# Activity Guide: Center of Mass

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Standing on your tiptoes is hard enough, but imagine trying to do it while staying balanced on top of someone else’s head. Or, just as difficult, imagine staying upright with someone standing on your head. To keep balanced, the Nanjing acrobats must be aware of their centers of mass, and the various forces—called torques—that might cause them to rotate and fall out of balance. In this unit, students will learn how these two concepts make it possible for the acrobats to achieve their amazing acts of balance.

## How to Incorporate the Video into Instruction

This video can be used to motivate the study of center of mass and torque. It can also serve as an extra illustration to reinforce previous lessons on these topics. If you watch the video in class, ask students to pause it at different points in the routine and have them identify pivots, lever arms, and torques that they see present in the video. Have students pause the video and estimate where the woman’s center of mass is relative the pivot point.

### Questions to Ask Students Before Watching the Video

1. How is the woman able to balance on the man?
2. How is her balancing like a seesaw?
3. Where is her center of mass as she balances?
4. What happens when she becomes unbalanced?
5. Why does the man move beneath her?

## Watch the Video

### Questions to Kick-Start Class Discussion After the Video

1. What do we mean by center of mass? How do you find it?
Center of mass is more commonly known as the balancing point. It’s usually in the center of an object, depending on how the weight is distributed.
2. What causes something to fall over?
When an object’s center of mass is not supported, an unbalanced torque ensues, causing the object to rotate and tip over.
3. Why does the woman extend her arms and kick out her leg? How does this help her balance?
Jessica’s extended limbs act as lever arms, generating counter-balancing torques, which help keep her from rotating out of balance.
4. Why does the man move slightly under her?
Anan shifts slightly to make sure Jessica’s point of contact is directly under her center of mass.

### Demonstration Opportunity

Have students try to pick up a chair while keeping their heels against a wall. Why can’t they do it? With heels against the wall, the center of mass of the student+chair is usually out in front of the student’s feet somewhere, meaning it is unsupported. Males and females have different centers of mass.

### Connections to Everyday Life

Mobiles, such as those made by Alexander Calder, are a good example of balancing torques in action. Old-style scales use weights and lever arms to weigh objects. Dragsters are often very long to offset the rotation generated by the wheels at the back. If they weren’t so long, their front ends would flip up.

## Suggested Classroom Activities

### Activity 1: State Center of Mass

Have students cut out the State they were born in out of rigid paper. By hanging it from any two points and drawing the vertical line, the center of mass of the state will be roughly where the two lines intersect. As a bonus, you can ask them to find out which towns are near it. Which State capitols are near the center of mass of the state?

You can ask students from mountainous States how the non-uniform distribution of mass in the State might affect the location of its center of mass. This leads to a simple calculus problem.

### Activity 2: Balancing Act

Students can recreate the Nanjing balancing act by balancing a meter stick vertically in their hands. Ask students where the center of mass is. Try it again with two-meter sticks; one taped perpendicularly to the other’s mid-point (forming a cross). Have kids try to balance again. The center of mass is in the same position, but the cross (theoretically) should be easier to balance. Finally, put weights on the ends of the crossbar; ask students if they think this will make it easier or harder to balance.

### Activity 3: Center of Mass Video Analysis

To do this activity you will need to download the video "Video Analysis: Newton's Laws of Motion (QT)". Use VideoPoint or similar software for graphing and analysis.

This activity looks at the center of mass of the performer during the balancing act. We will assume that the center of mass is located at her belly button and look at the graph of the position of that point over time. A screen capture of the situation is displayed below.

Notice that the lines are essentially flat. In other words, the center of mass does not move. On more careful inspection, have the students advance the movie back and forth. Note the times when the performer kicks her leg out or moves the fan in her hand back and forth, you will see that her belly button moves in the opposite direction to keep her center of mass over the tightrope.