Direct Measurement Videos > Activities > Airplane on a String - Student Activity

Airplane on a String - Student Activity

by Matt Vonk, University of Wisconsin River Falls
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This video is a fun example of the classic conical pendulum problem. Students will analyze a video featuring an airplane on a string. The tension in the string can be read from an on-screen scale, timing measurements can be made from the frame-counter, and the angle of the string can be determined from an overlaid protractor. While this doesn't seem like enough information, it's actually enough to allow students to calculate the angular and linear velocity of the plane, the mass of the plane, the radius of its circular path, and the length of the string.

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.

Learning Goals

The primary goal of this activity is to give students a chance to apply concepts of circular motion and centripetal acceleration.

Context for Use

This activity should be used with students who are familiar with drawing free-body-diagrams, applying Newton's 2nd Law, and calculating centripetal acceleration. It is designed for small-group use in an algebra-based introductory physics course. It can be used as in-class work, homework, or pre-lab work. The activity requires approximately a half hour of time, but requires no special equipment other than a computer. It would not be difficult to adapt this activity to other settings such as a conceptual physics class.

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.

This activity uses the Direct Measurement Video, Airplane on a string. Students can access this video via the student video library which allows access to all videos, but without links to instructor materials.

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.


This activity requires students to make calculations based on measurements they have made. If students are able to successfully calculate the mass and velocity of the plane, and the length of the string then the students will have demonstrated a proficiency at solving a problem with centripetal acceleration.

References and Resources