Re: "Simple pendulum"

["Inge H. A. Pettersen" <ingep@ONLINE.NO>]

Ludwik Kowalski wrote:

> This begs for a definition. What are misconceptions?

> Let me
> follow the advice and express myself by the way of an example.
>
> As a student (and also when I started teaching) I accepted the
> convention that acceleration is positive while deceleration is
> negative. It prevented me from solving some kinematics
> problems in one step. The vertical throw problem, for example,
> would be solved with the y axis up till v becomes zero and
> with y axis down for the free fall step. I do not remember the
> origin of this. Then I learned a better way (see below) and I
> solve the same problem in one step, with y pointing up.

I guess most physics teachers in introductory courses tell their students to
choose what seems to be
the most useful coordinate system and then "stick to it" by drawing a free
body diagram, relying on Newtons laws.
I think your teacher made a * pedagogical/methodological* mistake by
changing his coordinate system, even though this is
from a physical point of view possible to do. For a beginning student of
physics a change of direction might lead to confusion
and maybe even the errorous idea that "if the velocity changes direction, I
have to change the direction of the axis".
When the student has got confidence in calculations one could show an
example where the change in coordinate system will simplify the discussions,
pointing out that Newtons laws are true for all inertial observers. In that
case one should also point out that velocities and positions will in general
depend on the choice of coordinate system. Nevertheless, as a high school
teacher I would not do so except when I have a very good class and I am sure
they understand the basics.

> Was a less effective way of practicing kinematics a
> misconception? Is it worth of being described as an item
> on our list? What is a better name for the "list of
> misconceptions"?

1st question :
I would consider it not as a misconception, but a bad pedagogical
methodology for a beginning physics student as argued above.
2nd :
Given my view of the first: no. Even though you might not agree: Why not
start at a restrictive end and let the project evolve ?
I am pretty sure that you will get enough feedback when you have a first
version. The simple fact that physics instructors at least initially
disagree on a certain introductory physics concept should probably be reason
enough to put it on the list. Another problem is that often a concept is may
have slightly different content in different contexts (Newtonian rigidness
can't be *directly*  transferred to SR as its definition assumes Newtonian
absolute time - but can be consistently defined in a Bornian way etc.) or
may be consistent in some contexts and not in others (for instance
arbitrarily accurate simultaneous specification of position and its
conjugated momentum for a 1 dimensional "particle"). In these cases you
simply has to distinguish different cases. But again, let's start with
simple subjects (or not so simple simple after all?) - with Newtonian
mechanics, thermodynamics and electromagnetism - that a beginning student
would meet.
3rd:
As I have english only as my second language, I should be careful here :-),
but I think the following is correct:
My "Concise Oxford Dictionary" associates concept with "general notion", "an
idea or mental picture of a group or class of objects formed by combining
all their aspects". A misconcept should then be a false notion/idea/mental
picture.

> As stated, for example,  in vol I of "Physics, a Contemporary
> Perspective" by R.D. Knight, "The sign of acceleration has
> nothing to do with weather or not the object is speeding up
> or slowing down". The correct interpretation is that a positive
> acceleration vector points away from a chosen origin (for
> example, along the positive x axis) while a negative
> acceleration vector points toward the origin (for example,
> against the positive x axis).
>
> In other words, a component of an acceleration vector is
> positive when its direction coincides with the direction of

the change of the corresponding (be careful :-)

> the velocity component.

> And it is negative otherwise. The
> convention that "the direction of v is positive when an object
> moves away from the origin (and negative otherwise)", does
> not confuse students as much, when they learn kinematics,
> as what we say about a.

Nevertheless I think one should stress the kinematic definitions when
deciding the sign in 1D: A positive velocity at time t (= delta x / delta t)
means that the change of  the position during a small time interval
thereafter (t,t+delta t) will be positive, i.e. the particle will move in
the direction of the *positive* x-axis and similar for acceleration.

> Acceleration and deceleration terms are used in plain English
> as references to opposite things (see also contaminate versus
> decontaminate, activate versus deactivate, etc.), That is the
> source of confusion. Fortunately the sign rules become
> less confusing after the F=m*a formula is digested by
> students.
>
> Ludwik Kowalski

I guess my bottom line is: Start simple and I am sure you will get response.