move the dowel through the loop of string until it balances while hanging in a horizontal position.
4. Mark the position of the string on the dowel.
5. Use the yardstick (meterstick) to measure the distance to the mark from each end of the dowel.

### Results

Your measurements will show that the mark is at the center of the dowel. The dowel balances when supported at this mark.

### Why?

The place on a space figure (geometric figure that is three-dimensional), such as the dowel, where it can be balanced is in line with a point called its center of gravity (point where the weight of an object appears to be concentrated). If the space figure is perfectly symmetrical (having matching halves) on either side of the center of gravity and its density (mass per volume) is uniform (the same throughout; unchanging), then the balancing point is in the geometric center, as you found in your experiment. Note that mass is the amount of matter (substance of which physical objects consist) in an object.

A force is a push or a pull on an object. Gravity is the force of attraction between all objects in the universe. Weight is the measure of the force of gravity, which on Earth is a measure of the force with which Earth's gravity pulls an object toward Earth's center. The dowel is made of many particles, each having weight. Figure 1.2 diagrams a few of the weight vectors (quantities with directions that are expressed by arrows). The position of the string is shown by the large arrow F. The string supports the dowel with a force equal to the sum of all the weights of the particles. In addition, each of the particles exerts a rotating effect, called torque, because of its weight and position. Torque is the product of a force and its perpendicular distance from a point about which it causes rotation. Rotation is the turning motion of an object about its axis (imaginary line through the center of an object and around which the object turns). Because the dowel is supported at one point, the torques of the particles on one side of the support rotate the dowel clockwise, and the torques of the particles on the opposite side of the support rotate the dowel counterclockwise. The dowel balances when the string is placed at the point around which the sum of the clockwise torques equals the sum of the counterclockwise torques. The string is above the center of gravity. When an object is supported by a single force, the force goes through the center of gravity of the object.

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