## Overview

Students investigate movement around a pivot.  What path is followed?  How does the length of the path change with its distance from the pivot?

## Procedure

1. Introduce the concept of path: Demonstrate a pegboard base with the 0” hole of the strip connected to the bottom of the base. The strip is a lever and the connection to the base is a fixed pivot. It is a pivot because it allows the lever to turn around it.  It is a fixed pivot because it attaches the lever to the base.  Place a marker at the end of the lever and move the lever from one side of the base to the other.  Discuss the shape of the path that is followed by the marker. Introduce the term “arc” to describe this path. Later in the lesson students will see that this arc is part of a circle.  Ask: How could you know how far the marker goes?

2. Paths with a rope: Clear a corner of the classroom (or go on the playground). One student, the fixed pivot, holds the end of the rope tight to his waist while standing against the front wall. A second student holds the rope at the 5’ point and a third holds the rope at the 10” point.  Keeping the rope straight and taut, challenge the two students at the 5’ and 10’ points to walk in a straight line to the back of the room.

• Could they walk in a straight line to the back of the room?
• What shape of path did each student follow?
• Who had the longest path? How do you know?

Let two more students hold the rope at the 5’ and the 10’ marks. This time let the class suggest how to measure how far each one goes. Again, be sure the rope is taught and straight.

• Who had the longest path? How do you know?
• How far did the student at 5’ go? How far did the student at 10’ go?
• Why do you think the student at 5’ had a shorter distance than the one at 10’?

All students should have the experience of being prevented from going in a straight line. This provides a kinesthetic grounding for seeing how a link also moves in an arc around a pivot.

Students may suggest that a fair test of the lengths of the paths at the 10’ marker and the 5’ marker requires that the same student count steps at each location.  If so, this is a good experiment to do.  You can collect data on the number of steps taken at the 5’ and 10’ markers by different students, and comparing results.

3. Paths of inputs on a pegboard.  Students investigate the path followed by points on a lever as the lever is moved back and forth.  Provide each student with a base, two numbered strips, six rivets, and pre-punched paper on which to trace input paths. Here are a video and printed directions to set up the experiment.

Students trace, then measure, the arcs made as a lever is moved between two points.  The arcs are drawn at 2", 4" and 8" from the fixed pivot. Here are directions and a video for the experiment

 Science Notebooks Place your tracing of the input paths at 2”, 4” and 8” from the pivot in your science notebook. Complete Lesson 2 Worksheet and place it in your science notebook.

4. Whole-class meeting and discussion:

Encourage children to discuss what is similar between the rope experiment and the tracings on the pegboard.  In the experiments

1. the paths followed by the students and the input link (or floating pivot) are arcs,
2. the further the student or input link is from the fixed pivot, the longer the path.

Discuss the path followed by the input to the lever if the stops are removed.  What paths would be followed by the students holding the rope if there were nothing to stop their movement?

Outcomes

In the course of this lesson, students should learn that

• The path of a point (or input) moving around a (fixed) pivot is an arc.
• An arc is a piece of a circle
• The further the input is from the (fixed) pivot, the longer is the path of the input, or arc.