**Finding the center of gravity of a symmetric object with non-uniform density is an effective way of understanding the equilibrium point.**

**SCIENCE** – An object can achieve balance when placed in the right position. This position is at or in line with a point called the center of gravity. In this project or experiment, we will learn how to find the center of gravity of a three-dimensional symmetric object (each part is exactly the same) with either uniform density or irregular objects with non-uniform density. We will also find the center of gravity of a flat surface (a geometric object lying flat on a surface). Then, we will investigate how the height of the center of gravity of an object and the width of the object’s base surface affect its mechanical stability (how easily it can tip over).

**Learning Objective**

This experiment aims to find the center of gravity of a symmetric three-dimensional object with uniform density. Materials 45 cm of string 1 wooden stick, 90 cm long with a diameter of 1 cm insulation tape marker wooden meter stick

**Procedure**

- Tie one end of the string to the stick.
- Attach the free end of the string to the edge of the table using insulation tape. The wooden stick should hang freely.
- Move (slide) the wooden stick through the circle formed by the string’s attachment until it balances in a horizontal position.
- Mark the position where the wooden stick is balanced using the marker.
- Use the wooden meter stick to measure the distance from the marked point to each end of the wooden stick.

**Results**

The measurement results will show that the marked point is located in the middle of the wooden stick. The wooden stick achieves balance when supported at this marked point.

**Why?**

The point on a three-dimensional object, such as a wooden stick, that allows the object to achieve balance, lies on a line known as the center of gravity (the point where the weight of an object is concentrated). If the 3D object is perfectly symmetrical on both sides of the center of gravity and has uniform density (mass per volume), then the equilibrium point is at the geometric center, as you found in your experiment.

Note that mass is the amount of substance contained in an object. Force is a push/pull on an object. Gravitation is the force of attraction between objects in the universe. Weight is a measure of gravitational force, which on Earth is the force with which an object is pulled toward the Earth by gravity. In this experiment, the wooden stick is composed of many particles, each with its weight. Figure 2 shows several vectors (quantities with direction indicated by arrows) representing weights. The location of the string is indicated by the large arrow F. The string supports the wooden stick with a force equal to the sum of all particle weights. Additionally, each particle exerts a rotational effect called torque due to its weight and position. Torque is generated by a force and has a perpendicular distance from a point that causes rotation.

Rotation is the motion of a body spinning around its axis (an imaginary line passing through the center of the body around which it rotates). Since the wooden stick is supported at one point, the torques of particles on one side of the stick rotate the wooden stick clockwise. Meanwhile, the torques of particles on the other side rotate the wooden stick counterclockwise. The wooden stick is balanced when the string is at a point where the sum of clockwise torques equals the sum of counterclockwise torques. The string is above the center of gravity. When an object is supported by a force, that force passes through the center of gravity of the object.

**Try a New Approach**

Where is the center of gravity of a non-symmetric object with non-uniform density? Repeat the experiment by changing the weight, for example, by placing a walnut-sized load at one end of the wooden stick. Where is the center of gravity after adding the load? b. Repeat the experiment by attaching the load at different positions along the wooden stick. Science Fair and Exhibition Tips: Create a diagram illustrating each of your experiments as shown in Figure 2.”