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UNIT 4 ROTATIONAL MOTION
Structure
4.1 Introduction
Objectives
4.2 Introducing Rotational Motion
4.3 Teaching-Learning of the Concepts
Angular Vclocit) and Angular Accclerallon Vectors
Torque
Kolat~orlal Inertia
Angular Momentum and its Conservation
Kinetlc Energy of Rotation
4.4 General Motion of a Rigid Body: Concept of Centre-of-mass
4.5 Summary
4.6 Terminal Questions
4.7 Solutions and Answers
4.1 INTRODUCTION
In the previous units, we have discussed various strategies to help students learn
difficult concepts related to translational motion of point masses. We hope that you
have used these methods with your students and they have been able to acquire a good
grasp of the concepts of inertia, force, linear momentum, impulse. \r~ork, energy, as
well as the laws of conservation uf linear momentum and energy.
We now turn our attention to difficult concepts related to rotational motion of
You know that the world around us abounds in
extended bodies about an axis.
systems undergoing rotation. These range from rotating galaxies, stellar clouds and
planets to giant wheels, merry-go-rounds, bicycle wheels, grinding stones, potter's
wheel etc. As you know, the motion of a rotating object as a whole can be analysed
quite siniply in terms of its torque, rotational inertia, angular velocity, angular
acceleration and angular momentum.
In this unit, we discuss how we can help our students learn the physics of rotational
We share various experiences about the kind of difficulties faced by students
motion.
in learning the associated concepts. For example, many JNV physics teachers told us
that their students found the concepts of torque, rotational inertia and angular
motnentilm quite difficult to understand. To this list we have added the concepts of
angular velocity, angular acceleration and kinetic energy of rotation. We suggest some
strategies, methods, and activities to take care of the learning difficulties of students
and help them learn these concepts. You can look upon them as examples and devise
aim is to enable them to
your own strategies in the context of your students. Our
acquire a better understanding of rotational motion so that they can solve problems
based on it with confidence. Of course, this kind of teaching-learning would involve
quite a bit of planning and preparation on your part.
In the next unit, we consider issues related to the teaching-learning of the mechanics
of solids and fluids.
Objectives
After stud) ing this unit you should be able to:
generate interest amongst your students in the physics of rotational motion;
devise activities and strategies to help your students learn better. the concepts
related to rotational motion, e.g., torque, rotational inertia, angular momentum etc.
mathematical Tools and assess whether you have succeeded in improving your students' grasp and
Mechanics resolving their difficulties related to the concepts of rotational motion; and
inculcate independent thinking and cooperative learning behaviour in your
students.
4.2 INTRODUCING ROTATIONAL MOTION
You would agree that a good way of introducing any concept in physics is to relate it
to your students' everyday experiences and make thcm understand why they need to
study it. If you could also put in some activities or games. it would surely add to their
interest. So here are some suggestions about how you could introduce rotational
motion to your students. You have at your disposal 15 periods for teaching rotational
motion. Perhaps you could use your first classroom session on rotational motion to
introduce it through activities and games. You could divide your students into groups
to economise on time.
Example 1: Some suggestions for introducing rotational motion
Your students are intuitively familiar with rotating objects. They may have taken
joyrides on giant wheels, merry-go-rounds or the see-saw, ridden bicycles, opened
nuts or bolts, or played with spinning tops. Of course, they are opening and shutting
doors all the time. But they might still ask you why they should study the physics of
rotational motion. So, you could begin by mentioning some rotating objects they
encounter everyday such as wheels (of bicycles, buses, cars and trains), potter's
wheel, spinning tops. rotating hands of a clock, etc. To add variety to your teaching,
you may like to put up a blank chart paper, with the title "Things around us that
Rotate or Roll", on the wall and write the names of these objects on it. Encourage
your students to name a few more which you could add to the list on the chart.
You could read Unit I0 of the You could point out to them that we live on a rotating object, the earth. Ask them to
IGNOU u.s~. physics elective mention some natural phenomena that occur due to its rotation (e.g., the occurrence of
entitled 'Elementary day and night). Add to their list: For instance, the occurrence of tides and cyclones,
Mechanics' or thc chapter on the washing away of river banks and the wearing off of railway tracks on one side
Rotating! Non-inertial frames happens due to the rotation of the earth. Writc all these things on the chart which
of rcfcrence in any standard could serve as a future reference material.
book on Mechanics to be
prepared for any questions
related to the earth's rotation. You could arouse their curiosity with questions from their experiences. Some
examples are:
a Why do we find it easier to loosen a bolt with a spanner rather than our hand?
a Can we open a door if we push it at its hinges?
a Why does a raw egg spin longer than a hard boiled one?
a Why is the rod connecting the pedal of a bicycle wheel (or the handle of the
grinding stone) perpendicular to the wheel's (or the grinding stone's) plane?
a How do we set a potter's wheel or a merry-go-round moving?
a Is it possible for a thin child to lift a hefty child on a see saw?
a Why do gymnasts and divers bend before they flip or turn?
How do we rotate or orient a satellite?
a Why are the sun and the planets situated almost in a plane?
And, so on.
Rotational Motion
Allow your students time to think about and come up with similar questions by
involving them in group discussions. They would perhaps find it interesting to know
that such questions and many others could be explored through the study of rotational You are already well versed
motion. with the methods of
cnsuring group learning,
You could show them the actual rotational motion of some of these objects, e.g., a cooperative learning etc.
from the course on
rotat~ng door, spinning top, spinning raw and boiled eggs, bicycle wheel, simple teaching-learning and
balance used in shops, rotating hands of a clock, etc. Let them have some fun pedagogy being given in
You could even take them out to the school playground, if this programme. So here we
rotating various objects. will focus only on the
IOU have merry-go-rounds and see-saws in it. physics part and not talk
how to carry out the
about
You could ask them to think about how rotational motion of objects is different from group activities.
their translational motion about which they have learnt so far. Show them translational
motion (motion from one point in space to another). For example, you could move the
duster across your desk. Make your students do activities to compare it with pure
rotational motion.
Through activities, questions and suggestions you could help them
arrive at the characteristic feature of pure rotational motion (Fig. 4.1) of an extended
body:
An object undergoing pure rotational motion constantly changes its orientation
with respect to other fixed points in space. Its centre- of-mass (CM) remains
located at the same position in space.
Explain that any rotation about an axis through the CM is pure rotational motion. You
could also introduce the term 'axis of rotation' which is the axis about which the
object rotates. Show it for some rotating objects. Ask your students to point it out for
other rotating objects. Do give them enough time to explore and grasp these ideas
without overloading their mind. You may also like to point out at this stage itself or
any rotation
after discussing the concept of the centre of mass, the subtle point that
about an axis passing through the centre of mass is a pure rotation.
Fig.4.1: Pure rotational motion of an extended rigid body: the body changes its orientation with
e.g., the points on the axis of rotation
respect to other fixed points in space,
Now you may like to ask them whether we can analyse rotational motion of an object
by applying the usual form of Newton's laws. Again through questions and
suggestions you must help them understand that, in principle, we can do so. By
applying the laws to each particle of the object, we can determine its acceleration,
velocity and displacement at any time, if we know the net force acting on it. But, in
practice, it is a difficult task as the particles in extended objects number in millions
and we will have to apply Newton's laws to millions of particles to analyse rotational
Is there a way out to handle this problem in a simple manner?
motion.
This is one way by which you could establish the need for learning new concepts to
explain rotational motion in a simple manner.
Rlathematical Tools and From the second period onwards. you may like to begin teaching the concepts. Let us
hlechanics see how we can help them learn these concepts. But before you proceed further, try
this exercise.
SAQ 1
a) You have studied various theories of teaching-learning in this programme as well
as in your earlier studies. Clearly explain, which aspects of these theories you see
reflected in Example I, and in what ways?
b) HOW do you normally introduce rotational motion to your students? You may like
to improve upon the suggestions given in Example 1 or use any other method to
introduce rotational motion to your students in a different way from the one that
you normally use. You may also like to use audio-visual aids, CD-ROMs or the
INTERNET, if possible.
Describe your experience of introducing rotational motion (in this manner) to
J our students and analyse their response. Your description must include a
statement of your aim, the planning that was involved in this exercise, a brief
account of the method you used (including whatever you said or did) and the
students' reactions, the time and preparation involved, and an analysis of whether
your aim was met.
Give your comments on how well the method you used worked with your
students. If it did not, explain why. What other options could you have tried out?
How did you gauge whether your students were able to learn what rotational
motion is and appreciate the need for introducing new concepts?
We now consider some aspects of rotational motion, that students find difficult to
understand. Specifically we shall take up their difficulties in understanding the
concepts of
angular velocity, angular acceleration, torque, rotational inertia,
angular momentum, and kinetic energy of rotation.
4.3 TEACHING-LEARNING OF THE CONCEPTS
As we discuss each concept in this section, we will underscore the need to set up your
teaching-learning objectives, share somc of the common problems students have and
describe a few strategies that have led to better student learning. We will also
highlight some points that need to be emphasized while building up these concepts.
Since you will be dealing largely with the rotational motion of rigid bodies, you need
to briefly explain what a rigid body is: Put simply (as also given in the NCERT
Senior Secondary physics book), it is a body that maintains its shape under the
action of forces. More rigorously, a rigid body is defined as an aggregate of point
masses such that the relative separation between any two points always remains
invariant. Give familiar examples of a rigid body from amongst the ones you have
shnwn your students and ask them to name some more. Let them handle various
objects and identify the rigid bodies amongst them. For example, the wooden duster
you use is a rigid body, but the piece of foam on its top is not.
For the sake of simplicity, you may like to first consider pure rotational motion of a
rigid body with the axis of rotation passing through it. To begin with, you could
take only those
exan~ples for which the axis of rotation remains fixed. Point out that
the axis of rotation is a straight line joining all points inside the body that remain
Any other point on or inside the body executes
stationary as the body rotates.
circular motion in the plane perpendicular to the axis of rotation (Fig. 4.2). The
centre of the circle lies on this axis.
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