Includes
Teacher's Notes
and
Typical
Experiment Results
Instruction Manual and
Experiment Guide for
012-03051F
3/95
the PASCO scientific
Model ME-9341
INTRODUCTORY
ROTATIONAL APPARATUS
© 1987 PASCO scientific $5.00
012-03051F Introductory Rotational Apparatus
T able of Contents
Section........................................................................................................Page
Copyright, Warranty and Equipment Return...................................................ii
Introduction .....................................................................................................1
Equipment........................................................................................................2
Setup .............................................................................................................4
Timing with a Photogate..................................................................................6
Five Copy-Ready Experiments:.......................................................................7
Experiment 1: Angular Acceleration—1..................................................9
Experiment 2: Angular Acceleration—2.................................................11
Experiment 3: Gravitational - Rotational Energy....................................15
Experiment 4: Frictional Torque .............................................................17
Experiment 5: Rotational Collisions........................................................19
Teacher's Guide ..............................................................................................23
Appendix ........................................................................................................33
Technical Support.................................................................................... back cover
i
Introductory Rotational Apparatus 012-03051F
Copyright, Warranty and Equipment Return
Please—Feel free to duplicate this manual
subject to the copyright restrictions below.
Copyright Notice
The PASCO scientific Model ME-9341 Introductory
Rotational Apparatus manual is copyrighted and all rights
reserved. However, permission is granted to non-profit
educational institutions for reproduction of any part of
this manual providing the reproductions are used only for
their laboratories and are not sold for profit. Reproduction under any other circumstances, without the written
consent of PASCO scientific, is prohibited.
Limited Warranty
PASCO scientific warrants this product to be free from
defects in materials and workmanship for a period of one
year from the date of shipment to the customer. PASCO
will repair or replace, at its option, any part of the product
which is deemed to be defective in material or workmanship. This warranty does not cover damage to the product
caused by abuse or improper use. Determination of
whether a product failure is the result of a manufacturing
defect or improper use by the customer shall be made
solely by PASCO scientific. Responsibility for the return
of equipment for warranty repair belongs to the customer.
Equipment must be properly packed to prevent damage
and shipped postage or freight prepaid. (Damage caused
by improper packing of the equipment for return shipment will not be covered by the warranty.) Shipping
costs for returning the equipment, after repair, will be
paid by PASCO scientific.
Equipment Return
Should the product have to be returned to PASCO
scientific for any reason, notify PASCO scientific by
letter, phone, or fax BEFORE returning the product.
Upon notification, the return authorization and
shipping instructions will be promptly issued.
ä
NOTE: NO EQUIPMENT WILL BE
ACCEPTED FOR RETURN WITHOUT AN
AUTHORIZATION FROM PASCO.
When returning equipment for repair, the units
must be packed properly. Carriers will not accept
responsibility for damage caused by improper
packing. To be certain the unit will not be
damaged in shipment, observe the following rules:
➀ The packing carton must be strong enough for the
item shipped.
➁ Make certain there are at least two inches of
packing material between any point on the
apparatus and the inside walls of the carton.
➂ Make certain that the packing material cannot shift
in the box or become compressed, allowing the
instrument come in contact with the packing
carton.
Credits
This manual authored by: Ed Pitkin
This manual edited by: Dave Griffith
Teacher’s guide written by: Dave Griffith
Address: PASCO scientific
10101 Foothills Blvd.
Roseville, CA 95747-7100
Phone: (916) 786-3800
FAX: (916) 786-3292
email: techsupp@pasco.com
web: www.pasco.com
ii
012-03051F Introductory Rotational Apparatus
Introduction
With the PASCO ME-9341 Introductory Rotational
Apparatus, your students can perform a variety of
experiments in rotational mechanics, including investigations into torque, angular acceleration, moment of
inertia, and conservation of angular momentum.
Setup is quick and operation is simple. As shown in
Figure 1, a platter spins on low-friction ball bearing
supports. Torques can be applied to the platter with
various torque arms and forces, and the angular
velocity of the platter can be monitored over time to
determine angular acceleration. The moment of inertia
of the rotating system can be varied by adding a
second platter, a steel ring, or a steel block.
The motion of the platter is described mathematically
by Newton's Second Law in its rotational form: t = Ia,
where t is the applied torque, I is the moment of inertia
of the spinning platter, and a is the angular acceleration of the platter.
F
r
τ = r x F = Ια
Timing with the Smart Pulley
The Smart Pulley (see Figure 1) connects to your
Apple II computer (II+, IIe, IIc, or IIGS), or IBM PC
or compatible, providing automatic data collection,
analysis, and graphing. As the platter spins, the pulley
is held lightly against the rim of the platter, and
therefore spins with the platter. The Smart Pulley
photogate monitors the rotation of the pulley, sending
its signals to the computer for timing and analysis.
The software for the Smart Pulley includes options
designed specifically for use with the Introductory
Rotational Apparatus, producing tables and graphs
showing angular displacement, velocity, and acceleration as a function of time.
The Smart Pulley is more than just a computer timer
for the Rotational Apparatus. When used with an
Apple II or IBM PC computer and standard laboratory
equipment such as an air track or dynamics carts, the
Smart Pulley provides a complete introductory lab in
linear mechanics. See the PASCO catalog for more
information about the Smart Pulley System, or Smart
Pulley Timer and Accessories.
Smart Pulley with photogate
(not included)
Figure 1 Rotational Diagram
Timing the Rotational Motion
A variety of timing systems can be used to measure the
motion of the Introductory Rotational Apparatus. The
most versatile option is the PASCO Smart Pulley.
However, standard photogate timers such as the PASCO
model ME-9206A or ME-9215A can also be used.
➤ NOTE: The original 3-hole Smart Pulley has been
replaced . The new PASCO Smart Pulley has 10
spokes and less friction than the 3-hole pulley. If you
currently have 3-hole pulleys and wish to replace
them with 10-spoke pulleys an upgrade kit is available from PASCO. The upgrade kit includes software
that allows use of either the 3-hole or 10-spoke
pulleys. This manual makes reference to both pulleys.
➤ IMPORTANT: If you are using the Smart
Pulley to time the motion of the Rotational
Apparatus, you should begin by familiarizing
yourself with the setup and operation of the
Smart Pulley. See the Smart Pulley manual and
the Smart Pulley Timer Software Manual.
Timing with a Standard Photogate
Timing for the Rotational Apparatus can also be
performed using a standard photogate timer, such as
PASCO model ME-9206A or ME-9215A. The five
ready-to-use experiments in this manual assume you
are using the Smart Pulley to time your experiments
with the Rotational Apparatus. However, each of
these experiments can be modified for standard
photogate timing. See the section, "Timing with a
Photogate." For more information about photogate
timers, see the current PASCO catalog.
1
Introductory Rotational Apparatus 012-03051F
Equipment
The following equipment is included with the ME-9341
Introductory Rotational Apparatus (see Figure 2):
– Base with leveling supports and main bearing
– Spindle
– Main platter with step pulley
– Pulley clamp
– Tensioning screw
– Level
– Photogate clamp
– Steel bar
– Auxiliary platter
– Steel ring
– Instruction manual and experiments guide
You will also need either:
A PASCO Smart Pulley System (Model ME-9420 or
ME-9421) or one of the Smart Pulley Timers (ME9382, ME-9384, ME-9386, or ME-9388) - (Please see
the PASCO catalog for complete details.) - and an
Apple II or IBM PC (or compatible) computer.
➂ To measure the radius of the Smart Pulley outer cir-
cumference, roll the Smart Pulley over a smooth,
flat surface. Measure the distance, L, over which
you pull the pulley for a predetermined number, n,
of LED flashes. Again, the radius of the outer circumference of the pulley is r = 3L/2 n for a 3-hole
pulley or r = 10L/2 n for a 10-spoke pulley. (You
can draw a mark on the edge of the rim of the Smart
Pulley to use as a reference mark for measuring L.)
➤NOTE: If you would rather not make the
measurements yourself, use the values in the box
below. They should be valid to within 10
percent for your Rotational Apparatus.
Main platter: Mass = 991 gm; Radius = 12.7 cm;
-3
Moment of inertia = 7.50 x 10
kgm
2
Step pulley: Radii = (1.50 cm, 2.00 cm, 2.50 cm)
Auxiliary platter: Mass = 894 gm; Radius = 12.7
-3
cm; Moment of inertia = 7.22 x 10
kgm
2
or
A photogate timing system such as PASCO Model
ME-9206A or ME-9215A.
Measuring Equipment Parameters
In experiments with the Rotational Apparatus, you
will often be comparing experimentally determined
values, such as moment of inertia or angular acceleration, with calculated values based on theory. These
listed, precalculated values may be helpful in those
calculations. For best results, however, we recommend that you make the necessary measurements
yourself. The following suggestions may be helpful
in making certain measurements accurately:
➀ To measure the radii of the step pulley, use calipers
to determine the diameter, then divide by two.
➁ To measure the radius of the Smart Pulley groove,
observe the LED on the top of the photogate as you
pull a string over the pulley. Measure the distance,
L, through which you pull the string for a predetermined number, n, of LED flashes. The radius of
the pulley groove is then r = 3L/2 n for a 3-hole
pulley or r = 10L/2 n for a 10-spoke pulley.
Steel bar: Mass = 690 gm; Dimensions = 22.2 x
5.1 cm; Moment of inertia = 2.98 x 10-3 kgm
2
Steel ring: Mass = 701 gm; Outer radius = 6.4 cm;
Inner radius = 5.4 cm;
Moment of inertia =2.46 x 10-3 kgm
Smart Pulley: 3-hole 10-spoke
radius inside groove 2.29 cm 2.38 cm
radius outside circum. 2.51 cm 2.54 cm
moment of inertia 15.3x10-7kgm
2
2
18.6x10-7kgm
Note: Platters of the earlier versions of the ME9341 were made from masonite. Their mass and
moment of inertia are given below.
Main platter: Mass = 776 gm; Radius = 12.7 cm;
-3
2
Moment of inertia = 6.01 x 10
kgm
Auxiliary platter: Mass = 694 gm; Radius = 12.7
cm; Moment of inertia = 5.82 x 10-3 kgm
2
2
2
012-03051F Introductory Rotational Apparatus
Bearing
Leveling
supports
Spindle
Step pulley
Base
Pulley clamp
Tensioning
screws (2)
Bubble level
Steel ring
Photogate
clamp
Main platter
Steel bar
Figure 2 Rotational Apparatus Equipment
Auxiliary platter
3
Introductory Rotational Apparatus 012-03051F
Setup
➀ Place the base on a flat table. Place the bubble
level on top of the base, then adjust the leveling
supports until the top of the base is level.
➤ NOTE: Leveling the base is important. Not
only does it ensure the accuracy of your experimental results, it also prevents uneven wear on
the bearings.
➁ Slide the spindle into the bushing of the bearing
assembly. Either end of the spindle can face up,
but you will want the long end facing up if you plan
on using the auxiliary platter, the ring, or the bar.
➂ Place the Main Platter over the spindle. The step
pulley can face up or down, but should face down
if you plan on using the auxiliary platter, the ring,
or the bar.
If you are using a standard photogate timer:
➃ See the "Timing with a Photogate" section.
If you are using the Smart Pulley:
➄ Slide the stem of the Smart Pulley clamp into ei-
ther of the two bushings near the edge of the base.
➅ Place the Smart Pulley rod through the hole in the
Smart Pulley clamp, level the pulley, and tighten
the screw. (Use the upper hole in the clamp if the
Step pulley is facing down, the lower hole if the
step pulley is facing up.)
➆ If you wish, attach a rubber band (not included)
over the rod of the Smart Pulley and a leg under
the base, as shown in Figure 3. This can be useful
in collision experiments, in which an extra "hand"
may be needed to keep the Smart Pulley in contact
with the platter.
➇ See the Smart Pulley System manual for connect-
ing and using the Smart Pulley. For most experiments using the rotational apparatus, you will want
to use Option M – MOTION TIMER from the
Smart Pulley main menu. When you are ready to
begin timing, just press the Smart Pulley lightly
against the edge of the platter.
If you are applying torque with a hanging mass:
➉ Thread the thread through the holes in the step pul-
ley to the desired level. (For instance, thread it
through one hole if you are using the smallest pulley, two holes if you are using the medium size pulley, etc.)
Smart Pulley
Spindle
Main platter
(SIDE VIEW)
Main platter
Spindle
Tensioning Screws
(TOP VIEW)
Figure 3 Setting Up the Rotational Apparatus
Smart Pulley
Smart Pulley clamp
Rubber band
Pulley
Universal
Clamp
Hanging
Mass
Universal
Clamp
Hanging
Mass
Pulley
Rubber band
Smart Pulley clamp
Thread parallel to
platter.
➈ Attach a piece of thread to the step pulley using the
screw to hold the thread, or tying it to the hole in
the smallest pulley (see Figure 4).
Figure 4 Threading the Step Pulley
4
012-03051F Introductory Rotational Apparatus
11 Attach a pulley to the base of the apparatus using
the Smart Pulley table clamp as shown in Figure 3.
If you don't have the table clamp, a pulley mounted
to a ring stand can be used, as long as the height
and angle of the pulley are adjustable.
NOTE: When using a falling mass to accelerate
the platter, there are two setup options.
Option a—This option requires the Smart Pulley
and a second pulley, set up as shown in Figure 3.
This method is slightly less accurate than option
b, but conceptually simpler. When entering the
graphing mode of the Smart Pulley software, you
will be asked to identify the type of device being
used to interrupt the photogate. If you are using
the version of Smart Pulley Timer software that
functions with either 10-spoke or 3-hole pulleys,
simply choose ROTATIONAL APPARATUS.
If you are using an older version of Smart Pulley
Timer and a 3-hole pulley, choose ROTATIONAL
APPARATUS. However, if you are using an
older version of Smart Pulley Timer software and
a 10-spoke pulley, choose OTHER (ANGULAR
MEASUREMENT). The computer will ask you
to enter the angle in radians between the spokes.
Enter 0.125 [calculated by using θ = 2π/10
(R
SMART PULLEY/RMAIN PLATTER)]. The computer
will then automatically convert the measured
times to determine the angular displacement,
velocity, and acceleration of the platter. The
slight decrease in accuracy results from the
friction caused by the pressure of the Smart
Pulley on the rim of the spinning platter.
12 Pass the thread over the pulley and adjust the pulley
angle and height so the thread is parallel with the
platter surface and with the groove in the pulley.
Option b—In this option, use the Smart Pulley
as the pulley that supports the hanging weight.
No other pulley is needed. When asked by the
computer to identify the type of device being
used to interrupt the photogate, select option F—
OTHER (ANGULAR MEASUREMENT). You
will then be asked to enter the angle between
openings. Enter one of the values shown below,
depending on which tier of the step pulley you
are using and the type of Smart Pulley you have
(these values are the angle, in radians, through
which the platter turns for each signal sent to the
computer by the Smart Pulley).
Tier of step pulley used 3-hole 10-spoke
Smallest 3.20 1.00
Middle 2.49 0.75
Largest 1.92 0.60
These values can be calculated using the formula:
θ = 2 /3 (Rp/Rsp) for a 3-hole pulley
or θ = 2 /10 (Rp/Rsp) for a 10-spoke pulley
where Rp is the radius of the Smart Pulley
groove, and Rsp is the radius of the tier of the
step pulley that is being used.
5
Introductory Rotational Apparatus 012-03051F
Timing with a Photogate
If you don't have the Smart Pulley system, a PASCO
photogate can be used to time the Rotational Apparatus. Other photogates can be used as well. The
Rotational Apparatus includes a mounting clamp that
should work with most photogates.
To Use a Photogate:
➀ Mount the photogate in the photogate clamp, and
mount the photogate clamp in the pulley clamp, as
shown in Figure 5.
➁ Tape a piece of cardboard to the top of the platter
to trigger the photogate. The shape of the cardboard depends on which of the following timing
techniques you choose.
PASCO photogates have three timing modes: Pulse,
Gate, and Pendulum. If your photogate has these
timing modes, any of the following four timing
techniques can be used:
1. PULSE MODE (Method 1)—In pulse mode, the
photogate will be triggered each time the leading
edge of the cardboard interrupts the photogate
beam (see Figure 5). The times displayed will
therefore show the time for one full revolution of
the platter. Experimenters will then have one
revolution to record the time before a new time is
displayed. (Just divide 2 by the measured time to
determine the angular velocity of the platter in radians/second.)
2. PULSE MODE (Method 2)—Tape two pieces of
cardboard to the main platter (see Figure 6). If the
cardboard pieces are accurately placed so the leading edges are along a single diameter of the platter,
the timing resolution is twice as good as with a
single cardboard piece. The displayed times will
show the time per 1/2 revolution of the platter.
Cardboard
Photogate
Figure 5 Pulse Mode (Method 1) and Pendulum
Mode
Figure 6 Pulse Mode (Method 2)
Pulley clamp
Photogate clamp
3. GATE MODE—Tape a one radian sector of card-
board to the top of the main platter (see Figure 7).
In gate mode, for each revolution of the platter, the
timer will display the time during which the cardboard interrupted the photogate. The reciprocal of
the measured times will therefore give the angular
velocity in radians/second. (See the Appendix for
a one radian sector that you can copy and use as a
template for cutting the cardboard.)
One Radian
Sector
Figure 7 Gate Mode
6
012-03051F Introductory Rotational Apparatus
4. PENDULUM MODE—If the rotational speed is
too great to record the times as they are displayed,
use a single cardboard piece, as in Figure 5, and set
the photogate to pendulum mode. The timer will
display the time for two full revolutions of the platter, allowing one revolution time for reading and
recording the value.
Five Copy-Ready Experiments
The following five experiments are written in worksheet form.
Feel free to photocopy them for use in your lab.
Some precautions will help keep your data as accurate as
possible:
5. Alternative Methods
• Use the PASCO Model AI-6577A Apple Com-
patible Photogate System. This system offers
many of the same advantages as Smart Pulley
timing. However, since it was not designed specifically for the Rotational Apparatus, experiments will have to be adapted somewhat.
➀ Before conducting any experiment, always level the base as
accurately as possible.
➁ When using a thread to apply a torque to the platter, keep the
thread as parallel to the platter as possible.
➂ When measuring the radius of a tier of the step pulley, use
calipers to measure the diameter, then divide by two.
➤ NOTE: For more information about each of these
labs, including relevant equations and suggested
alternatives, see the LAB NOTES section, near the end
of this manual.
7
Introductory Rotational Apparatus 012-03051F
Notes:
8