PASCO ME-8950A User Manual

012-05293F Complete Rotational System

Instruction Manual and

012-05293F

01/09

Experiment Guide for the PASCO scientific Model ME-8950A

COMPLETE ROTATIONAL

SYSTEM

Complete Rotational System 012-05293F

012-05293F Complete Rotational System

Table of Contents

Section Page

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

• Description

• About this Manual

• Computer Timing

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

Miscellaneous Supplies ................................................................................... 3

Assembly

ME-8951 Rotating Platform ......................................................................4

ME-8952 Centripetal Force Accessory ..................................................... 6

ME-8953 Rotational Inertia Accessory ..................................................... 8

Experiments Using the ME-8951 Rotating Platform

Exp 1 Conservation of Angular Momentun (Projectile Version)........ 9

Exp 2 Rotational Inertia of a Point Mass............................................ 15

Experiments Using the ME-8952 Centripetal Force Accesory

Exp 3 Centripetal Force...................................................................... 19

Exp 4 Conservation of Angular Momentum Using Point Mass.........25

Experiments Using the ME-8953 Rotational Inertia Accessory

Exp 5 Rotational Inertia of Disk and Ring ......................................... 31

Exp 6 Rotational Inertia of Disk Off-Axis (Fixed/Rotating).............. 37

Exp 7 Conservation of Angular Momentum Using Disk and Ring.... 41

Technical Support........................................................................................... 45

Complete Rotational System 012-05293F

Please—Feel free to duplicate this manual subject to the copyright restrictions below.

The PASCO scientific Model ME-8950A Complete Rotational System manual is copy right ed and all rig hts reserved. However, per mis si on i s gr anted 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, wi thout the written consent of PASCO scientific, is prohibited.

Limited Warranty

PASCO scientific warrant s thi s produc t to be fre e from defects in material s and workmanship for a period o f one year from the date of shipment to the customer. PASCO will repair or replace, at its opti on, any part of the product which is deemed to be defecti ve in material or workmanship. This warranty does not cov er damage to the product caused by abuse or improper use. Determination of whether a product failur e is the result of a manufacturing defect or improper use by the customer shall be made solely by PASCO scientif ic. Responsibility for the retur n 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 improp er packing of the equipment fo r return shipment will not be covered by the war ranty.) Shipping costs for returning the eq uipment, after repair, will be paid by PASCO scientific.

Equipment Return

Should this product have to be returned to PASCO scientific, for whate ver reason, not ify PASCO scientifi c 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

ACCEPTED 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 ru les:

1. The carton must be strong enough for the item shipped.

2. Make certain there is at least two inches of packing material between any poi nt on the appa rat us and the inside walls of the carton.

3. Make cer tain that the packing material can not shift in the box, or become co mpressed, thus letting the instrument come in contact wit h th e edge of the box.

Address:PASCO scientific

10101 Foothills Blvd. P.O. Box 619011

Credits

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

Roseville, CA 95678-9011

Phone: (916) 786-3800 FAX: (916) 786-8905 email: techsupp@pasco.com web: www.pasco.com

012-05293F Complete Rotational System

Introduction

PASCO’s Complete Rotational System provides a full range of experiments in centripetal force and rotational dynamics. The system consists of three separate components:

Description

The ME-8951 Rotating Platform consists of a sturdy 4 kg base with low friction bearings and a rotating arm which serves as a versatile base for rotation experiments. This platform is a general purpose base upon which you may mount anything (having a mass under 3 kg) you wish to rotate. The T-slots in the track supply a convenient way to mount objects to the track using thumbscrews and square nuts. To use the Centripetal Force Accessory (ME-

8952) or the Rotational Inertia Accessory (ME-8953), each must be mounted on this base. A photogate/pulley mount and two 300 g masses are also included.

The ME-8952 Centripetal Force Accessory is comprised of two vertical posts which can be mounted to the Rotating Platform with thumbscrews. These posts are adjustable and can be positioned virtually anywhere along the length of the platform. The radius indicator is at the center of the apparatus so it can be clearly seen while the apparatus is rotating. This accessory requires the Rotating Platform (ME-8951) to operate. The PASCO Centripetal Force Accessory can be used to experiment with centripetal force and conservation of angular momentum. For the centripetal force experiments it is possible to vary the mass and radius to see the resulting change in the centripetal force. The force can also be held constant while other quantities are varied. The Centripetal Force Accessory is powered by hand and the rate of rotation can be counted manually or read by a computer. Variable hanging masses are included.

The ME-8953 Rotational Inertia Accessory includes a disk and a metal ring. The disk can be mounted to the rotating base in a variety of positions and at any radius. This accessory requires the Rotating Platform (ME-8951) to operate. The Rotational Inertia Accessory allows you to perform rotational inertia experiments and conservation of angular momentum experiments.

About This Manual

The following Equipment section describes each component in detail and the subsequent Assembly section provides instructions for component assembly and setup.

The Experiment section contains several experiments that can illustrate some of the basic theory of centripetal force, rotational inertia, etc.

Computer Timing

You can use a PASCO computer interface with a PASCO Photogate Head to measure the motion of the apparatus. Some of the experiments describe how to use DataStudio, the software program that supports every PASCO computer interface.

If you are using a computer interface such as a Science- Workshop 750 or ScienceWorkshop 500, you can connect the cable of the Photogate Head directly into the interface.

If you are using a PASPORT interface such as a USB Link, PowerLink, Xplorer, or Xplorer GLX, you will need to use a PASPORT Digital Adapter (PS-2159) to connect the Photogate Head to the interface.

See the PASCO web site at www.pasco.com for more information on PASCO interfaces, sensors, and software.

Complete Rotational System 012-05293F

Equipment

300g square mass (2) with thumbscrews and

square nuts

low-profile thumb-

screw assemblies (2)

photogate

mounting rod

accessory

mounting rod

aluminum rotating

platform

cast iron "A" base

"E" rings (2, 1 extra)

ME-8951 Rotating Platform Equipment

The ME-8951 Rotating Platform includes the following:

- PASCO cast iron “A” base with rotating shaft and pulley with 10 holes

- aluminum track

- two square masses (about 300 g) with thumb screw and square nut

spool of thread

clamp-on

pulley

rotating vertical shaft

with 10-hole pulley

- two additional low-profile screws and square nuts to act as stops for the square mass in the Conservation of Angular Momentum experiment

- accessory mounting rod for mounting a 10-spoke pulley with or without the optional PASCO Photogate Head

- photogate mounting rod for mounting a PASCO Photogate Head (ME-9498A)

side post

50g masses (2)

100g mass with 3 open

hooks

plastic

indicator disk

ME-8952 Centripetal Force Accessory Equipment

The ME-8952 Centripetal Force Accessory includes:

- center post that supports an indicator mechanism which consists of a small pulley, a movable spring holder, a movable indicator, a spring, and a plastic indicator disk

spring

center post

- side post for hanging hooked mass

- mass (100 g) with 3 open hooks

- 2 additional 50 gram masses

- clamp-on pulley

- 1 spool of thread

012-05293F Complete Rotational System

mass ring

(12.7 cm outside

diameter)

rotational disk

(25.4 cm diameter)

ACCESSORY

ROTATIONAL INERTIA

Super Pulley and rod

rotating platform

adapter

ME-8953 Rotational Inertia Accessory Equipment

The ME-8953 Rotational Inertia Accessory includes:

- disk with bearings in the center

- ring (12.7 cm diameter)

- adapter to connect disk to platform

- 10-spoke pulley and rod

Other Equipment Needed:

The following is a list of equipment recommended for the experiments described in this manual. See the PASCO catalog for more information.

- Projectile Launcher

- Projectile Collision Accessory

- Photogate Head (and a compatible PASCO computer interface)

- Mass and Hanger Set

- Stopwatch

- String

- Balance (for measuring mass)

- Calipers

-Meter Stick

Miscellaneous Supplies:

- graph paper

- carbon paper

- white paper

- rubber bands

- paper clips

Compatible PASCO Computer Interfaces:

The Photogate Head connects directly to a

ScienceWorkshop interface (such as the

ScienceWorkshop 500), and connects through a Digital

Adapter (PS-2159) to a PASPORT interface (such as a

USB Link, PowerLink, Xplorer, or Xplorer GLX).

Complete Rotational System 012-05293F

Assembly

ME-8951 Rotating Platform

Assembling the Rotating Platform

1. Insert the cylindrical end of the shaft into the bearings on the top-side of the A-shaped iron base. Secure the shaft in place by inserting the "E" ring in the slot at the bottom of the shaft. See Figure 1.

2. Mount the track to the shaft and tighten the thumb screw against the flat side of the “D” on the shaft. See Figure 1.

rotating platform

thumbscrew

flat of vertical shaft

vertical shaft

"A" base

"E" ring

Figure 1: Attaching the Vertical Shaft to the Base and Rotating Platform Assembly

012-05293F Complete Rotational System

rotating plat-

form

191817161514131211 24232221

300g square

mass

Leveling the Base

"A" base

111213141516171819212224

leveling feet

010

123456789

987654321

adjust this foot

Figure 2: Leveling the Base

Some experiments (such as the Centripetal Force experiments) require the apparatus to be extremely level. If the track is not level, the uneven performance will affect the results. To level the base, perform the following steps:

1. Purposely make the apparatus unbalanced by attaching the 300 g square mass onto either end of the aluminum track. Tighten the screw so the mass will not slide. If the hooked mass is hanging from the side post in the centripetal force accessory, place the square mass on the same side.

2. Adjust the leveling screw on one of the legs of the

rotating platform

(rotated 90° as shown)

010

123456789

111213141516171819212224

first

191817161514131211 24232221

then adjust this

foot

987654321

base until the end of the track with the square mass is aligned over the leveling screw on the other leg of the base. See Figure 2.

3. Rotate the track 90 degrees so it is parallel to one side of the “A” and adjust the other leveling screw until the track will stay in this position.

4. The track is now level and it should remain at rest regardless of its orientation.

300g square

mass

Using an Optional Photogate Head

The optional Photogate Head (ME-9498A) can be mounted to the Rotating Platform in two ways:

• Photogate Mount Rod can be used to mount the Photogate Head directly to the base as shown in Figure 3.

• Accessory Mounting Rod can to be used to mount a Pulley Mounting rod and a Super Pulley along with the Photogate Head to the base in order to run a string over the Super Pulley. See Figure 4.

To Mount the Photogate Head Only:

1. Mount the Photogate Head on the threaded end of the photogate mount rod.

2. Remove the swivel clamp from the top of the Photogate Head.

3. Slide the non-threaded end of the photogate mount rod into a hole in the A-base and clamp it in place with the thumbscrew.

4. Adjust the Photogate Head so that its infrared beam can be interrupted by the 10 spoke pulley on the vertical shaft as the shaft turns.

10-spoke pulley on vertical shaft

accessory

mounting rod

thumbscrew

"A" base

photogate mount rod

Photogate Head

(optional)

Figure 3: Using the Photogate Mount Rod With the

Photogate Head

Make sure that the Photogate Head does not rub against

the 10 spoke pulley or any other part of the apparatus.

5. Connect the cable to the Photogate Head and a PASCO interface.

Complete Rotational System 012-05293F

6. When the Photogate Head is powered by a computer interface, you can tell when the photogate is blocked by watching the LED indicator on the photogate.

10-spoke pulley on

vertical

shaft

nylon thumb-

screw

To use the Super Pulley and Photogate Head with the Pulley Mounting Rod:

1. Attach the Super Pulley -- and the Photogate Head if needed -- to the Pulley Mounting Rod.

2. Insert the pulley mounting rod into the hole in the Accessory Mounting Rod and tighten the thumb screw. See Figure 4.

accessory

mounting rod

3. Rotate the accessory mounting rod so that a string from the pulley on the center shaft will be aligned with the groove on the Super

"A" base

Pulley.

4. Adjust the position of the base so the string passing over the Super Pulley will clear the edge of the table.

Figure 4: Using the Accessory Mounting Rod With the Pulley

Mounting Rod, Super Pulley, and Photogate Head

pulley

mounting rod

Super Pulley

Photogate Head

(optional)

ME-8952 Centripetal Force Accessory

Center Post Assembly

Assemble the center post as shown in Figure 5:

1. Attach one end of the spring to the spring bracket and connect the indicator disk to the other end of the spring. Insert the spring bracket into the slot on the center post and tighten the thumb screw.

2. Tie one end of a string (about 30 cm long) to the bottom of the indicator disk and tie a loop in the other end of the string.

3. Insert the indicator bracket into the slot on the center post, placing it below the spring bracket. Tighten the thumb screw.

4. Attach the pulley in the higher of the two holes on the center bracket.

5. Insert the thumb screw at the bottom of the center post and attach the square nut.

spring

bracket

spring

pulley

reference mark (center of post)

square nut

Figure 5: Center Post Assembly

center

post

indicator

disk

indicator

bracket

thumbscrew

012-05293F Complete Rotational System

holes for

thread

nylon thumbscrew

Side Post Assembly

Assemble the side post as shown in Figure 6:

1. Insert the thumb screw at the bottom of the side post and attach the square nut.

single length

of thread

(30cm long)

side post

2. Using a string about 30 cm long, tie the string around the screw head on the top of the side post. Then thread the other end of the string down through one of the holes in the top of the side post and then back up through the other hole. Do not pull the string taut.

3. Loosen the screw on the top of the side post and wrap

100g mass

the loose end of the string around the threads of the screw and tighten the screw.

square nut

Figure 6: Side Post Assembly

thumbscrew

Threading the Centripetal Force Accessory

1. Mount the center post in the T-slot on the side of the track that has the rule. Align the line on the center post with the zero mark on the rule and tighten the thumb screw to secure it in place. Then mount the side post on the same side of the track. See Figure 7.

2. Hang the 100 g mass from the string on the side post and adjust the height of the mass so the string coming from the center post will be level when the mass is hanging straight down.

rotating

platform

100g mass

thread

zero mark

of rule

side post

indicator

disk

indicator

bracket

center post

pulley

reference mark (center of post)

Figure 7: Threading the Centripetal Force Accessory

Complete Rotational System 012-05293F

bearing of

"D" hole on top sur-

face of rotational

ACCESSORY

ROTATIONAL INERTIA

rotational disk

square

nut

platform

adapter

rotational disk

platform

adapter

rotating platform

Figure 8: Rotational Inertia Accessory Including Platform Adapter Assembly

ME-8953 Rotational Inertia Accessory

Rotational Inertia Accessory Assembly

Little assembly is required to use the Rotational Inertia Accessory. The rotational disk can be placed directly onto the axle of the rotating base or can be used with the rotating platform via the included platform adapter.

Platform Adapter Assembly

1. Attach the square nut (supplied with the Rotational Inertia Accessory) to the platform adapter.

2. Position the platform adapter at the desired radius as shown in Figure 8.

3. Grip the knurled edge of the platform adapter and tighten.

The rotating disk can be mounted in a variety of positions using any of the four holes on the rotation disk.

• Two “D” holes exist on the edge of the disk, located at 180° from one another.

• One “D” hole is located at the center on the top surface (the surface with the metal ring channel and the PASCO label) of the disk.

• One hole is located at the center on the bottom surface of the disk and is actually the inner race of a bearing. This enables the rotational disk to rotate (in either direction) in addition to other rotating motions applied to your experiment setup.

012-05293F Complete Rotational System

Experiment 1: Conservation of Angular Momentum

(Projectile Version)

EQUIPMENT NEEDED

- Rotating Platform (ME-8951) - Rubber band

- Projectile Launcher (ME-6800) - White paper and carbon paper

- Projectile Collision Accessory (ME-6815) - Thread

- Photogate/Pulley System (ME-6838) - Meter Stick (SE-6895)

- DataStudio Software - Mass and Hanger Set (ME-8967)

- PASCO Interface (see Note) - Calipers (SF-8711)

Purpose

The muzzle velocity of the Projectile Launcher can be determined by shooting the ball into the catcher mounted on the platform and conserving angular momentum during the collision. This result can be checked by finding the muzzle velocity of the Launcher by shooting the ball horizontally off the table.

Note: If you are using a PASPORT interface, you will also need a Digital Adapter (PS-2159)

Theory

A ball is launched horizontally and embeds in the catcher mounted on the platform. The platform then rotates. See Figure 1.1.

Angular momentum is conserved during the collision but energy is not conserved. The angular

Projectile Launcher

Rotating Platform

"A" base

Projectile Collision Accessory

("catcher")

Figure 1.1 Conservation of Angular Momentum

momentum before the collision is equal to the angular momentum after the collision:

Lmbv0RIω==

3 2

7 1

where m

is the mass of the ball, vo is the muzzle velocity of the ball, R is the distance between the ball

and the axis of rotation, I is the rotational inertia of the catcher, ball, and rotating platform after the collision, and ω is the angular velocity of the system immediately after the collision.

Solving for the muzzle velocity of the ball gives:

Complete Rotational System 012-05293F

Iω

----------

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

---

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 base of the apparatus, and

τ rT=

where r is the radius of the step 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 1.2):

ΣFmgT– ma==

Rotating Platform

"A" base

hanging

mass

Figure 1.2: Rotational Apparatus and Free-Body Diagram

Solving for the tension in the thread gives:

Tmga–()=

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.

For comparison, the initial speed (muzzle velocity) of the ball is determined by shooting the ball horizontally off the table onto the floor and measuring the vertical and horizontal distances through which the ball travels.

For a ball shot horizontally off a table with an initial speed, v

ball is given by x = v

t, where t is the time the ball is in the air. No air friction is assumed.

The vertical distance the ball drops in time t is given by .

, the horizontal distance traveled by the

---

The initial velocity of the ball can be determined by measuring x and y. The time of flight of the ball can be found using:

------=

and then the muzzle velocity can be found using v

= x/t.

012-05293F Complete Rotational System

Part I: Determining the initial velocity of the ball

Setup

Projectile Launcher

1. Clamp the Projectile Launcher to a sturdy table near one end of the table.

2. Adjust the angle of the Projectile Launcher to zero degrees so the ball will be shot off horizontally. See Figure 1.3.

WEAR SAFETY GLASSES WHEN IN USE.

6 0

5 0

4 0

3 0

2 0

ME-6800

Procedure

1. Put the ball into the Projectile Launcher and cock it to the long range position. Fire one shot to locate where the ball hits the floor. At this position, tape a piece of white paper to the floor. Place a piece of carbon paper (carbon-side down) on top of this paper and tape it down. When the ball hits the floor, it will leave a mark on the white paper.

2. Fire about ten shots.

3. Measure the vertical distance from the bottom of the ball as it leaves the barrel (this position is marked on the side of the barrel) to the floor. Record this distance in Table 1.1.

Table 1.1 Determining the Initial Velocity

4. Use a plumb bob to find the point on the floor that is directly beneath the release point on the barrel. Measure the horizontal distance along the floor from the release

Horizontal distance to edge of paper =

Vertical distance =

Initial velocity =

point to the leading edge of the paper. Record in Table 1.1.

5. Measure from the leading edge of the paper

Trial Number

to each of the ten dots and record these distances in Table 1.1.

6. Find the average of the ten distances and record in Table 1.1.

7. Using the vertical distance and the average

horizontal distance, calculate the time of flight and the initial velocity of the ball. Record in Table 1.1 and Table 1.4.

clamp

Figure 1.3 Projectile

Launcher Setup

Distance

LONG

MEDIUM

RANGE

CAUTION!

DO NOT LOOK

DO NOT LOOK DOWN BARREL!

DOWN BARREL!

DOWN THE BARREL.

PROJECTILE LAUNCHER

CAUTION!

SHORT RANGE

Yellow Band in Window Indicates Range.

Launch

Use 25 mm

Position of Ball

balls ONLY!

Alternate Method: Determining the Muzzle Velocity with Photogates

1. Attach the photogate bracket to the

Launcher and attach two Photogates to the bracket. Plug the Photogates into a computer or other timer.

Average

Total Distance

2. Put the ball into the Projectile Launcher and cock it to the long range position.

3. Run the DataStudio program. Set it to measure the time between the ball blocking the two Photogates as it comes out of the Launcher.

4. Shoot the ball three times and take the average of these times. Record in Table 1.2.

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