# Airplane on a String

#### Summary

It's an engaging problem that forces students to think clearly about some concepts that they frequently find confusing, like tension, circular motion, and centripetal acceleration.

The video at right is a preview of the video students use for the activity. A downloadable QuickTime video that allows students to step through frame-by-frame is below.

## Learning Goals

## Context for Use

## Description and Teaching Materials

Here is an airplane on a string worksheet (Microsoft Word 2007 (.docx) 959kB Nov13 13) that can guide students through this activity.

Airplane on a string worksheet Solutions (Acrobat (PDF) 74kB Aug25 14).

This worksheet has fairly explicit directions for which *measurements* the students should make, but does not give much support for how students are to use those quantities to complete the required *calculations.* I would recommend that the instructor be on-hand to give tips if students get stuck.

The Airplane on a string video page contains all the available file types for this video.

## Teaching Notes and Tips

- Students are sometimes confused that there are really two different angles that are important. The first angle is the angle between the string and the vertical (this is the angle that's measured by the overlaid protractor.) The second angle is the is the radial angle as the plane moves around the center (the angular velocity, omega, is a measure in the change of this angle).
- Also, my students always ask if the protractor angle on one side (the left side, for example) should be negative. I see the acceleration as being *inward* the whole time, so it makes sense to call the angle on the left
**and**the right positive. - It is possible to use this video before the concept of angular velocity has been taught. In that case, skip the question about angular velocity and base the other calculations on linear velocity instead.
- I thought that once students calculated the radius of the circle it would be obvious to them how to use trigonometry to find the length of the string, since sin(theta)=radius/Length, but what I actually found was that my students tried to find the length of the string by using the free body diagram that they had drawn. I think they were confused since the tension is in the same direction as the string. That error places forces and distances on the same triangle and illustrates a serious misunderstanding of units.
- The worksheet contains a bonus calculation for students who get done early. They are asked to calculate the largest angle the string could support if it had a maximum strength of 10N.
- This video pairs well with the "Steel Ball in a Rotating Glass Bowl" video. The situation looks very different, but the math is identical.

## Assessment

## References and Resources

The Hyperphysics treatment of circular motion.

See a solution to a similar conical pendulum problem.