X Marks the Spot: Finding the Center of Mass

Introduction

You can probably find the center of simple shapes, like circles and squares, pretty easily. But, how do you find the "middle" of an irregular shape, like a drawing of a dog or a cat? This project will show you how to do it using nothing but string and paper clips!

Background

How do you define the exact center of an object? One way to do this is to find the object's center of mass. The center of mass is the point about which an object will balance if you try to rest it on your fingertip. Or, if you hang an object, for example a picture frame from a nail, the center of mass will hang directly below the nail.

For symmetrical objects, finding the center of mass is easy. For example, for a rectangular picture frame, you know the center of mass is in the middle of the rectangle, and you can find it with a ruler. When you hang the picture frame, you will make sure it is centered on the nail so it will be level – otherwise it will tip to one side. The same applies to other symmetric objects, like a spherical basketball – you know the center of mass is in the middle of the sphere.

What about irregularly shaped objects, like a dog or a cat or a person? Now finding the center of mass is not so easy! This activity will show you how to find the center of mass for any two-dimensional shape you cut out of paper, using a trick that has to do with the hanging picture frame mentioned above. If you hang a shape from a single point, you know the center of mass will always rest directly below that point. So, if you hang a shape from two different points (one at a time), and draw a line straight down from each point, the center of mass is where those lines intersect. This technique can be used for any irregular 2D shape. Don't believe it? Try this activity to find out!

Materials

Procedure

Observations and Results

You should have found that the center of mass of the rectangle is right in the middle of the page – halfway along the width, and halfway along the height. You can easily locate this spot with a ruler. Then, when you hang the rectangle from a hole on its edge, the string should always pass through this point, regardless of which hole you use. While it is much harder to predict the center of mass for an irregular shape, the same principle holds true. Regardless of what point you hang the irregular shape from, the string will always pass through the center of mass. So, if you hang it from two or more points (one at a time), you can find the intersection of these lines and that is the center of mass.

Note that, due to small errors in the experiment (like friction on the hook that prevents the paper from rotating perfectly, or the holes not being close enough to the edge of the paper), if you draw multiple lines, they might not all intersect in exactly the same place, but they should still be fairly close to each other.

More to Explore

• Fun with Gravity and Center of Mass, from GRACE Education Curriculum
• Science Activities for All Ages!, from Science Buddies

Credits