Rotational Motion: Various Spools: Investigating Moment of Inertia and Torque

This activity is designed for students to use their understanding of torque. This activity also will guide students through the use of the moment of inertia. Higher-order thinking skills such as synthesis of ideas and data analysis, are required. The students should be familiar with a way of measuring the acceleration of an object and converting linear acceleration to angular acceleration. Students should review their ability to accurately draw free-body diagrams. This activity will also develop the difference between static friction and kinetic friction and the calculations that can be done with each. Through the activity, students should discover the vocabulary word moment of inertia. Students will review their vocabulary including forces, friction, tension, torque, and acceleration.

This activity would be appropriate for an advanced physics class studying rotational motion. A 12th grade physics class of 15 students would be ideal. This activity would be suited for a high school setting with about 2 hours allowed for completion. The students can bring in spools that they have found or built. Apparatus to measure the acceleration of the spool and the tension in the string is recommended. Students should have mastered the force and torque concepts before starting this activity. This activity will be situated in the study of rotational motion for practice in calculating moment of inertia and the effect of moment of inertia on rotational motion. This activity could be adapted for younger students as a demonstration of the effect of torque, friction, and distribution of mass on the motion of an object.

See the free-body diagram attached. The lesson can be introduced as a demonstration. Show how the spool will roll forward whether the string is wrapped over or under the inner cylinder. Show the students how at a certain angle the spool will slide instead of roll. The spool can be a ribbon spool or a larger spool made for the demonstration.
Ask the students to draw a free-body diagram for the spool. Be sure that the entire class is able to draw the free-body diagram.
Ask students to identify some of the factors that affect the motion of the spool. Elicit "torque" and review torque.
Elicit friction and develop an understanding among the students that rolling friction is a type of static friction and is equal to or less than the coefficient of static friction times the normal force. Sliding friction is a type of kinetic friction and IS the coefficient of kinetic friction times the normal force. Be sure to remind students that as the angle the spool is pulled at, the normal force also changes.
Introduce or review moment of inertia and ways of calculating it. Ask students how they think the moment of inertia affects the angular acceleration (if it does at all).
Let students investigate with some spools and become comfortable with what they expect from those spools.
Challenge the students to modify at least two spools or build two spools for the investigation. They should choose to change only one variable from the list below and keep the remaining factors constant.
Mass of outside cylinders
Mass of inside cylinder
Radii of outside cylinders
Radius of inside cylinder
Coefficient of friction
Distribution of mass on outside cylinders
The lesson can be closed with a review of the demonstration and questions posed to the students as a class assessment and as a review of the ideas that should have been learned. Some of the questions could be: What happens if the moment of inertia is increased? What happens if the radius is changed? What happens if the friction increases? etc. lab report (Microsoft Word 21kB Sep4 08) free-body diagram ( 414kB Sep4 08) spool ( 109kB Sep4 08)

The spool may pivot when pulled. Using a wider "string", such as ribbon, changing the width of the spool, or increasing the mass of the spool, will help prevent the spool from pivoting. Some of the students who want to try to work through all the math should be encouraged to, but the math should not be required so that it does not ruin the activity for other students. I have done this activity in the past as a demo to help explain force diagrams to younger students, but I have never had older students investigate rotational motion concepts.

The student understanding of forces will be assessed by their diagram. The understanding of torque, friction, and moment of inertia will be assessed by their answers to lab report questions and calculations. Students should hand in a lab report that will include everything that will be assessed.

9-12.II.D.1 laws of motion, 9-12.II.D.2 friction and gravity