PASCO CI-6538 User manual

Instruction Manual
Manual No. 012-06053B
Rotary Motion
Sensor
Model No. CI-6538

Rotary Motion Sensor Model No. CI-6538
2®
Table of Contents
Equipment List........................................................... 3
Optional Accessories................................................. 4-5
Mini-Rotational Accessory ............................................................................................................4
Linear Motion Accessory...............................................................................................................4
Chaos Accessory ............................................................................................................................4
“A” Base Rotational Adapter.........................................................................................................5
RMS/Gyroscope Mounting Bracket...............................................................................................5
IDS Mount Accessory....................................................................................................................6
3-Step Pulley Accessory ................................................................................................................6
Introduction ............................................................. 7
Equipment Setup Options ............................................... 8
Mounting the Rotary Motion Sensor on a Support Rod ................................................................8
Mounting the Rotary Motion Sensor to a Dynamics Track ...........................................................9
Mounting the Rotary Motion Sensor to the “A” Base .................................................................10
Mounting the Rotary Motion Sensor to the Gyroscope ...............................................................11
Attaching the Mini-Rotational Accessory to the RMS .......................................................... 12-13
Attaching the “A” Base Rotational Adapter to the RMS.............................................................14
Using the Chaos Accessory with the RMS ..................................................................................15
Operating the Sensor with Data Collection Software ............. 16
Using the Rotary Motion Sensor with DataStudio Software .......................................................16
Suggested Experiments
Experiment 1: Rotational Inertia of a Point Mass.................................................................. 17-21
Experiment 2: Rotational Inertia of Disk and Ring ............................................................... 22-26
Experiment 3: Conservation of Angular Momentum ............................................................ 27-29
Appendix A: Specifications............................................ 30
Appendix B: Calibration ............................................... 31
Appendix C: Technical Support ....................................... 32
Appendix D: Copyright and Warranty Information .................. 33

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Model No. CI-6538 Rotary Motion Sensor
3
Rotary Motion Sensor
Model No. CI-6538
Equipment List
*Use Replacement Model Numbers to expedite replacement orders.
NA = not sold separately from PASCO
Included Equipment Replacement
Model Number*
1. Rotary Motion Sensor CI-6539
2. O-ring NA
3. Ziplock Bag NA
Additional Equipment Required Model Number
Any PASCO data acquisition device ( ScienceWorkshop ®500 interface,
ScienceWorkshop 750 SCSI or 750 USB interface)
CI-6400 or CI-6450
or CI-7599
A computer NA
DataStudio®Software CI-6470C
Optional Items Part Number
Rotary Motion Sensor Experiment Manual 021-06053
1
2
3

Rotary Motion Sensor Model No. CI-6538
4®
Optional Accessories
Mini-Rotational
Accessory - The PASCO
CI-6691 Mini-Rotational
Accessory is used to
perform rotational inertia
experiments, conservation
of angular momentum
experiments, and pendulum
experiments. Included are
an aluminum disk, a steel
ring, a long thin rod, and two brass masses which can be attached at
any point on the thin rod to act as point masses. (For instructions on
attaching this accessory, see “Equipment Setup” in this manual).
Linear Motion Accessory - The
PASCO CI-6688 Linear Motion
Accessory is a 21 cm long rack that is
inserted into the t-slot in the side of
the RMS to convert a linear motion
into a rotary motion. The teeth on the
rack engage a gear inside the RMS,
causing it to rotate as the rack is
pushed through the slot. The rack may
be inserted into either side of the
RMS. Sensors can be mounted to the
rack using the rod clamp which can be attached to either end of the
Linear Motion Accessory rack. (For instructions on using this
accessory, see “Equipment Setup” in this manual).
Chaos Accessory - The PASCO CI-
6689 Chaos Accessory consists of an
aluminum disk (identical to the one
provided with the Mini-Rotational
Accessory), a mass which attaches to
the edge of the disk to form a physical
pendulum, two springs for putting
tension in the thread, a mounting
bracket for mounting the RMS to the
PASCO Introductory Dynamics
System tracks (1.2 meter ME-9435A
or 2.2 meter ME-9458), and an adjustable-gap magnet which attaches

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Model No. CI-6538 Rotary Motion Sensor
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to the side of the RMS to provide variable magnetic damping. (For
instructions on using this accessory, see “Equipment Setup” in this
manual).
The Chaos Accessory is a driven damped physical pendulum. Various
types of phase plots can be made as the driving frequency, driving
amplitude, initial conditions, and the amount of damping are varied.
“A” Base Rotational Adapter -
The CI-6690 “A”-base Rotational
Adapter is used to mount the Rotary
Motion Sensor to the “A” base of the
ME-8951 Rotating Platform or the
ME-8960 Gyroscope. The RMS
provides higher resolution than a
Smart Pulley, and precession of the
Gyroscope can be plotted since the RMS keeps track of direction of
rotation. The adapter includes a mounting bracket, a shoulder screw, a
drive belt (o-ring), and a 3-step Pulley. (For instructions on attaching
this accessory, see “Equipment Setup” in this manual).
RMS/Gyroscope Mounting Bracket
The PASCO ME-8963 RMS/
Gyroscope Mounting Bracket
attaches the Rotary Motion Sensor to
the ME-8960 Gyroscope so the angle
of nutation can be detected. (For
instructions on attaching this
accessory, see “Equipment Setup” in this manual).

Rotary Motion Sensor Model No. CI-6538
6®
IDS Mount Accessory
The PASCO CI-6692 IDS Mount Accessory
is a bracket that allows the Rotary Motion
Sensor to be attached to the Introductory
Dynamics System tracks.
3-Step Pulley Accessory (CI-6693)
The PASCO CI-6693 3-step Pulley
Accessory includes an additional
pulley for mounting a 3-step Pulley on
each end of the Rotary Motion Sensor
rotating shaft. It also includes an o-
ring.

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Model No. CI-6538 Rotary Motion Sensor
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Introduction
The PASCO CI-6538 Rotary Motion Sensor is a bidirectional position
sensor designed for use with the PASCO ScienceWorkshop™ 750
Interface. It contains an optical encoder which gives a maximum of
1440 counts per revolution (360 degrees) of the Rotary Motion Sensor
shaft. The resolution can be set in the ScienceWorkshop software to
360 or 1440 times per revolution (1 degree or 1/4 degree). The
direction of rotation is also sensed.
The Rotary Motion Sensor has two phone plugs which plug into any
two adjacent digital channels on the 750 interface box.
The rod clamp can be mounted on three sides of the sensor case,
allowing the Rotary Motion Sensor to be mounted on a rod stand in
many different orientations. The 3-step Pulley keys into the rotating
shaft and can be mounted on either end of the shaft. A rubber o-ring is
intended to be slipped over the largest pulley step so the RMS can be
pressed against a surface to sense the relative motion between the
sensor and the surface. The end of the Rotary Motion Sensor where
the cord exits the case provides a platform for mounting a clamp-on
Super Pulley. The t-slot in either side of the RMS is for inserting the
optional Linear Motion Accessory rack. This allows you to measure
linear motion over the length of the rack.
thumbscrew
rod clamp
3-step Pulley
rotating shaft
platform
case
phone plugs
o-ring additional
mounting position
for rod clamp
t-slot
Figure 1: Rotary Motion Sensor Parts

Rotary Motion Sensor Model No. CI-6538
8®
General Setup Options
1) Mounting the Rotary Motion Sensor (RMS)
a) Mounting the RMS on a Support Rod
The Rotary Motion Sensor can be mounted on a support rod using the
supplied rod clamp. The rod clamp can be mounted in three different
locations on the Rotary Motion Sensor: at the end opposite the cable
and on either side of the case. A Phillips screwdriver is required to
remove the two screws that hold the rod clamp on the Rotary Motion
Sensor case.
It is possible to mount the RMS horizontally on a support rod, with the
3-step Pulley facing up or vertically, with the pulley facing forward.
RMS case
Figure 2: Rod clamp positions
rod clamp
RMS (vertical)
RMS (horizontal)
Figure 3: Rotary Motion Sensor positions on a support rod
Note: When setting
up the rotational
inertia experiment
with the thin rod for
the mini-rotational
accessory, the
Rotary Motion Sen-
sor must be
mounted at the top
of the support rod,
so that the support
rod does not inter-
fere with the rota-
tion of the thin rod.

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Model No. CI-6538 Rotary Motion Sensor
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b) Mounting the RMS to a Dynamics Track
The Rotary Motion Sensor can be mounted to a Dynamics Track using
the IDS Mount Accessory. To mount the RMS to the track, do the
following: a) Slide the square nut into the insert on the side of the
track. b) Slide the horizontal rod from the IDS mount through the hole
on the clamp of the RMS. Tighten the screw on the RMS clamp to
hold the rod in place. c) Tighten the screw on the IDS mount to the
square nut in the track. (See Figures 5a and 5b.)
thin rod
space
RMS
3-step Pulley
support rod
Figure 4: Mounting the Rotary Motion Sensor with the
thin rod from the mini-Rotational Accessory
Figure 5a: Attaching the IDS bracket to the track
IDS mount
track

Rotary Motion Sensor Model No. CI-6538
10 ®
The Rotary Motion Sensor can be used as a “Smart Pulley” in this
configuration by threading a string over the Rotary Motion Sensor
pulley and hanging a mass on the string.
c) Mounting the RMS to the “A” base
The Rotary Motion Sensor can be mounted to the Rotating Platform or the
Gyroscope using the “A”-base Rotational Adapter. This allows the
precession angle of the Gyroscope to be detected.
Dynamics Cart
IDS Mount
Accessory
Dynamics Track
Adjustable End-Stop
mass and hanger RMS with 3-step Pulley
string
Figure 5b: Mounting the Rotary Motion Sensor to a Dynamics Track
with the IDS Mount Accessory
Figure 6: Mounting the Rotary Motion Sensor to
the “A”-base Rotational Adapter
RMS
adapter bracket
3-step Pulley
“A” base

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Model No. CI-6538 Rotary Motion Sensor
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d) Mounting the RMS to the Gyroscope
The Rotary Motion Sensor can be mounted to the Gyroscope using the
RMS/Gyroscope Accessory. This allows the nutation angle of the
Gyroscope to be detected.
ME-8960
DEMONSTRATIO N
GYROSCOPE
slotted guide arm
Gyroscope
RMS without pulley
mounting bracket
with rod clamp
RMS
slotted
guide arm
Figure 7: Mounting the RMS to the Gyroscope

Rotary Motion Sensor Model No. CI-6538
12 ®
Attaching Accessories to the Rotary Motion Sensor (RMS)
a) Attaching the Mini-Rotational Accessory to the RMS
To attach the thin rod to the RMS, orient the 3-step Pulley so the rod
guides on the underside of the pulley face up. The 3-step Pulley and
the rotating shaft on the RMS are keyed to assemble only in one
position. Assemble the apparatus as illustrated.
The rod can be used for two purposes:
• The center of the rod can be attached to the RMS rotating shaft and
used with the point masses to find the rotational inertia of point
masses.
captive panel screw
rod
rod guides
3-step Pulley
key
rotating
shaft
slot
RMS
rod clamp
support rod
Figure 8: Attaching the Mini-Rotational Accessory
to the Rotary Motion Sensor
rod clamp
support rod
rod with masses
Sensor
Rotary Motion
Figure 9: Center of the rod attached to the RMS shaft

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Model No. CI-6538 Rotary Motion Sensor
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•The end of the rod can be attached to the Rotary Motion Sensor
rotating shaft to use it as a pendulum.
Using the Disk and Ring
For rotational inertia
experiments, wrap
around string attached to
a mass around the 3-step
pulley included with the
Rotary Motion Sensor.
Hang the mass over the
clamp-on Super Pulley
to accelerate the
apparatus. Perform a
conservation of angular
momentum experiment
by dropping a ring onto
the rotating disk.
support rod
rod with mass
Rotary Motion
Sensor
Figure 10: Using the rod as a pendulum
ring
disk
string
clamp-on
Super Pulley
hanger
mass and
RMS with
3-step pulley
Figure 11: Disk and ring on the RMS
rod clamp
rod

Rotary Motion Sensor Model No. CI-6538
14 ®
b) Attaching the “A” Base Rotational Adapter Accessory to the RMS
The drive belt links the 3-
step Pulley mounted on the
“A” base to the 3-step Pulley
on the RMS. For a one-to-
one correspondence,
connect the two pulleys
using the o-ring on the
middle step of each pulley.
Each revolution of the
Rotating Platform or
Gyroscope corresponds to
one revolution of the RMS.
If desired, a 5-to-1 ratio can
be attained by putting the o-
ring on the top or bottom
steps.
The pulley attaches to the
underside of the rotating
shaft with the shoulder screw. Please note the pulley orientation
illustrated in Figure 13. The bracket connects to the “A” base of the
Rotating Platform or the Gyroscope and to the RMS rod clamp.
adapter
bracket RMS
3-step
pulley
rotating shaft
“A” base
shoulder
screw
3-step
pulley
Figure 12: Attaching the RMS
Base
to the “A”
“A” base
bracket
To p v i e w Bottom view
drive belt 3-step
pulley
RMS
RMS
Figure 13: RMS attached to the “A” base

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Model No. CI-6538 Rotary Motion Sensor
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c) Using the Chaos Accessory with the RMS
The Chaos Accessory is
a driven damped
physical pendulum.
Various types of phase
plots can be made as the
driving frequency,
driving amplitude,
initial conditions, and
amount of damping are
varied.
The adjustable magnet
attaches to either side of
the RMS (See Figure
14) The mass attaches to
the edge of the disk to form a physical pendulum.
A PASCO ME-8750 Mechanical Oscillator/Driver is also required to
drive the Chaos Accessory. The 1.2 m Dynamics Track is used as a
convenient way to mount and align all the components (See Figure
15). However, if a Dynamics Track is not available, components can
be mounted on a separate rod stand.
rod clamp
support rod
3-step Pulley
disk
magnet
RMS
magnetic damping
attachment
to interface
Figure 14: Rotary Motion Sensor with
Magnetic Damping Attachment
mass
RMS with
3-step pulley
magnetic damping
attachment
spring (2)
IDS Mount
Accessory
Adjustable
End-Stop
string
string
disk
(phantom view)
rod clamp
Mechanical
Oscillator/Driver
Figure 15: Chaos Accessory with Mechanical Oscillator
on a Dynamics Track
Note: The sample rate
should be as fast as pos-
sible. If the sample rate
is too fast, lines in the
graph become chunky.

Rotary Motion Sensor Model No. CI-6538
16 ®
Using the Rotary Motion Sensor with Data
Collection Software
To operate the Rotary Motion Sensor, you must plug it into the
ScienceWorkshop 750 interface and perform the necessary setup in
DataStudio. Calibration of the sensor is not required, but optional for
those who wish better accuracy. For calibration instructions, see
Appendix B of this manual.
1. Insert the two stereo phone plugs into any two adjacent digital
channels (1 and 2 or 3 and 4) on the 750 interface box.
Note: If the direction of movement of the Rotary Motion Sensor
produces a negative displacement when you desire a positive
displacement, simply reverse the order of the plugs in the channels.
2. Open DataStudio. When the "Welcome to DataStudio" window
appears, double click "Create Experiment."
3. In the Sensors list of the Experiment Setup window, drag the Rotary
Motion Sensor icon to the digital channels on the picture of the
interface in the setup window. (To open the setup window, click
the Setup button on the main toolbar.)
4. Double click on the Rotary Motion Sensor icon to open the Sensor
Properties dialog.
5. In the General tab of the Sensor Properties dialog, accept the
default sample rate or change the rate using the plus and minus
buttons.
6. In the Measurement tab of the Sensor Properties dialog, select the
desired measurements and units.
7. In the Rotary Motion Sensor tab of the Sensor Properties dialog,
select the desired resolution (360 or 1440). Under “Linear
Calibration,” select the type of accessory you will use.
Note: The required resolution depends on the rate at which the Rotary
Motion Sensor will rotate during the experiment. See the “Suggested
Experiments” section of this manual for suggested resolutions. In
general, if the RMS will turn quickly during the experiment, select 360
divisions per rotation, so that the data rate will not be too high. If the
RMS will turn slowly during the experiment, and a finer resolution is
required, choose 1440 divisions per rotation.

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Model No. CI-6538 Rotary Motion Sensor
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Experiment 1: Rotational Inertia of a
Point Mass
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 Mis the mass, and Ris 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 Mtotal = M1+ M2, the total mass of both point masses.
To find the rotational inertia experimentally, a known torque is applied to the
object and the resulting angular acceleration is measured. Since
τ = I α ,
where
α is the angular acceleration, which is equal to a/r (a = linear
acceleration),and
τ is the torque caused by the weight hanging from the
thread that is wrapped around the 3-step Pulley.
where ris the radius of the chosen pulley about which the thread is wound,
and Tis the tension in the thread when the apparatus is rotating.
Applying Newton’s Second Law for the hanging mass, m, gives
Equipment Required
ScienceWorkshop ® 750 Interface (CI-
6450 or CI-7599)
Rotary Motion Sensor (CI-6538)
Mini-Rotational Accessory (CI-6691) Mass and Hangar Set (ME-9348)
Base and Support Rod (ME-9355) Triple Beam Balance (SE-8723)
Paper clips (for masses <1 g) Calipers
Itotal MtotalR2 =
Iτα⁄=
τrT=
ΣFmgT–ma==

Rotary Motion Sensor Model No. CI-6538
18 ®
(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.
Experiment Setup
1. Attach a mass on each end
of the rod (part of the Mini-
Rotational Accessory)
equidistant from the rod
center. You may choose
any radius you wish.
2. Tie one end of the string to
the Mass Hanger and the
other end to one of the
levels of the 3-step Pulley
on the RMS.
3. Mount the thin rod to the
pulley on the Rotary
Motion Sensor. Please
note the orientation of the
3-step Pulley.
4. Mount the RMS to a support rod and connect it to a computer. Make sure
that the support rod does not interfere with the rotation of the accessory
rod. See Figure 1.1.
5. Mount the clamp-on Super Pulley to the Rotary Motion Sensor.
6. Drape the string over the Super Pulley such that the string is in the groove
of the pulley and the Mass Hanger hangs freely (see Figure 1.1).
Note: The clamp-on Super Pulley
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 (Figure 1.2).
7. Adjust the Super Pulley height
so that the thread is level with
the 3-step pulley.
Tmga–()=
T
mg
a
and Free Body Diagram
Figure 1.1: Rotary Motion Sensor
rod and masses
3-step Pulley
Mass hangar
mass
string support rod
RMS rod
clamp
clamp-on
Super Pulley
Figure 1.2: Super
Pulley Position
Super Pulley

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Model No. CI-6538 Rotary Motion Sensor
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Procedure
Part I: Measurements for the Theoretical Rotational Inertia
1. Weigh the masses to find the total mass Mtotal and record in Table 1.1.
2. Measure the distance from the axis of rotation to the center of the masses
and record this radius in Table 1.1.
Part II: Measurement for the Experimental Method
a) Finding the Acceleration of the Point Masses and Apparatus
1. Open DataStudio and create an experiment.
2. In the Sensors list of the Experiment Setup window, click and drag the
Rotary Motion Sensor icon to the two digital ports that the RMS is
plugged into on the interface.
3. In the Experiment Setup window, double click on the Rotary Motion
Sensor icon to open the Sensor Properties dialog.
4. In the Measurement tab of the Sensor Properties dialog, select "Angular
Velocity (rad/s)."
5. In the Rotary Motion Sensor tab, select 360 divisions/rotation, and
choose the appropriate pulley in the Linear Calibration menu; click OK.
6. Put the 50 g mass on the Mass Hanger and wind up the thread. Click
on the Start button; then release the 3-step Pulley, allowing the mass to
fall. Click the Stop button to end the data collection.
HINT: Click the Stop button before the mass reaches the floor or the end
of the thread to avoid erroneous data.
7. In the Graph Display window, click on the Statistics button; then select
the linear curve fit from the pop-up menu.
The slope of the linear fit represents the angular acceleration (α) and should
be entered in Table 1.2.
Total mass
Radius
Table 1.1:Theoretical Rotational Inertia Data