 Lab Moment of Inertia of a Bicycle Wheel
Purpose

The purpose of this lab is to have students investigate the rotational inertia of a suspended bicycle wheel. The use of a motion detector and data analysis techniques will show the relationship between the variables for the falling mass and its acceleration.

Laboratory set-up

Each group of three students will need the following equipment:

• 1 suspended bicycle wheel with a string securely wrapped along its circumference
• 1 50-gram mass hanger
• 1 set of slotted masses
• 1 LabPro
• 1 motion detector

First verify that the string attached to your bicycle wheel is securely attached and has a loop at the end to hold the mass hanger. Next, unroll about one meter of string, place the mass hanger on the end of the string and then hold the rim of the wheel stationary so that you can position the motion detector on the floor as shown in the diagram below. diagram courtesy of Daniel Weaver (c/o 2008)

When you think everything is aligned, one student should start LoggerPro 3.1. With the motion detector properly connected, the program should display graphs of position versus time and velocity versus time. When you are ready to obtain data, hit the Collect button on the top right-hand side of the program window and run a few test trials to make sure that the detector can "see" the bottom of the hanger as the wheel rotates and the hanger descends. You will be watching for the classic parabolic position-time graph signifying that the hanger is accelerating in a negative direction as the string unwraps and it descends towards the ground. Once this graph has formed, stop collecting data.

To analyze your velocity-time graph highlight a central section of your parabola, click on the velocity-time graph, and the linear fit, R=, button in the top toolbar. The acceleration for that trial will be displayed as the slope of your velocity-time graph. In this case it was -0.1105 m/s/s. Repeat each trial two times, taking the average as your final value for each mass.

Data Collection

 mass(grams) trial 1(m/sec2) trial 2(m/sec2) average(m/sec2) 50 60 70 80 90 100

Data Analysis and Conclusions

We will now use EXCEL to graph 1/a vs 1/m and data analysis techniques to determine the bicycle wheel's Moment of inertia. Open the file 1-bicycle.xls on the file system and input your data.

 What is the equation of your line?

 If the radius of the wheel is 0.28 meters, use the slope of your line to determine its moment of inertia.

 If the mass of the wheel is 1.75 kg, what is the wheel's radius of gyration, k?

If the length of string was 1.5 meters and the hanger was released from a position of rest, use the data from your final trial to answer the following questions.

 What was the average acceleration for your last trial?

 Determine how fast the mass hanger was traveling at the end just as the mass hanger stopped falling and was jerked upwards.

 Determine how fast the wheel was rotating just as mass hanger stopped falling and was jerked upwards.

 What was the wheel's angular momentum just before the mass hanger stopped falling and was jerked upwards?

 What was the total KE in the system (the wheel's rotational KE plus the mass hanger's linear KE) just before the mass hanger stopped falling and was jerked upwards?

 What was the total PE in the system prior to the mass hanger's release?

 Was energy conserved during this final trial? Why or why not?