Experiencing Linear and Angular Velocity

Linear and angular velocity can be one of the trickier units for high school math students.  The formulas and computations themselves aren’t all that imposing, mostly just some quick multiplications and divisions, but the vocabulary and scenarios can be intimidating.

We encounter some new terms here and their symbols, like angular velocity (ω), arc length (s), linear velocity (v) and using angles (θ) measured in radians rather than degrees.  It’s a lot of new ideas to absorb, and the problems often require a student to assess and utilize multiple formulas.  An activity which I wrote a few years ago has been taken over and perfected by a colleague.  “Trig whips” allows students to experience and communicate linear and angular velocity, and provides a great excuse to get outside and move around.

TRIG WHIPS

This activity has a simple premise.  In groups of 4, students stand shoulder to shoulder.  One student shoulder acts as the center, and the group works together as a radius, walking in a circle.  Each group records:

• Individual student distance from the center
• Time required to complete 3 revolutions
• Angular displacement

A worksheet for this activity allows students to keep track of their data.  Encourage students to switch positions and experience the effect of being the outside point.

My colleague reports that one class was able to complete the activity with a “record” 11 students.  Not only did the outside student need to run hard to keep up with the group, but the inside students worked together to slow the middle.

If we had a group of 20 students, how fast would the outside student need to “walk”?

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UPDATE: More kids, a longer conga line, more chaos, more fun!

Human Chain from Bob Lochel on Vimeo.

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