PASCO ME-8960 User Manual

Instruction Manual and
Experiment Guide for
the PASCO scientific
Model ME-8960

DEMONSTRATION

GYROSCOPE

012-05327B

4/94

ME-8960

DEMONSTRATION

GYROSCOPE

© 1994 PASCO scientific $10.00

10101 Foothills Blvd. • P.O. Box 619011 • Roseville, CA 95678-9011 USA

Phone [phone] • FAX [phone] • TWX 910-383-2040

better

ways to

teach physics

012-05327B Demonstration Gyroscope

T able of Contents

Section Page

Copyright, Warranty, and Equipment Return..................................................ii

Introduction .....................................................................................................1

Equipment........................................................................................................2

Assembly

ME-8960 Demonstration Gyroscope.........................................................3

ME-8961 Additional Gyroscope Disk....................................................... 5

Experiments

Experiment 1: Precession ....................................................................7

Experiment 2: Counter-rotating Disks - Demonstration.....................13

Experiment 3: Precession - Demonstration ........................................15

Experiment 4: Nutations - Demonstration..........................................17

Technical Support................................................................................. Back Cover

i

Demonstration Gyroscope 012-05327B

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-8960 Demonstration
Gyroscope 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 this product have to be returned to PASCO
scientific, for whatever reason, notify PASCO scientific
by letter or phone BEFORE returning the product. Upon
notification, the return authorization and shipping instruc­tions will be promptly issued.

➤ NOTE: NO EQUIPMENT WILL BE AC-
CEPTED FOR RETURN WITHOUT AN AU­THORIZATION.

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 carton must be strong enough for the item

shipped.

➁ Make certain there is 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 can not shift in

the box, or become compressed, thus letting the instru­ment come in contact with the edge of the box.

Address: PASCO scientific

10101 Foothills Blvd.

Credits

This manual authored by: Jon Hanks
This manual edited by: Jon Hanks

P.O. Box 619011

Roseville, CA 95678-9011
Phone: [phone]
FAX: [phone]

ii

012-05327B Demonstration Gyroscope

Introduction

The PASCO ME-8960 Gyroscope has an open design
that makes all the parts easily accessible to the student.
The gyroscope consists of a disk that can be rotated by
hand or by pulling a string that is wrapped around the
pulley. A movable counterweight balances the disk.

The small counterweight is used to make fine adjust­ments to the balance. An add-on mass can be easily
placed on the end of the shaft to cause a torque and
precession. The rotational inertia of the disk is easily
obtained by accelerating the disk using a string around
the pulley that is attached to the disk.

1

Demonstration Gyroscope 012-05327B

Equipment

cast iron
“A” base

“E” rings (2,

one extra

for rotating

axle)

rotating disk

rotating axle

“E” rings (3,
one extra for
rotating disk)

gyroscope

axle

ME-8960

DEMONSTRATION

GYROSCOPE

45 cm

support rod

right angle
rod clamp

900g

counterweight

30g

counterweight

150g add-

on mass

thumbscrews (2)

ME-8960 Demonstration Gyroscope Equipment

The ME-8960 Demonstration Gyroscope includes
the following:

– PASCO cast iron “A” base with rotating shaft
– axle (48 cm long) with pivot block, protractor

plate, and pointer
– one 900g large counterweight
– one 30g small counterweight
– one 150g add-on mass

The ME-8961 Additional Gyroscope Disk includes
the following:

– 25cm diameter rotating disk with pulley
– one 900g large counterweight

– 25cm diameter rotating disk with pulley
– 45 cm support rod
– right angle rod clamp
– extra “E” rings to secure rotating shaft and rotat-

ing disk

– two thumbscrews

rotating disk

900g

counterweight

2

ME-8961 Additional Gyroscope Disk

012-05327B Demonstration Gyroscope

Assembly

900g

counterweight

thumbscrew

thumbscrew

rotating disk

30g

counterweight

gyroscope axle

rotating axle

“E” ring for

rotating axle

ME-8960

DEMONSTRATION

GYROSCOPE

flat of

rotating axle

cast iron “A” base

“E” rings (2) for

rotating disk

add-on mass

thumbscrew

Figure 1: Demonstration Gyroscope Assembly

ME-8960 Demonstration Gyroscope

Assembling the Demonstration Gyroscope

➀ Insert the cylindrical end of the vertical shaft into

the bearings on the top-side of the A-shaped iron

base. Secure the shaft in place by inserting the re-

taining ring in the slot at the bottom of the shaft.

See Figure 1.

➁ Attach the gyroscope axle to the vertical shaft and

tighten the thumb screw against the flat side of the

“D” on the vertical shaft.

➂ Slide the smaller of the two counterweights (30g)

onto the long side of the gyroscope axle and tighten

the thumbscrew. Then slide the larger of the two
counterweights (900g) onto the same end of the
shaft and tighten its thumbscrew.

➃ Put the disk on the other end of the gyroscope axle

with the pulley side of the disk facing the center of
the gyro. Secure the disk in place with the retaining
rings (2). See Figure 1.

➄ Screw the thumbscrew into the end of the shaft un-

til the nut is tight against the end of the shaft

3

Demonstration Gyroscope 012-05327B

gyroscope axle

gyroscope axle

“A” base

(rotated 90˚)

adjust this foot first

rotating

disk

leveling feet

Figure 2: Leveling the Base

Leveling the Base

➀ Purposely make the apparatus unbalanced by mov-

ing the 900g counterweight towards the center.

➁ Adjust the leveling foot on one of the legs of the

base until the gyroscope disk is aligned over the
leveling foot on the other leg of the base. See Fig­ure 2.

900g

counterweight

then adjust this foot

➂ Rotate the gyroscope 90 degrees so the gyroscope

axle is parallel to one side of the “A” and adjust the
other leveling foot until the shaft will stay in this
position. See Figure 2.

➃ Adjust the position of the 900g counterweight until

the gyroscope is balanced without the add-on mass.
The 30g counterweight can be used to fine tune the
balance.

rotating

disk

Using the Rotating Disk Pulley

➀ Make sure the rotating disk is secure on the gyro-

scope axle and decide which direction you want the
disk to rotate.

➁ Tie a loop in the end of a length of thread (approxi-

mately 1.5 meters long) and put the loop around the
dowel pin located on the surface of the rotating disk
pulley and wind the thread around the surface of
the pulley. See Figure 3.

➂ Holding the gyroscope axle in place, pull the thread

to rotate the disk at the desired speed.

rotating disk

dowel pin

gyroscope

axle

pulley

thread

Figure 3: Using the Rotating Disk Pulley

4

012-05327B Demonstration Gyroscope

included 900g
counterweight

additional

gyroscope axle

(part of ME-8960)

Demonstration

ME-8960

Gyroscope

ME-8960

DEMONSTRATION

GYROSCOPE

gyroscope disk

add-on mass

(part of ME-8960)

Figure 4: Using the Additional Gyroscope Disk

ME-8961 Additional Gyroscope Disk

Using the Additional Gyroscope Disk

➀ Slide the included 900g counterweight onto the

long side of the gyroscope axle and tighten the
thumbscrew.

thumbscrew (part of

ME-8960)

➁ Put the Additional Gyroscope Disk on the other end

of the gyroscope axle with the pulley side of the
disk facing away from the center of the gyroscope
apparatus. Secure the disk in place with the sup­plied thumbscrew. See Figure 4.

5

Demonstration Gyroscope 012-05327B

Notes:

6

012-05327B Demonstration Gyroscope

dt

d

φ

dt

Experiment 1: Precession

EQUIPMENT NEEDED

– Gyroscope (ME-8960) – meter stick
– stopwatch (SE-8702) – table clamp for pulley
– Super Pulley (ME-9450) – thread (1.5 meters)
– Pulley Mounting Rod (SA-9242) – computer (optional)
– Mass and Hanger Set (ME-9348) – Smart Pulley (optional)
– balance – Smart Pulley software (optional)

Purpose

The purpose of this experiment is to measure the precession rate of a gyroscope and com­pare it to the theoretical value.

Theory

A torque is applied to the gyroscope by hanging a mass on the end of the shaft. This torque
causes the gyroscope to precess at a certain angular speed, Ω.

Assume that the gyroscope is initially balanced in the horizontal position, θ = 90˚. The disk
is spun at an angular speed (ω) and then a mass, m, is attached to the end of the gyroscope
shaft at a distance, d, from the axis of rotation. This causes a torque: τ = mgd. But the
torque is also equal to dL/dt, where L is the angular momentum of the disk. As shown in
Figure 1.1, for small changes in angle, dφ, dL = L dφ.

dφ

→

L

130

120

110
100
90

80

70

60

50

side view

d

ω

140

CAUTION
MAGNET

ME-8960

DEMONSTRATION

GYROSCOPE

40

30

mg

top view

Figure 1.1: Torque Applied to Horizontal Gyroscope

dL

→

→

L

Substituting for dL in the torque equation gives

τ

= mgd =

dL

= L

7

Demonstration Gyroscope 012-05327B

Ω

ω

τ
α

F

Since dφ/dt = Ω, the precession speed,

mgd = L

and the precession rate is given by

mgd

Ω

=

I

where I is the rotational inertia of the disk and ω is the angular speed of the disk.
To find the rotational inertia of the disk experimentally, a known torque is applied to the

disk and the resulting angular acceleration is measured. Since τ = Iα,

I =

where α is the angular acceleration which is equal to a/r and τ is the torque caused by the
weight hanging from the thread which is wrapped around the pulley on the disk.

τ

= r

where r is the radius of the pulley about which the thread is wound and F is the tension in
the thread when the disk is rotating.

Applying Newton’s Second Law for the hanging mass, m, gives (See Figure 1.2)

Σ

F = mg – F = ma

F

pulley

hanging

mass

rotating disk

mg

Figure 1.2: Rotating Disk and Free-Body Diagram

α

Solving for the tension in the thread gives

F = m (g – a)

8

012-05327B Demonstration Gyroscope

So, once the linear acceleration of the mass (m) is determined, the torque and the angular
acceleration can be obtained for the calculation of the rotational inertia. The acceleration is
obtained by timing the fall of the hanging mass as it falls from rest a certain distance (y).
Then the acceleration is given by

2y

a =

2

t

Part I: Measuring the Precession Rate

Setup

➀ Level the gyroscope base as described on page 4 in the Assembly section of this manual.
➁ Adjust the position of the large counterweight until the gyroscope is balanced without the

add-on mass. The small counterweight can be used to fine-tune the balance.

Procedure

➀ Weigh the add-on mass and record its mass in Table 1.1. Attach the add-on mass to the end

of the shaft. Measure the distance (d) from the axis of rotation to the center of the add-on
mass. Record this distance in Table 1.1

➁ While holding the gyroscope so it can’t precess, spin the disk at about two revolutions per

second. Time 10 revolutions of the disk to determine the angular speed (ω) of the disk.
Record in Table 1.1.

➂ Let the gyroscope precess and time two revolutions to find the precession rate. Record in

Table 1.1.

➃ Immediately repeat the measurement of 10 revolutions of the disk. The before-and-after

Table 1.1: Angular Speed Measurements

Add-On Mass

Distance (d)

Time for 10 Revolutions (initial)

Time for Precession

Time for 10 Revolutions (final)

data will be used to find the average angular speed of the disk during the precession.

9

Demonstration Gyroscope 012-05327B

Part II: Measuring Quantities For the Theoretical Value

Setup

➀ Clamp the gyroscope shaft in the horizontal position. See Figure 1.3.
➁ Attach a Super Pulley with rod to the table using a table clamp.
➂ Wind a thread around the pulley on the center shaft and pass the thread over the Super

Pulley.

right angle rod

clamp

140

130

120

110

100

CAUTION
MAGNET

90

80

70

60

ME-8960

DEMONSTRATION

50

GYROSCOPE

40

30

rotating disk

support rod

Figure 1.3: Experiment Setup

Procedure

Accounting For Friction

Because friction is not included in the theory, it will be compensated for in this experiment
by finding out how much mass over the pulley it takes to overcome kinetic friction. When
the mass drops at a constant speed, the weight of the mass is equal to the kinetic friction.
Then this “friction mass” will be subtracted from the mass used to accelerate the apparatus.

➀ To find the mass required to overcome kinetic friction, put just enough mass hanging over

the pulley so that the velocity is constant. Record this friction mass in Table 1.2.

Finding the Acceleration of the Disk

➀ To find the acceleration, put about 30 g (record the exact hanging mass in Table 1.2) over

the pulley. Wind the thread up and let the mass fall from the table to the floor, timing the
fall.

➁ Repeat this for a total of 5 times, always starting the hanging mass in the same position.
➂ Measure the height that the mass falls and record this height in Table 1.2.

10

012-05327B Demonstration Gyroscope

Alternate Computer Method:

If a computer and Smart Pulley are used, the acceleration of the disk can be obtained by
finding the slope of the velocity vs. time graph.

Measure the Radius

➀ Using calipers, measure the diameter of the pulley about which the thread is wrapped and

calculate the radius. Record the radius in Table 1.2.

Table 1.2 Rotational Inertia Data

Friction Mass

Hanging Mass

Height Mass Falls

Radius of Pulley

Times

Average:

Analysis

➀ Using the average time from Table 1.2, calculate the acceleration and record the result in

Table 1.3.

➁ Calculate the rotational inertia:

(a) Subtract the “friction mass” from the hanging mass used to accelerate the disk to

determine the mass, m, to be used in the equations.

(b) Calculate the experimental value of the rotational inertia and record it in Table 1.3.

➂ Using the times for 10 revolutions in Table 1.1, divide by 10 to find the periods. Average

these two periods and calculate the average angular speed (ω = 2π/T). Record the angular
speed in Table 1.3.

➃ Find the experimental value for the precession rate by dividing the precession time by two

and calculating Ω = 2π/T. Record in Table 1.3.

➄ Calculate the theoretical value for the precession rate and record in Table 1.3.
➅ Calculate the percent difference between the experimental and theoretical values of the

precession rate.

11

Demonstration Gyroscope 012-05327B

Table 1.3: Results

Acceleration

Rotational Inertia
Average Angular Speed of Disk
Experimental Precession Rate

Theoretical Precession Rate

% Difference

Questions

➀ What happens to the direction of precession if the spin of the disk is reversed?
➁ How does the rate of precession change if the angular speed of the disk is increased?

12

012-05327B Demonstration Gyroscope

Experiment 2: Counter-rotating Disks

- Demonstration

EQUIPMENT NEEDED

– Gyroscope (ME-8960)
– Accessory Disk and Extra Counterweight (ME-8961)
– Physics String (SE-8050)

Purpose

It is shown that two disks spinning in opposite directions at the same angular speed will not
precess when a torque is applied.

Setup

➀ Remove the screw in the end of the shaft and slide the second disk onto the shaft with the

pulley side facing away from the first disk. Secure the second disk by tightening the screw
in the end of the shaft. See Figure 2.1.

➁ Put the second counterweight on the other end of the shaft and slide the counterweights

until the gyroscope is balanced. Spin the disks and check the balance by seeing if the
gyroscope precesses. If it precesses, the balance needs further adjustment.

➂ Cut two pieces of string, each 1 meter long. Tie one end of each string to the ends of a pen.

The pen will be used to pull the two strings simultaneously. Tie a loop in the other end of
each string to hook over the dowel pins.

➃ To make the direction of rotation more visible to the students, stick a white paper dot on the

edge of each disk.

rotating disk (part of

additional 900g

counterweight (part

of ME-8961)

900g counterweight

(part of ME-8960)

“A” base

ME-8960)

140

130

120

110

100

CAUTION
MAGNET

90

80

70

60

ME-8960

DEMONSTRATION

50

GYROSCOPE

40

30

add-on mass

additional rotating disk

(part of ME-8961)

Figure 2.1: Counter-rotating disks

13

Demonstration Gyroscope 012-05327B

Procedure

➀ Use your hand to spin both disks in the same direction. Show that the gyroscope does not

precess.

➁ Put the add-on mass on the end of the shaft and secure with a screw. Spin both disks in the

same direction and show that the gyroscope now precesses.

➂ Stop the disks and reverse the spin of both disks to show that the gyroscope now precesses

in the opposite direction.

➃ Now counter-rotate the disks. To do this, wrap an equal number of turns of string in oppo-

site directions around the pulleys on each of the disks. Pull on both strings simultaneously
using the pen as a handle. Point out that even though a torque is still being applied to the
gyro, the gyroscope does not precess when the two disks are spinning in opposite directions.

14

012-05327B Demonstration Gyroscope

Experiment 3: Precession - Demonstration

EQUIPMENT NEEDED

– Gyroscope (ME-8960)

Purpose

It is shown that if a precessing gyroscope is restricted from precessing, the disk will fall.
See Figure 3.1.

rotating disk

140

130

120

110

100

CAUTION
MAGNET

90

80

70

60

ME-8960

DEMONSTRATION

50

GYROSCOPE

40

30

add-on mass

counterweights

rotating

axle

Figure 3.1: Precession

Procedure

➀ Adjust the counterweights until the gyroscope is balanced.
➁ Put the add-on mass on the end of the shaft.
➂ Spin the disk and allow the gyroscope to precess.

“A” base

rotating

axle

100
90

80

130

120

110

70

60

50

140

CAUTION
MAGNET

ME-8960

DEMONSTRATION

GYROSCOPE

40

30

rotating disk

➃ Slow or stop the precession by grabbing the center vertical shaft with your hand. As you do

so, the disk will fall.

➄ You can also cause the disk to rise by spinning the center vertical shaft in the same direc-

tion as the precession.

15

Demonstration Gyroscope 012-05327B

Notes:

16

012-05327B Demonstration Gyroscope

Experiment 4: Nutations - Demonstration

EQUIPMENT NEEDED

– Gyroscope (ME-8960)

Purpose

Three different types of nutation are shown.

Procedure

➀ Adjust the counterweights until the gyroscope is balanced.
➁ Put the add-on mass on the end of the shaft.
➂ Spin the disk and release the gyroscope from rest at an angle of about 30˚. See Figure 4.1.

rotating disk

140

counterweights

110
100
90

80

70

130

120

60

DEMONSTRATION

50

40

CAUTION
MAGNET

ME-8960

GYROSCOPE

30

add-on mass

rotating

axle

“A” base

Figure 4.1: Release Position of Gyro

➃ The resulting nutation will look like pattern (A) in Figure 4.2.
➄ Stop the precession and spin the disk again. Release the gyroscope from the same angle but

give it an initial push in the direction of precession. The resulting nutation will look like
pattern (B) in Figure 4.2.

➅ Stop the precession and spin the disk again. Release the gyroscope from the same angle but

give it an initial push in the direction opposite to the precession. The resulting nutation will
look like pattern (C) in Figure 4.2.

➆ Spin the disk at a different speed and check the effect this has on the speed of the nutation.
➇ Release the disk from a different angle and check the effect this has on the nutation.

17

Demonstration Gyroscope 012-05327B

(A) Released from rest

(B) Released with

forward speed

Figure 4.2: Patterns of Resultant Nutations

(C) Released with

backward speed

18

012-05327B Demonstration Gyroscope

T echnical Support

Feed-Back

If you have any comments about this product or this
manual please let us know. If you have any sugges­tions on alternate experiments or find a problem in the
manual please tell us. PASCO appreciates any cus­tomer feed-back. Your input helps us evaluate and
improve our product.

To Reach PASCO

For Technical Support call us at 1-800-772-8700 (toll­free within the U.S.) or [phone].

Contacting Technical Support

Before you call the PASCO Technical Support staff it
would be helpful to prepare the following information:

• If your problem is computer/software related, note:
Title and Revision Date of software.
Type of Computer (Make, Model, Speed).
Type of external Cables/Peripherals.

• If your problem is with the PASCO apparatus, note:
Title and Model number (usually listed on the label).
Approximate age of apparatus.

A detailed description of the problem/sequence of
events. (In case you can't call PASCO right away,
you won't lose valuable data.)

If possible, have the apparatus within reach when
calling. This makes descriptions of individual parts
much easier.

• If your problem relates to the instruction manual,

note:
Part number and Revision (listed by month and year

on the front cover).

Have the manual at hand to discuss your questions.

19