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PS-3220

 Experiment 2: Rotational Inertia of Disk and Ring

19

013-15949A

Procedure

Measurements for the Experimental Method

A. Finding the Acceleration of the Ring and Disk

1.

In the data collection software, create an experiment to measure the angular velocity (in radians per second) 
versus time (in second) of the ring and disk.

In PASCO Capstone, for example, drag the Graph icon from the Displays palette to the workbook. Select 
“Angular Velocity (rad/s)” for the vertical axis, and “Time (s)” for the horizontal axis.

Click the Hardware Setup icon in the Tools palette to open the “Hardware Setup” panel. In the panel, click the 
properties button (it looks like a gear wheel in the lower right corner).

In the Properties window for Linear Accessory, select the size of the 3-step Pulley you are using. The default 
setting is “Large Pulley (Groove)”. Click OK.

2.

Put a 50-g mass on the Mass Hanger and turn the 3-step Pulley to wind up the thread so the hanger is just 
below the Super Pulley. Hold the 3-step Pulley.

3.

Click Record to begin recording data, and release the 3-step Pulley, allowing the hanger to fall. 

4.

Caution! Click Stop to end data recording BEFORE the hanger reaches the floor or the thread completely 
unwinds from the 3-step Pulley.

5.

In the Graph display, select the region of the data that represents when the ring and disk were accelerating.

6.

In the Graph display, select “Linear” from the curve fit menu.

The slope, m, of the linear fit represents the angular acceleration 
(

) for the Point Mass and Apparatus

7.

Record the value of the slope, m, as the angular acceleration in Data Table 2.

Data Table 2: Experimental Rotational Inertia Data

C. Finding the Acceleration of the Disk Alone

1.

In “Finding the Acceleration of Ring and Disk,” both the disk and the ring are rotating; therefore, it is necessary 
to determine the acceleration and the rotational inertia of the disk by itself so this rotational inertia can be sub-
tracted from the total, leaving only the rotational inertia of the ring.

2.

Take the ring off the apparatus and repeat the steps under “Finding the Acceleration of the Ring and Disk” for 
the disk alone. Record the results in Data Table 3.

Calculations

3.

Calculate the experimental value of the rotational inertia of the ring and disk together, and record the value in 
Data Table 3.

Ring and Disk 

Combined

Disk Alone

Hanging Mass

Slope, m

Radius

Summary of Contents for PS-3220

Page 1: ...w Check under Resources Equipment Included Equipment Included Wireless Rotary Motion Sensor Three step Pulley O ring Small Thumbscrew Micro USB Cable 1 meter Thumbscrew Required Item Part Number PASCO...

Page 2: ...he sensor has a platform for mounting a Super Pulley with Table Clamp optional Using the Sensor The sensor is designed to work with PASCO data collection software to measure position velocity and acce...

Page 3: ...hen the unit is fully charged The battery status LED will shine yellow as the battery is charging and will shine green when the battery is charged The battery is partially charged at the factory Initi...

Page 4: ...oth For SPARKvue select the Bluetooth icon In the Wireless Devices list The sensors are ordered by proximity to the device Select the correct address that matches the Device ID XXX XXX number found on...

Page 5: ...begin recording data Troubleshooting the Sensor If the sensor loses Bluetooth connection and will not reconnect try cycling the ON button Press and briefly hold the button until the status LEDs blink...

Page 6: ...side of the sensor To provide a known torque wrap a string around one of the steps of the 3 step Pulley Arrange the end of the string over the Super Pulley and attach a hanging mass Adjust the Super P...

Page 7: ...to the 3 step Pulley and shaft Mount a cylindrical mass on the rod to use the rod as a pendulum Investigate the period of oscillation of the pendulum when the amount of mass or the position of the mas...

Page 8: ...onto the shaft of the Wireless Rotary Motion Sensor Replace the gyroscope assembly on the vertical shaft See the PASCO web site at www pasco com for more information Experiments Experiments for the W...

Page 9: ...0 Experiments 9 013 15949A Rotational Resolution 0 00157 radian Maximum Rotation Rate 30 rotations per second Optical Encoder Bidirectional indicates direction of motion 4 000 divisions rotation Item...

Page 10: ...at vary by country and region It is your responsibility to recycle your electronic equipment per your local environmental laws and regulations to ensure that it will be recycled in a manner that prote...

Page 11: ...the More Info button Click the System Report button Select Bluetooth from the sidebar on the left underneath Hardware Scan down the list of information until you find LMP Version If your Mac is equip...

Page 12: ...Wireless Rotary Motion Sensor Appendix A Compatibility 12 013 15949A...

Page 13: ...and the resulting angular acceleration is measured Since I where is the angular acceleration which is equal to a r a linear acceleration and is the torque caused by the weight hanging from the thread...

Page 14: ...iddle of the groove on the clamp on Super Pulley 7 Adjust the Super Pulley height so that the thread is level with the 3 step pulley Procedure Part 1 Measurements for the Theoretical Rotational Inerti...

Page 15: ...unwinds from the 3 step Pulley 5 In the Graph display select the region of the data that represents when the Point Masses and Apparatus were accelerating 6 In the display select Linear from the curve...

Page 16: ...the calculation in Data Table 3 2 Calculate the experimental value of the rotational inertia of the apparatus alone and record the calculation in Data Table 3 3 Subtract the rotational inertia of the...

Page 17: ...ion is measured Since I where is the angular acceleration which is equal to a r a acceleration and is the torque caused by the weight hanging from the thread that is wrapped about the 3 step Pulley on...

Page 18: ...ead over the Super Pulley such that the thread is in the groove of the Super Pulley and the Mass Hanger hangs freely 5 Adjust the Super Pulley with Clamp to an angle so that the thread runs in a line...

Page 19: ...he hanger to fall 4 Caution Click Stop to end data recording BEFORE the hanger reaches the floor or the thread completely unwinds from the 3 step Pulley 5 In the Graph display select the region of the...

Page 20: ...le 3 5 Subtract the rotational inertia of the disk from the total rotational inertia of the ring and disk and record this as the rotational inertia of the ring alone 6 Use a percent difference to comp...

Page 21: ...her The rotational inertia of a disk is given as and the final rotational inertia of a disk and ring together is where M1 is the mass of the disk M2 is the mass of the ring R is the radius of the disk...

Page 22: ...gion of the data that represents when the ring was dropped onto the disk 6 In the Graph display select the data analysis tool that shows the coordinates of any point in the plot of data and move the c...

Page 23: ...lost during the collision Calculate the energy lost and record the results in the Data Table Data Table Data and Results Initial angular velocity Final angular velocity experimental value Mass of dis...

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