PASCO PS-3220 Reference Manual

Reference Guide

ON/OFF Button

Micro USB Port

O-Ring for

Three-step Pulley

Three-step Pulley

Battery LED

Small Thumbscrew

Thumbscrew

Micro USB Cable

Support Rod Hole

Support Rod Hole

013-15949A

Wireless Rotary Motion Sensor

PS-3220

For downloadable experiments, go to www.pasco.com and enter PS-3220 in the Search window. 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 Data Collection Software: Capstone or SPARKvue see www.pasco.com

*See the PASCO catalog or the PASCO web site for more information.

www.pasco.com

PS-3220 Introduction

Platform

Equipment used with the sensor Equipment used with the sensor

Rotational Inertia Accessory Kit (ME-3420) (includes Ring and Disk Set (ME-3419), Pendulum

Accessory (ME-8969), and Super Pulley with Clamp (ME-9444B))

Physical Pendulum Set (ME-9633) Track String Adapter (ME-6569)

Rotating Platform (ME-8951) Centripetal Force Pendulum (ME-9821)

Gyroscope Mounting Bracket (ME-8963) Polarization Analyzer (OS-8533A)

Dynamics Track Mount Accessory (CI-6692) Three-Axis Gyroscope (ME-8960)

Three-Step Pulley Accessory (CI-6693)

Introduction

The PASCO Wireless Rotary Motion Sensor is a versatile position and motion measuring
device. It measures angles to a resolution of 0.18°, and detects the direction of motion.
Markings on the outside of the case indicate which is the default positive direction. The
maximum speed is between 20 and 80 revolutions per second.

The sensor comes with a removable three-step pulley (10 millimeter (mm), 29 mm, and
48 mm diameters), and a rubber “O”-ring that fits into the largest diameter step. The
three-step pulley can be placed large-diameter down or large-diameter up on the shaft. A
tab on the inside of the pulley matches a notch on the outside of the shaft. The pulley has
a notch and a small hole in the outer edge of the largest and second largest steps for
attaching a string. One side of the 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
acceleration. Use it to study optics, dynamics, centripetal force, or motion of a pendulum.

Data Collection Software

PASCO Capstone SPARKvue

• Mac OS X • Mac OS X

• Windows • Windows

• iOS

• Android

• Chromebook

See the PASCO web site at

www.pasco.com/software

for help in selecting the right PASCO software and to check for the latest versions.

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2

PS-3220 Introduction

[]

To Micro USB port

Micro USB cable

To USB port

Micro USB

Port

ON/OFF

Button

Platform

Software Help

See the SPARKvue Help or PASCO Capstone Help for information about collecting, displaying, and analyzing data.

• In SPARKvue, select the HELP button ( ) in any screen including the Home Screen.

• In PASCO Capstone, select PASCO Capstone Help from the Help menu, or press F1.

Compatibility

For more information about wireless compatibility, see the PASCO website at:

www.pasco.com/compatibility

Platform Bluetooth SMART Compatibility

iOS iPad 3 and later

SPARK LX / LXi All models

Android Android 4.4 and later

Chromebook Chrome OS (requires PS-3500 Adapter*)

Mac OS X Models introduced July 2011 or later*

Windows Windows 7 and later (requires PS-3500 Adapter*)

See Appendix B for more information about the PS-3500 Adapter and Mac OS X models.

iPhone 4S and later
iPod touch 5 and later

Initial Step: Charge the Battery

• Connect the Cable: Use the Micro USB Cable to

connect the micro USB port on the side of the sensor
to a USB port or USB charger such as the PASCO
PS-2575 USB Single Port Charger. Charging begins
automatically. The charger circuit inside the sensor
turns itself off when 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. Initial charging time may be three hours or
longer depending on the power source and the
condition of the battery.

ON/OFF Information

To turn the sensor on, press the ON button. The status
LEDs will blink. To turn the sensor off, press and hold the ON button for a moment until the status LEDs stop
blinking. The sensor puts itself to sleep after one hour of inactivity if connected, and after several minutes if not
connected.

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3

Wireless Rotary Motion Sensor Set Up the Software

LED Information

The Bluetooth and the Battery Status LEDs operate as follows:

For a wireless Bluetooth connection:

Bluetooth LED Status Battery LED Status

Red blink Ready to pair Red blink Low power

Green blink Connected

Yellow blink Logging*

For a micro USB cable connection to a USB port:

Bluetooth LED Status Battery LED Status

OFF -- Yellow ON Charging

OFF -- Green ON Charged

Yellow blink Logging*

For a micro USB cable connection to a USB charger:

Bluetooth LED Status Battery LED Status

Red blink Ready to pair Yellow ON Charging

Green blink Connected Green ON Charged

Yellow blink Logging*

*Logging: PASCO wireless sensors can either stream live data to a compatible device or log data (save it to the
sensor’s memory). The data can then be uploaded to the device for display and analysis at a later time. Logging
capability supports long-term or remote data collection while not connected to the device.

Note: The latest versions of SPARKvue and PASCO Capstone support logging. Check the PASCO Web page at:

www.pasco.com/software

for the latest software version.

Set Up the Software

SPARKvue

Connecting the Sensor to a Tablet or a Computer via Bluetooth

• 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 the sensor.
Select Done.

Connecting the Sensor to a Computer with the Micro USB Cable

• Connect the micro end of the included Micro USB Cable into the micro USB port on the side of the sensor.

Connect the other end of the Micro USB Cable to a USB port on the computer, or into a powered USB hub
connected to the computer.

• In the SPARKvue Home Screen, select a measurement from the list under the sensor’s name. A graph of the
measurement versus time opens.

4

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PS-3220 Mounting the Wireless Rotary Motion Sensor

Case

Collecting Data

• Select the Start button to begin collecting data.

PASCO Capstone

Connecting the Sensor to a Tablet or a Computer via Bluetooth

• For PASCO Capstone, select Hardware Setup in the Tools palette. In Hardware Setup the sensors are

ordered by proximity to the device. Select the address that matches the Device ID XXX-XXX number on the
sensor.

Select a display in the main window or from the Display palette. In the display, use the <Select Measurement>
menu to pick a measurement to be shown.

Connecting the Sensor to a Computer with the Micro USB Cable

• Connect the micro end of the included Micro USB Cable into the micro USB port on the end of the sensor.

Connect the other end of the Micro USB Cable to a USB port on the computer, or into a powered USB hub
connected to the computer.

• In PASCO Capstone, select a display in the main window or from the Displays palette. In the display, use the

<Select Measurement> menus to pick the measurement to be shown.

Collecting Data

• Select Record to 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 in sequence, and then release the button. Start the sensor in the
usual way.

• If the sensor stops communicating with the computer software or tablet application, try restarting the software

or application. If the problem remains, press and hold the ON button for 10 seconds and then release. Start the
sensor in the usual way.

• Turn Bluetooth off and then back on. Retry.

Mounting the Wireless Rotary Motion Sensor

The sensor case has two support rod holes that fit rods up to 12.7 mm
in diameter, such as the ME-8736 45 cm Stainless Steel Rod, and the
case can be put on the support rod using either of the support rod
holes.

It is possible to mount the Wireless Rotary Motion Sensor horizontally
on a support rod with the Three-step Pulley facing up or facing
sideways. You can mount the sensor vertically with the pulley facing
forward.

When mounted on a track as shown, a Rotary Motion Sensor could be
used to measure the motion of a PASCO Cart as it is pulled by a string
suspended over the Three-step Pulley of the sensor and attached to a
hanging mass.

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5

Wireless Rotary Motion Sensor Mounting the Wireless Rotary Motion Sensor

Super Pulley

with Table

Clamp

Disk

Wireless Rotary Motion

Sensor with 3-step

Pulley

Hanging

Mass

T

mg

a

Attaching Accessories to the Wireless Rotary Motion Sensor

Using the Disk from the Disk and Ring Set (ME-3419)

For rotational inertia experiments, mount the
Wireless Rotary Motion Sensor with the Disk
horizontal. The underside of the Disk has a
square shaped indent that fits the
square-shaped top of the 3-Step Pulley. Mount
a Super Pulley with Clamp (ME-9448B) on the
platform at the 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 Pulley on the platform so that
the string is tangent to the step on the 3-step
Pulley on the sensor.

Perform a conservation of angular momentum
experiment by dropping a second Disk onto the
first Disk as it is rotating. Alternately, attach one
of the Ring Alignment Devices to the first Disk
and then drop the Ring onto the first disk.(See
the suggested experiments.)

6

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PS-3220 Mounting the Wireless Rotary Motion Sensor

Pendulum

Accessory Rod

Rod

guides

Cylindrical

mass

Shaft

Screw

Point Mass Setup

Dynamics

Track Mount

Accessory

Square

nut into

T-slo t

Mounting rod

Attaching the Pendulum Accessory Rod (part of ME-8969 Pendulum Accessory) to the Wireless Rotary Motion Sensor

To mount the rod of the Pendulum Accessory to the Wireless Rotary
Motion Sensor, orient the 3-step Pulley so that the large diameter step is
away from the sensor case. The large diameter step has two pair of rod
guides opposite each other on the top edge. Align the rod with the rod
guides and use the captive screw in the center of the rod to attach the rod
and pulley onto the sensor’s shaft.

Point Mass Setup Attach the center of the rod to the 3-step Pulley and
shaft and mount the cylindrical masses at the ends of the rod to
investigate the rotational inertia (moment of inertia) of point masses.

Pendulum Setup Attach the end of the rod 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 mass is changed. Investigate the period of oscillation as the amplitude of the
swing is changed.

.

Mounting the Wireless Rotary Motion Sensor on a PASCO Track

The sensor can also be mounted on the short rod that is part of the
Dynamics Track Mount Accessory (CI-6692).

Slide the square nut of the Dynamics Track Mount Accessory into the
T-slot on the side of the track. Adjust the position of the mounting
rod.on the Dynamics Track Mount Accessory.

When mounted on the track as shown, the Wireless Rotary Motion
Sensor could be used to measure the motion of a PASCO Cart as it
is pulled by a string suspended over the Three-step Pulley of sensor
and attached to a mass hanger.

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7

Wireless Rotary Motion Sensor Experiments

Hanging

mass

PAS CO

Cart

PAS CO

Track

Mounting rod

Gyroscope

Mounting

Bracket

Slotted

guide

arm

See the PASCO web site at www.pasco.com for more information.

Mounting the Wireless Rotary Motion Sensor to a Gyroscope

Use the Gyroscope Mounting Bracket (ME-8963, available separately) to
mount the Wireless Rotary Motion Sensor to the Three-Axis Gyroscope
(ME-8960). Remove the gyroscope assembly from the vertical shaft of the
large “A” base. Mount the Gyroscope Mounting Bracket onto the vertical
shaft. Remove the three-step pulley from the Wireless Rotary Motion
Sensor, and mount the sensor on the Gyroscope Mounting Bracket with the
thumbscrews included with the bracket. Mount the slotted guide arm 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 Wireless Rotary Motion Sensor in electronic format are available to download from the PASCO
web site.

www.pasco.com

Go to the web site, enter PS-3220 in the Search window, and check under Resources.

Three suggested experiments are:

• Rotational Inertia of a Point Mass

• Rotational Inertia of Disk and Ring

• Conservation of Angular Momentum.

Specifications

Item: Value

Three-step Pulley 10, 29 and 48 mm diameter

Sensor Dimensions 9 cm by 6.5 cm by 4 cm, 6.35 mm diameter shaft

Resolution ±0.09° or 0.0078 mm

0.02 mm (linear) and 0.09° (angular) at 2,000 points per revolution

8

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PS-3220 Experiments

Item: Value

Rotational Resolution 0.00157 radian

Maximum Rotation Rate 30 rotations per second

Optical Encoder Bidirectional, indicates direction of motion, 4,000 divisions/rotation

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9

Wireless Rotary Motion Sensor Technical Support

Technical Support

For assistance with any PASCO product, contact PASCO at:

Address: PASCO scientific

Web: www.pasco.com
10101 Foothills Blvd.
Roseville, CA 95747-7100

Phone: [phone] (worldwide)

Email [e-mail]
877-373-0300 (U.S.)

Check the PASCO website for the latest version of the instruction manual.

www.pasco.com/manuals

Limited Warranty For a description of the product warranty, see the PASCO catalog. Copyright The PASCO scientific Instruction Manual is
copyrighted with all rights reserved. Permission is granted to non-profit educational institutions for reproduction of any part of this manual,
providing the reproductions are used only in their laboratories and classrooms, and are not sold for profit. Reproduction under any other
circumstances, without the written consent of PASCO scientific, is prohibited. Rev: 11/18. Trademarks PASCO, PASCO Capstone, and
SPARKvue are trademarks or registered trademarks of PASCO scientific, in the United States and/or in other countries. For more information
visit

www.pasco.com/legal.

Product End of Life Disposal Instructions:

This electronic product is subject to disposal and recycling regulations that 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 protects human health and the environment. To find out where you can drop off
your waste equipment for recycling, please contact your local waste recycle/disposal service, or the place where
you purchased the product.

The European Union WEEE (Waste Electronic and Electrical Equipment) symbol (to the right)
and on the product or its packaging indicates that this product must not be disposed of in a
standard waste container.

Appendix A: Compatibility

Check the PASCO Web page at

www.pasco.com/compatibility

for the latest information on Bluetooth SMART compatibility.

Platform Bluetooth SMART Compatibility

iOS iPad 3 and later

SPARK Element All models

Android Android 4.3 and later

Chromebook Chrome OS (requires PS-3500 Adapter*)

Mac OS X

Windows 7 and 8 Requires PS-3500 Adapter*

1

iPhone 4S and later
iPod touch 5 and later

Models introduced July 2011 or later

Windows 10 Bluetooth SMART compatible

10

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PS-3220 Appendix A: Compatibility

PS-3500 USB
Bluetooth 4.0

Adapter

*The PS-3500 USB Bluetooth 4.0 Adapter, when connected to a USB port, allows up to three
Bluetooth SMART devices, such as this PASCO wireless device, to connect to Windows
computers, Chromebooks, and older Macintosh computers.

Note: The PS-3500 USB Bluetooth 4,0 Adapter is the only adapter we can currently recommend.
Many other Bluetooth 4.0 adapters are available but this adapter has a specific design that
enables in-app pairing of Bluetooth SMART sensors.

1

To check the Mac computer’s Bluetooth compatibility, do the following:

• Click the

 (Apple) Menu.

• Select About This Mac

• Click 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 equipped with Bluetooth SMART, the LMP Version will show 0x6. (Anything lower than 0x6

means an older version of Bluetooth. Your device will need the PS-3500 USB Bluetooth 4.0 Adapter.)

1

The Mac Mini and MacBook Air were updated with Bluetooth SMART support in 2011. The MacBook Pro was

updated in 2012. The Mac Pro that debuted in December 2013 has Bluetooth SMART support.

Exception: Before you upgrade to El Capitan (Mac OS X 10.11.x), if you have a Macintosh with LMP version “0x4”
that requires the PS-3500 USB Bluetooth 4.0 Adapter, please contact PASCO Technical Support for further
instructions.

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11

Wireless Rotary Motion Sensor Appendix A: Compatibility

12

013-15949A

PS-3220 Experiment 1: Rotational Inertia of a Point Mass

I

total

M

total

R

2

=

I =

 rT=

FmgT– ma==

Tmga–=

Experiment 1: Rotational Inertia of a Point Mass

Equipment Required* Equipment Required*

Wireless Rotary Motion Sensor (PS-3220 Base and Support Rod (ME-9355)

PASCO Data Collection Software Mass and Hanger Set (ME-8979)1

Rotational Inertia Accessory Kit (ME-3420) Triple Beam Balance (SE-8723)

Calipers (SF-8711) Paper clips (for masses <1g)

*See the PASCO Web site at www.pasco.lcom for more information

Purpose

The purpose of this experiment is to find the rotational inertia of a point mass experimentally and to verify that this
value corresponds to the calculated theoretical value.

Theory

Theoretically, the rotational inertia, I, of a point mass is given by I = MR2, where M is the mass, and R is the
distance the mass is from the axis of rotation. Since this experiment uses two masses equidistant from the center of
rotation, the total rotational inertia will be

where M

To find the rotational inertia experimentally, a known torque is applied to the object and the resulting angular
acceleration is measured. Since

where
weight hanging from the thread that is wrapped around the 3-step Pulley.

where r is the radius of the chosen pulley about which the thread is wound, and T is the tension in the thread when
the apparatus is rotating.

Applying Newton’s Second Law for the hanging mass, m, gives

(see Figure 1.1). Solving for the tension in the thread gives:

After the angular acceleration of the mass (m) is measured, the torque and the linear acceleration can be obtained
for the calculation of the rotational inertia.

= M1 + M, the total mass of both point masses.

total

 = I

,,



is the angular acceleration, which is equal to a/r (a = linear acceleration), and  is the torque caused by the

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13

Wireless Rotary Motion Sensor Experiment 1: Rotational Inertia of a Point

Rod and Masses

3-Step Pulley

Wireless Rotary

Motion Sensor

Super Pulley

with Clamp

Hanger

and Mass

Support

Rod

Figure 1.1: Rotary Motion Sensor and Free

Body Diagram

Equipment Setup

1. Attach a mass on each end of the rod (part of the Rota-

tional Inertia lAccessory Kit) equidistant from the rod
center. You may choose any radius you wish.

2. Tie one end of a thread to a Mass Hanger and tie the
other end to one of the levels of the 3-step Pulley on the
Wireless Rotary Motion Sensor (WRMS).

3. Mount the rod and masses to the pulley on the Wireless
Rotary Motion Sensor. Please note the orientation of
the 3-step Pulley.

4. Mount the WRMS on a support rod. Make sure that the
support rod does not interfere with the rotation of the
rod and masses. See Figure 1.1.

5. Mount the Super Pulley with Clamp (part of the
ME-3420) on the platform of the Wireless Rotary Motion
Sensor.

6. Drape the thread over the Super Pulley such that the thread is in the groove of the pulley and the Mass Hanger

Note: The Super Pulley with Clamp must be adjusted at an angle, so that the thread runs in a line tangent to the
point where it leaves the 3-step Pulley and straight down the middle 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 Inertia

1. Weigh the two masses from the ends of the thin rod to find the total mass M

2. Measure the distance from the axis of rotation to the center of the masses and record this radius in Data Table

Part 2: Measurement for the Experimental Method

A. Finding the Acceleration of the Point Masses and Apparatus

1. In the data collection software, create an experiment to measure the angular velocity (in radians per second)

• In PASCO Capstone, for example, drag the Graph icon from the Displays palette to the workbook. Select

hangs freely (see Figure 1.1).

and record the value in Data

total

Table 1.

1.

Data Table 1: Theoretical Rotational Inertia

Total Mass

Radius

versus time (in seconds) of the point masses and apparatus.

“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).

14

013-15949A

PS-3220 Experiment 1: Rotational Inertia of a Point Mass

• 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 Point Masses and Apparatus were

accelerating.

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

The slope, m, of the linear fit represents the angular acceleration (a) for the Point Mass and Apparatus

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

8. Using calipers, measure the diameter of the pulley about which the thread is wrapped and calculate the radius.

Record the radius in Data Table 2.

In the previous procedure, the apparatus is rotating and contributing to the total rotational inertia. The next step is to
find the rotational inertia of the apparatus by itself so that this rotational inertia can be subtracted from the total.

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15

Wireless Rotary Motion Sensor Experiment 1: Rotational Inertia of a Point

B. Finding the Acceleration of the Apparatus Alone

1. Take the point masses off the ends of the rod.

2. Repeat the procedure from Part A for finding the angular acceleration of the apparatus alone.

• You may need to decrease the amount of hanging mass so that the apparatus does not accelerate too fast for

smooth data collection.

• Remember that the value of the slope, m, is the angular acceleration.

3. Record the data in Data Table 2.

Data Table 2: Experimental Rotational Inertia Data

Point Masses and

Apparatus

Hanging Mass

Slope, m

Radius

Apparatus Alone

Calculations

1. Calculate the experimental value of the rotational inertia of the point masses and apparatus together and

record 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 apparatus from the total rotational inertia of the point masses and
apparatus together. Record this in Data Table 3 as the rotational inertia of the point masses alone.

4. Calculate the theoretical value of the rotational inertia of the point masses and record the calculation in Data
Table 3.

5. Calculate the percent difference to compare the experimental value to the theoretical value, and record the
percent difference in Data Table 3.

Point Masses and Apparatus Combined

Apparatus Alone

Point Masses (experimental value)

Point Masses (theoretical value)

Percent Difference

16

Data Table 3: Results

Component Rotational Inertia

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PS-3220 Experiment 2: Rotational Inertia of Disk and Ring

Figure 2.1: Ring about

center of mass

R1

R2

I

1
2

---

MR

1

2

R

2

2

+=

I

1
2

---

MR

2

=

Figure 2.2: Disk about

center of mass

R

I





---

=

 rT=

FmgT– ma==

Tmga–=

Experiment 2: Rotational Inertia of Disk and Ring

Equipment Required* Equipment Required*

Wireless Rotary Motion Sensor (PS-3220 Base and Support Rod (ME-9355)

PASCO Data Collection Software Mass and Hanger Set (ME-8979)1

Rotational Inertia Accessory Kit (ME-3420) Triple Beam Balance (SE-8723)

Calipers (SF-8711) Paper clips (for masses <1g)

*See the PASCO Web site at www.pasco.lcom for more information

Purpose

The purpose of this experiment is to experimentally find the rotational inertia of a ring and a disk and verify that
these values correspond to the calculated theoretical values.

Theory

Theoretically, the rotational inertia, I, of a ring about its center of mass is given by:



where M is the mass of the ring, R

is the inner radius of the ring, and R is the outer

radius of the ring. See Figure 2.1.

The rotational inertia of a disk about its center of mass is given by:

where M is the mass of the disk and R is the radius of the disk. See Figure 2.2. To find
the rotational inertia experimentally, a known torque is applied to the object and the
resulting angular acceleration is measured, Since

where



is the angular acceleration, which is equal to a/r (a = acceleration), and  is the

 = I

,

torque caused by the weight hanging from the thread that is wrapped about the 3-step
Pulley on the Rotary Motion Sensor. The torque is given by:

where r is the radius of the pulley step about which the thread is wound, and T is the tension in the thread when the
apparatus is rotating.

Applying Newton’s Second Law for the hanging mass, m, gives:

See Figure 2.3. Solving for the tension in the thread gives:

Once the angular acceleration is measured, the radius and the linear acceleration, a, can be obtained for the
calculation of the torque.

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17

Wireless Rotary Motion Sensor Experiment 2: Rotational Inertia of Disk and

Figure 2.3: Rotary Motion Sensor

Setup and Free Body Diagram

Super Pulley

with Table

Clamp

Hanging

mass

Disk

Wireless Rotary Motion

Sensor with 3-step

Pulley

Thin
Ring

T

mg

a

Disk Alignment

Guide

Procedure

Measurements for the Theoretical Rotational Inertia

1. Weigh the ring and the disk to find their masses and record these masses in Data Table 1.

2. Measure the inside and outside diameters of the ring and calculate the radii, R

and R2. Record in Data Table

1

1.

3. Measure the diameter of the disk and calculate the radius, R, and record into Data Table 1.

Data Table 1: Theoretical Rotational Inertia.

Mass of ring

Mass of disk

Inner radius of ring

Outer radius of ring

Radius of disk

Setup

1. Mount the Wireless Rotary Motion Sensor

(WRMS) on a support rod.

2. Mount the Super Pulley with Clamp on the
side of the WRMS as shown in Figure 2.3.

3. Tie one end of a thread to a Mass Hanger
and the other end of the thread to one of the
levels of the 3-step Pulley on the RMS.

4. Drape the thread 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 tangent
to the point where it leaves the 3-step Pulley
and is straight down the middle of the groove
on the Super Pulley.

6. Remove the thumbscrew from the 3-Step
Pulley. Place the disk directly on the
square-shaped top of the 3-step Pulley as
shown in Figure 2.3.

7. Place one of the disk alignment guides on the
disk. Replace the thumbscrew to the 3-Step
Pulley so that the disk alignment guide is
firmly held in place.

8. Place the thin ring on the disk alignment guide on top of the disk as shown in figure 2.3..

18

013-15949A

PS-3220 Experiment 2: Rotational Inertia of Disk and Ring

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

Ring and Disk

Combined

Hanging Mass

Slope, m

Radius

Disk Alone

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 sub­tracted 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.

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Wireless Rotary Motion Sensor Experiment 2: Rotational Inertia of Disk and

4. Calculate the experimental value of the rotational inertia of the disk alone and record the value in Data Table 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 compare the experimental values to the theoretical values.

Data Table 3: Results

Item Rotational Inertia

Ring and Disk

Disk alone

Ring alone

Percent difference for the disk

Percent difference for the ring

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013-15949A

PS-3220 Experiment 3: Conservation of Angular Momentum

LIiiIf

f

==

I

i

1
2

---

M

1

R

2

=

I

f

1
2

---

M

1

R

2

1
2

---

M

2r1

2

r

2

2

++=



f

M1R

2

M1R2M2r

1

2

r

2

2

++

-------------------------------------------------------



i

=

Experiment 3: Conservation of Angular Momentum

Equipment Required* Equipment Required*

Wireless Rotary Motion Sensor (PS-3220 Base and Support Rod (ME-9355)

PASCO Data Collection Software Mass and Hanger Set (ME-8979)1

Mini-Rotational Accessory (CI-6691) Triple Beam Balance (SE-8723)

Calipers (SF-8711) Paper clips (for masses <1g)

*See the PASCO Web site at www.pasco.lcom for more information

Purpose

A non-rotating thin ring is dropped onto a rotating disk, and the final angular speed of the system is compared with
the value predicted using the principle of the conservation of angular momentum.

Theory

When the ring is dropped onto the rotating disk, there is no net torque on the system since the torque on the ring is
equal and opposite to the torque on the disk. Therefore, there is no change in angular momentum; angular
momentum (L) is conserved.

where I
and

is the initial rotational inertia and

i



is the final angular speed of the disk and the ring together.

f



is the initial angular speed of the disk and If is the final rotational inertia

i

The rotational inertia of a disk is given as:

and the final rotational inertia of a disk and ring together is:

where M

is the mass of the disk, M2 is the mass of the ring, R is the radius of the disk, and r1 and r2 are the inner

1

and outer radii of the ring.

Based on this, the final rotational speed is given by:

Setup

1. Mount the Wireless Rotary Motion Sensor to a support rod. Remove the thumbscrew from the 3-Step Pulley.

Place the disk directly on the square-shaped top of the 3-step Pulley as shown in Figure 3.1.

2. Place one of the disk alignment guides on the disk. Replace the thumbscrew to the 3-Step Pulley so that the

disk alignment guide is firmly held in place.

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21

Wireless Rotary Motion SensorExperiment 3: Conservation of Angular Momen-

Figure 3.1: Setup for Dropping Ring onto Disk

Disk

WRMS with

3-step Pulley

Figure 3.1 Setup for Conservation of

Angular Momentum

3. .In the data collection software, create an

experiment to measure the angular velocity (in
radians per second) versus time (in second)
of the disk before and after the ring is dropped
on top of it.

• 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.

Procedure

1. Hold the thin ring just above the disk align-

ment guide that is on the top of the disk.

2. Give the disk a spin with your hand and click
Record to begin recording data.

3. After about 25 data points have been
recorded, drop the thin ring onto the spinning
disk. See Figure 3.1.

4. Click Stop to end data recording after the disk
and ring have made a few rotations.

5. In the Graph display, select the region 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 cursor to the data point that is immediately before the collision. Record the Angular Velocity at
this point as the initial angular velocity in the Data Table.

7. Move the cursor to the data point immediately after the collision. Record the Angular Velocity at this point as
the final angular velocity in the Data Table.

8. Weigh the ring and disk and record their masses. Measure the inner and outer radii of the ring, and the radius
of the disk. Record these values in the Data Table.

Analysis

1. Calculate the theoretical value for the final angular velocity and record this value in the Data Table.

2. Calculate the percent difference between the experimental and theoretical values of the final angular velocity

and record it in the Data Table.

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013-15949A

PS-3220 Experiment 3: Conservation of Angular Momentum

% KE lost =

1
2

---

I

ii

2

1
2

---

I

ff

2

+

1
2

---

I

i

2



i

2

--------------------------------------











Questions

1. How does the experimental result for the final angular velocity compare with the theoretical value for the final

angular velocity?

2. What percentage of the rotational kinetic energy was “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 disk (M1)

Mass of ring (M2)

Inner radius of ring (r1)

Outer radius of ring (r2)

Radius of disk (R)

Final angular velocity
(theoretical value)

Percent difference between experimental and
theoretical values

Percent of kinetic energy lost

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