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Research in Science Education, 1984, 14, 136-145

CIRCULAR MOTION: SOME POST-INSTRUCTIONAL ALTERNATIVE FRAMEWORKS

Paul Gardner

INTRODUCTION

Despite the many personal experiences that physics students (and others) have

with objects which travel in circular paths, the dynamics of c i rcular motion is

arguably one of the most d i f f i cu l t topics in the senior seconary school physics course.

In an earl ier paper (Gardner, 1981) the popular but misleading concept of

centr i fugal force was analysed and the various meanings attached to this term by

some teachers, textbooks, and students were discussed. In certain situations - when

one describes circular motion from the vantage point of someone wi th in the

accelerated frame of reference - the concept has its uses. However, most usages of

the term 'centr i fugal force' are simply logically incompatible wi th Newtonian physics.

[t is obvious that some people have considerable d i f f i cu l ty wi th this concept.

For example, in a later issue of the same journal that had published a protracted

debate on centr i fugal force (Gardner, 1981; Deakin & Troup, 1982; Gardner, 1982),

we find this misconceived 'explanation':

How a centr i fugal clothes dryer works

Obtain a milk powder can and punch in its sides quite a number of

holes with a nail. Punch three holes equi-distant from each other

around the top of the can. Suspend with three cords and attach

these to the screw eye in the dri l l chuck. Make a cyl inder out of

cardboard or f ind a pail a l i t t le deeper than the can (a pneumatic

trough wi l l be suitable) and considerably wider. Place a bi t of wet

cloth in the can attached to the dr i l l . Lower the can into the

cyl inder or trough and spin i t rapidly wi th the dri l l . The water is

thrown out of the cloth and can by the centr i fugal force. (Note I)

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The fact that a science teacher can wr i te such an 'explanation' (and that the editor of

a science teachers' journal can accept i t for publication) indicates just how deeply

entrenched this misconception is.

Several wr i ters have drawn at tent ion to ter t iary students' conceptual d i f f icu l t ies

in this area of physics. Warren (1979) asked English university entrants to draw an

arrow representing the resultant force on a car t ravel l ing along a horizontal, c ircular

road at constant speed~ 40 per cent drew a resultant forward force while 28 per cent

drew a vector representing a centr i fugal force. In the U.S. McClosl<ey, Caramazza

and Green (1980) asked freshmen physics students to predict the subsequent path of

balls leaving a curved tube, or balls breaking away from a radial string. About a third

to a hal f of the students predicted that the balls would fol low a curved path, implying

a bel ief in a kind of conservation of curvi i inear motion. In Europe, Viennot (1979)

argued that many university students treat c i rcular motion as an example of an

equi l ibr ium situation~ and this leads them to invent an outward force to

counterbalance the inward force. The present paper draws upon this earl ier work and

describes a study designed to probe in general detai l the conceptual structures of a

small sample of Year 12 physics students fol lowing instruct ion on circular motion.

IN STRUMEN T

A 27-item test (mult iple-choice plus extended answer)~ as described in Gunstone

(]984) was used in the study.

SAMPLE

One state high school and one Cathol ic girls' school part icipated in the study~ 23

students answered the test a few weeks after studying the topic in class. The sample

is of course small, and no claims are made about the general izabi l i ty of the findings

to the wider school population. I merely make the point that even this small sample

has yielded an astonishing var iety of al ternat ive conceptual frameworks that students

use to account for the dynamics of c i rcular motion.

FINDINGS

The 'correct'~ 'official'~ 'scientific'~ (i.e., Newtonian) framework

Before considering the vast col lect ion of a l ternat ive explanations which students

in these two classes offered we should note that a few students, fol lowing instruct ion,

actual ly do accept the Newtonian view.

Student 8, for example, wrote

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The string exerts a constant, unbalanced force on the t in, which

accelerates the t in towards the point to which the string is connected.

This student ident i f ied the force of gravi ty as the only force acting on .]upiteffs moon,

and stated

The force ... acts at 90 ~ to the motion of the moon (directly towards

the centre of Jupiter).

Only two students (out of 23), however, offered consistent Newtonian explanations of

this kind. These explanations may be regarded as 'complete ~ in the sense that they

correct ly ident i fy both the direction of the force causing circular motion, and the

nature of that force (tension, gravity).

Part ia l Newtonian Frameworks

A few students offered Newtonian explanations, but fai led to explain the physical

basis of the force: i.e., they may have recognised that an unbalanced, centripetal

force is acting but they did not describe the nature of that force. The dist inct ion is

important. Warren (L979, p. 10) reports that some students describe the centr ipetal

force on a satel l i te as equal to the gravi tat ional force, but in terms which imply a

bel ief that these are two di f ferent forces. In our study, Student 5 offered an answer

which could be classified as part ly Newtonian:

The centr ipetal force acts on the t in continuously changing the

direction of motion of the t in. The force is directed towards the

centre ... The velocity is constantly changing because the direction

of motion is changing. There[fore?] there is a force acting on the

t in.

And, a similar response from student No. 14:

Centr ipetal force is the one acting towards the centre of the circle

to keep i t in its circular motion.

Note that there is no mention here of the physical basis of the force: the word

'centripetaP is used as i f i t were a description of a type of force, rather than simply a

synonym for 'towards the centreL Both students' explanations contain tautological

propositions. However, both students were able to explain the 3upiter/moon situation

in terms of 'an attract ing force between Jupiter and its moon' which is 'directed

towards 0upiter'.

So much for the good news. The remainder of the discussion of findings is devoted

to the many alternative frameworks which students employed to make sense of

c ircular motion.

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Shades of Aristotle: The Motive Force Framework

Watts (1983), in a study of the conceptual frameworks about force of 12 secondary

school students aged I 1-18, noted a common bel ief that forces are required to cause

and maintain motion: 'If a body is moving, there is a force acting upon i t in the

direction of the movement, (p. 226). Some pupils consider this force to be a net

force; others make no such distinction.

This motive force framework can be found in some students' explanations of

circular motion. Student 17, for example, agreed that there were forces acting on

Jupiter's moon - 'the gravi tat ional f ield strength pulling it in' - but then said that the

total force was 'not zero, and in the direction of motion ... because i t is moving'.

This student had earl ier given similar accounts for the total force acting on a tin

sliding horizontal ly at constant speed and on a car travell ing along a straight road at

constant speed. [n a later question on earth satell ites, he wrote about 'the force that

would make the satel l i te go in a straight l ine' as a force which is acting on the

satel l i te.

The common theme here is the Aristotel ian idea that forward motion requires a

forward force. Other Newtonian concepts - gravity, fr ict ion - have been grafted on

to this conceptual structure without disturbing i t too much.

The E q u i l i b r i u m Framework: Type I - Absence of Radial Forces

Many students regard circular motion as a phenomenon in which the moving object

is in some kind of balance, or equil ibrium. Circular motion at constant speed is

treated much like rect i l inear motion at constant speed. This bel ief in equil ibrium is

expressed in at least two distinct ways. One is to avoid all reference to radial forces,

as i f the constant speed of the object is the dominant characterist ic, and the

changing direction is simply not a phenomenon requiring a dynamic explanation at all.

For Student 21, for example, there were three forces acting on the revolving tin:

weight, normal (reaction) and a fr ict ion force (backwards). Her diagram contains the

word 'tension' but there is no arrow to show direction, and the word has been crossed

out from the l ist of forces acting. For Jupiter's moon, this student believed that

there were no forces acting at all= the moon 'is in space, therefore no fr ict ion,

therefore according to Newton's law this body wi l l not change its speed unless acted

upon by an external force. There is no acceleration, therefore force = 0'.

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Equi l ibr ium Framework Type lI: Two Counter-Balancing Radial Forces

A second, more complex manifestation of equi l ibr ium can be seen in explanations

which postulate a balance between a centr ipetal force and an equal and opposite

centr i fugal force. These explanations probably stem from attempts by students to

integrate the new knowledge (a centr ipetal force acts on a revolving body) wi th a

f i rmly held prior bel ief in equil ibrium.

The 'counter-balancing' account of c ircular motion has already been noted by

Viennot (1979)-

The circular motion of a stone on the end of a string ... is incorrect ly

seen as an equil ibrium situation (radial ly) so that there is an in tu i t ive

need for two 'equal' and opposite forces.

Student 3 provides a clear example of this. He drew four forces acting on the t in

(weight, normal reaction, inward force labelled 'F 1 = ma' and an outward Force

F 2. The total force, he said, was zero: i f not 'the t in w i l l not go in a c i rc le but in

[a] d i f ferent direction'. Similarly, the total force on Jupiter's moon was zero: ' I f the

centr ipetal force is greater than the force spinning r'~] outward, def in i te ly the moon

wi l l coll ide [wi th] Jupiter'. The physical basis of this outward force, i t w i l l be noted,

is not explained: i t is simply something which appears to be necessary to prevent

something else from happening.

inconsistent Frameworks : Newtonian and Non-Newtonian

Some students' responses show evidence of inconsistent frameworks: an answer to

one question may be couched in Newtonian terms, but an abiding bel ief in equi l ibr ium

takes over when a sl ight ly di f ferent question is asked. Student l ) , for example, when

asked for a description of forces on the revolving t in gave an apparently perfect

Newtonian reply:

There are several forces acting on the t in. The tension in the str ing

produces a centripetal force which acts inwards, towards the centre

of attachment of the t in. The forces due to gravi ty (the weight

force) and the reaction force of the table (as previously described)

continue to act. [In an earlier question, these two were described as

summing to zero.]

Neverthess, when asked for the total force on the tin~ he answered :

Zero ... the object moves with constant speed around the c i rc le.

Hence there cannot be any unbalanced force acting.

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He t reated the mot ion of a car on a c i rcu lar road in a s imi lar way:

... constant speed ... no unbalanced force. The cent r ipeta l force is

balanced by a force act ing in the opposite d i rect ion kvanting' to keep

the car moving in a stra ight l ine. Hence sum of a l l forces equals zero.

Rat ionales Underlyincj the Equi l ibr ium Framework

Why do many students bel ieve that a revolv ing object is in equ i l ib r ium? Viennot

(1979) proposes an explanat ion in terms of an assumed l inear re la t ionship between

force and ve loc i ty : zero ve loc i ty impl ies zero force. Thus, i f an object has no radia l

ve loc i ty , then i t has no radial force act ing on i t . Viennot was invest igat ing the

thought processes of univers i ty students. In the present study, however, i t would

appear that less complex bel iefs are held by students who adopt an equi l ibr ium

framework. Two such bel iefs emerge in some students' accounts:

Constant speed impl ies no accelerat ion and hence zero net force.

A force is required to hold a revolv ing object at a f ixed distance f rom the centre.

Student 13, c i ted ear l ie r , is qui te exp l i c i t in o f fer ing the former belief."

... the object moves wi th constant speed ... hence there cannot be any

unbalanced force ...

Student 16 exempl i f ies a be l ie f in the second proposition"

rThere is a] centr ipedal [sic] force between moon and 3upi ter . Force

towards 3upi ter , pul l ing moon towards 3upi ter and force holding moon

where i t is.

Student 19 combined both bel iefs in her account. She drew four forces on the t in, and

integrated a misuse of Newton's second law wi th her misconcept ion about

equi l ibr ium. The to ta l force, she said, was zero, because

i t is moving in constant speed, hence the accelerat ion is equal to

zero. As F = m a i t impl ies that the force is equal toO. The other

force which tend to equal both the opposite sides A = By C = O. This

helps to mainta in the posit ion of the t in.

Her account of Jupiter's moon is more complex:

the moon is movring] in a c i rcular path, which means that 3upi ter

should have some kind of force act ing on the moon in order to

mainta in ... Fit] ... in a c i rcular path. (Actual ly I never know whether

this is true or not, I just guessed i t . )

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But equil ibrium-as-posit ion-maintenance wins out : the total force is 'zero' because

i t is moving in a constant speed~ and always with the same distance

from Jupiter.

The Physical basis of the mythical centr i fugal force

I f one holds strongly to a Type II equi l ibr ium framework~ there is an obvious need

to introduce an outward (i.e. centr i fugal) force~ some students carry this through to

the point of 'explaining' the physical basis of this force. Various explanations are

offered:

A second c l ravi tat ional force

Student 23 deals with the revolving t in by labelling four force=

the weight~ the normal reaction~ and 'a centr ipetal force A which is

of the same magnitude but d i f ferent direction to B~ the centr i fugal

force'.

]n the case of Jupiter and its moon a physical 'explanation' is not introduced:

the [ tota l ] force [on Jupiter's moon] is zero since the moon does

not leave its orbi t . The force exerted by Jupiter is equivalent to

that exerted by the sun.

Misuse of the action-reaction principle

Some students at tempt to 'explain' centr i fugal force by appealing to Newton's

Third law,

Student 13 (whom we encountered earl ier wi th his beaut i ful Newtonian account

of c i rcular motion~ followed by the statement that the total force on the t in is zero)

now gives us an insight into the basis of the extra force in his discussion of the

Jupiter/moon problem:

The only force on Jupiter's moon .,, is the gravitat ional force on i t

exerted by Jupiter. The moon~ itseif~ exerts an equal and opposite

gravitat ional force on Jupiter; the total force must be zero.

[t is unclear from this whether he believes that the total force on the moon is zero~

or that he has misunderstood the meaning of the term 'total force',

I t is of course true that there is a centr i fugal reaction force acting~ but i t acts

on the object at the centre of the motion9 and not on the revolving object. The

action-reaction explanation stems from a failure to distinguish between these two

sets of forces.

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Some unusual conceptual frameworks

A few students wrote replies ref lect ing quite unusual conceptual frameworks:

Centr i fugal plus Ar istot le

One student (20) combined centr i fugal and Ar istote l ian concept~

The t in moves in a circle so a eentripedal rsic] force and a

centr i fucal [sic] must be applying ...

This was followed by a diagram in which a constant magnitude resultant force acts in

a tangent ial ly forward direction. The total force, she states, is not zero, because 'the

resultant of the forces applied (vector) is cont inual ly changing direct ion'.

An Ar istotel ian yet ant i -centr i fugal , f ramework

Student l postulated no less than si__x forces acting on the revolving tin-- gavity,

normal reaction~ an inward force 'due to the aceeleration in towards the nail'~ an

outward 'tension in the string caused by inert ia' , ' f r ic t ion i f i t is present' (tangential,

backward) and ' inert ia producing tension in the str ing' (tangential, forward). Apart

from the false dichotomy between the tension and the centr ipetal force in this

response~ the reply suggests that the tengential veloci ty/momentum of the t in is

being treated as i f i t were a kind of forward driving force. Later, in discussing

eareth-satel l i tes, he asserts that the

satel l i te has momentum. This produces inert ia, which combined

with gravi ty keeps the satel l i te in orbit.

This student does not believe in centr i fugal force:

t i t ) is non-existant [sic]. I t merely explains the apparent e f fec ts to

ignorant savages. A l l motion can create forces. Impetus is a

force. Momentum is a force. Kinet ic energy is a force.

Centr i fugal f r ic t ion

Student 7 gave clear Newtonian accounts of the motions of the t in and 3upiter's

moon, and recognised that in the ease of a ear on a c i rcular road, there was a

non-zero centr ipetal force. However, his diagram of the forces acting on the car

showed an outward fr ict ional force in addition to the centr ipetal force. This

explanation fai ls of course to recognise that the centr ipetal force here is f r ict ional ;

the misconception would seem to stem from a bel ief that f r ic t ion always acts in

opposition to some other force acting on an object.

Student 16 (who believed there was a force 'holding the moon where i t is')

maintains a similar view about cars on circular roads. Like Student 79 he explains the

motion of the car in terms of a centr i fugal f r ic t ional force.

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No consistent conceptual f ramework at a l l

And f ina l ly , some students do not appear to hold to any consistent conceptual

f ramework at al l . Individual s i tuat ions are t reated id iosyncrat ica l ly , w i thout any

overa l l logical coherence.

Student I I provides a c lear example of this. An equi l ib r ium s i tuat ion - a t in

sl iding hor izonta l ly at constant speed - was t reated as a non-equi l ibr ium si tuat ion:

The t in is not s t i l l , therefore there must be some net unba lanced

force act ing on i t ...

But a non-equi l ibr ium s i tuat ion was t reated as a Type I equi l ib r ium s i tuat ion. For a

car t rave l l ing on a c i rcu lar road, this student proposed a four - fo rce explanat ion:

weight , normal react ion, forward dr iv ing force, backward f r i c t iona l force, but no

radial force. The to ta l force, he stated~ was zero.

The 3upi ter /Moon problem was then t reated as a Type II equ i l ib r ium situat ion:

he recognised 'there is the force of grav i ty pul l ing i t in towards 3upiter ' , but then

stated that the to ta l force is zero because ' i t does not move inwards or outwards

f rom 3upit er'.

C O N C L U D I N G NOTE

This explorat ion of the thoughts of 23 Year 12 students leads to a simple

conclusion. The ghost of Ar is to t le must be dancing wi th mi r th , for two mi l lennia

la te r his ideas are al ive and wel l . Newton, on the other hand, must be turning in his

grave.

To end on a more pract ica l note, however, the f indings suggest that teachers

should recognise that the topic of c i rcu lar mot ion is conceptual ly ex t remely d i f f i cu l t ,

and that students come to i t (and leave i t ) wi th a wide var ie ty of explanatory

concepts, most of which are - in t rad i t iona l Newton ian terms - p la in ly wrong. Since

the dynamics of c i rcular mot ion a r e cent ra l to a proper understanding of so many

aspects of physics, there is a clear chal lenge to science educators to devise some

more e f fec t i ve inst ruct ional procedures.

REFERENCE NOTE

1.'3unior Secondary' section, The Austra l ian Science Teachers 3ournal t 1983, 2--9,(3),

67.

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REFERENCES

DEAKIN, M. & TROUP, G. Centrifugal force: An elucidation. The Australian

Science Teachers Journal, 1982, 28(3), 33-38.

GARDNER, P.L. On centrifugal force. The Australian Science Teachers Journalt

I981, 2_Z,(3), 69-74.

GARDNER, P.L. Centrifugal force: A reply to Oeakin and Troup. The Australian

Science Teachers 3ournal, 1982, 28,(3), 39-43.

GUNSTONE, R. Circular motion: Some pre-instruction alternative frameworks.

Research in Science Education, I984, 14, 125-135.

McCLOSKEY, M., CARAMAZZA, A., & GREEN, G. Curvilinear motion in the

absence of external forcem Naive beliefs about the motion of objects. Science,

1980, 21{3, 1139-41.

VIENNOT, L. Spontaneous reasoning in elementary dynamics. European Journal of

Science Education, 1979, I_., 205-221.

WARREN, 3.W. Understandin 9 force. London, John Murray, I979.

WATTS, D.M. A study of schoolchildren's alternative frameworks of the concept of

force. European Journal of Science Education, 1983, 5(2), 217-30.