Center of Gravity

Introduction

Show students how to locate the center of gravity of an irregularly shaped object. Then show them how the irregular object spins around its center of gravity.

Concepts

• Center of gravity
• Stability
• Rotation around the center of gravity

Background

According to Isaac Newton’s (1642–1727) laws of gravitation, the Earth attracts every tiny particle of mass of every object and pulls them toward its center. For any specific object (composed of many tiny particles), the center of gravity of the object is the location where all the individual gravitational forces acting on the individual particles add up and result in one net downward force. At this point we can assume all of the mass of the object is concentrated, and therefore this point is also referred to as the center of mass. The location of the center of gravity, especially for an irregularly shaped object, is critical for the overall stability and balance of an object on the Earth’s surface. An object is most stable on the Earth’s surface when the object’s center of gravity is at its lowest point and is centered about the object’s support base.

In general, when a force acts on an object, it can be assumed that the force acts on the center of mass of the object. If a force is specifically applied to an object at a position other than its center of mass (i.e., to the left, right, up or down, from the center of mass), then this force will cause the object to rotate about its center of mass. If the object is allowed to rotate about a point other than the center of mass, then the object will wobble instead of spinning smoothly. This wobble becomes very apparent when riding in a car that has poorly balanced tires.

Materials

Safety Precautions

The materials used in this demonstration are considered safe. Please follow all normal laboratory safety guidelines.

Disposal

Save the materials for future demonstrations.

Prelab Preparation

1. Use scissors to cut the string to approximately 40 cm.
2. Tie one end of the string to the sinker.
3. Tie a “looping knot” to the other end of the string (see Figure 1).
   {12505_Preparation_Figure_1}
4. (Optional) Use a dry erase marker to label the three holes at the center of the polygon 1, 2 and 3 (or A, B and C).

Procedure

1. Show the irregular pentagon shape to the students.
2. Ask students to predict which hole in the polygon is at the center of mass of the polygon. Students can also develop experiments to locate and test the center of mass position, if appropriate.
3. Obtain the handle with hook and the string and sinker.
4. Insert the hook through the hole at one of the corners of the polygon. Allow the polygon to hang freely.
5. Place the “looping knot” onto the hook and allow the sinker to hang freely.
6. Once the polygon and string stop swinging, determine which hole or holes in the center of the polygon is in line with the hanging string. (Optional) Hold the string tightly along the polygon and then use a dry erase marker to draw a line on the polygon along the string.
7. Repeat steps 4–6 from a different corner of the polygon. Which hole is in line with the hanging string? Is it the same hole as before?
8. Repeat steps 4–7 one more time. The third trial should verify which hole is located at the center of mass of the polygon.
9. Remove the hook from the polygon and obtain a sharpened pencil.
10. Insert the point of the pencil into the hole determined to be located at the center of mass of the polygon.
11. Spin the polygon on the pencil. Notice that the polygon will rotate smoothly and evenly (little or no wobbling) when it spins at this location.
12. Place the point of the pencil into one of the other holes at the center of the polygon and spin the polygon. Notice how the polygon wobbles when it spins from a location other than the center of mass.

Student Worksheet PDF

12505_Student1.pdf

Teacher Tips

• This polygon may also be tossed vertically into the air with a small rotation and one of the holes at the center of the polygon will appear to remain “still” while all the other holes rotate around it (i.e., rotate around the center of mass).
• Additional weights, such as clay or paper clips, may be added to the edge of the polygon to attempt to “balance” the polygon when it spins from a hole other than hole at the center of mass. This demonstrates the importance of having balanced car tires and how the balance is achieved by adding small weights to the rims of the wheels.

Answers to Questions

1. Define center of gravity.

   The center of gravity of the object is the location where all the individual gravitational forces acting on the individual particles add up and result in one net downward force. At this point we can assume all of the mass of the object is concentrated, and therefore this point is also referred to as the center of mass.

2. Explain how the center of gravity of the polygon was determined.

   The center of gravity was located by hanging the object from a corner and hanging string from the same corner. The hanging string lines up with the center of gravity of the object. Hanging the object and string from a second corner allows the center of gravity to be pinpointed—it is at the intersection between the imaginary lines created by the hanging string. Hanging the object and string from a third corner helps to verify the location of the center of gravity.

3. Describe how the polygon spins when it rotates about its center of gravity.

   The polygon spins smoothly about its center of mass, and it rotates for a long time.

4. Describe how the polygon spins when it rotates at a point other than the center of gravity.

   The polygon wobbles when it rotates from any of the other holes that are not located at the center of gravity of the polygon. The polygon does not spin smoothly and it slows down quickly.