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### Activity #6c - Getting a Feel for Rotation Curves

This activity is a kinesthetic exercise for students to experience rotation curves for themselves. Note that there is no student worksheet for this activity.

Divide the students into two groups. One group will participate in the activity while the other observes. The groups should switch for different parts of the activity.

1. Have students stand in a line, linking arms. Have the person at one end start to turn slowly. Ask the Observers, "How would you describe the motion of the other students? Can you plot their positions as they change with time? What would its rotation curve look like?"

• The students represent objects that are tightly bound together, e.g like a rod, or a CD or a vinyl record. So the students will likely move mostly in unison, but the inner students cover shorter distances than the outer students do in the same amount of time. The rotation curve would show a linear increase in student velocity as distance from the center increases. This mimics stars in the bulge of a galaxy.

2. Now have the students hold hands. Again have the person at one end turn slowly in place. Ask the Observers, "Now how would you describe the motion of the other students? What does the rotation curve look like now?"

• Now the students are not so tightly bound together, but they still move in a circle around the central point. The students will not move so much in unison. The rotation curve will initially rise but then level off as distance increases. This mimics stars in the spiral arms of a galaxy.

3. Now let the first half of the line links arms, and the rest of the students hold hands. Ask the Observers to describe the motion.

• The students linking arms will move mostly in unison, while velocity of the outer students will approach a constant value. Together, this mimics motions of stars in the bulge and spiral arms.

4. Finally, let the students walk freely in circles (i.e. as in orbits) around the student in the center.

• Here the rotation curve will vary depending on the creativity of the students. See if they can imitate the rotation curve of the solar system by having the inner students move more quickly than the outer students.