Greetings, we will begin with unit 5 in today's
class. This is an interesting topic, because
we will be talking about pseudo forces. The
word pseudo suggest that there is something
unreal about it and then we will see they
generate real effects. So that is part of
the reason that some of my students and I,
when we were talking about it, we decided
that we will call this as a real effects of
pseudo forces.
We will learn about moving coordinate systems.
In particular, our focus will be on understanding
what is meant by an inertial frame of reference
as a force to non-inertial frame of reference.
We will spend some time as simulating our
understanding of the deterministic cause effect
relationship, in an inertial frame of reference
and how this idea can be modified in non-inertial
frames. We have the important contributions
due to Gaspard Coriolis.
It is always said that Newton's laws hold
only in an inertial frame of reference, we
need to understand exactly what this means.
The reason this is so important is, despite
the fact that there is early introduction
to this idea in these schools, even in 7th
or 8th grade school education, one learns
about Newton's laws, one learns statements
of this kind that Newton's laws hold in an
inertial frame of reference. This course,
which is designed for first year students,
after the high school, in college, I like
to spend some time discussing this idea further.
The reason is this idea is extremely fundamental,
what it will tell us is, what we call is the
force or in modern language, what we call
as an interaction. Mean, this idea of a fundamental
interaction, what is the fundamental interaction
at all? That is what physics is about, physics
is about exploring fundamental laws of nature.
What is the fundamental interaction is something
that we really need to understand. This understanding
is incomplete without a very deep understanding
of Newton's laws. In particular remarks of
this kind that Newton's laws hold only in
an inertial frame of reference.
The fundamental forces that we understand
and width that we make use of in modern physics
or electromagnetic forces, electroweak forces,
nuclear strong or nuclear weak interaction
or the electroweak interaction, if you talk
about the unification between the nuclear
weak interaction and the electromagnetic interaction,
then there is gravity, which six's out, which
continues to pose major challenge. Then, we
also make use of pseudo forces, which are
not fundamental forces, but then their forces
nevertheless. There are other forces that
we talk about like friction and so on. We
really need a very clear understanding of
the differences between these, because most
often we do work in non-inertial frames of
references and yet we see causality. If causality
is to be reactivated in frames of references,
which are not inertial frame of references,
then how, what we do it? These are certain
question, nevertheless very settle, which
is why they do seek if further discussion.
So, these are some of the ideas that we shall
be discussing in this unit.
Now, what is it that we regard as an inertial
frame of reference, how do we define an inertial
frame of reference? Very often, the text book
definition in these schools is not very useful
in this particular situation, because in a
text book, inertial frame of reference is
often defined as one in which Newton's laws
hold or else, it is defined as one which moves
with respect to another inertial frame of
reference at a constant velocity. Neither
of these two definitions seem to help very
much, if you really ask what is it that these
definitions really mean? What we have to admit
as a starting point is the Galileo's interpretation
of inertia. That motion is self-sustaining
in an inertial frame of reference, if it is
determined completely by initial conditions.
Initial conditions alone determine the motion
completely. Now, if this is what happens in
a frame of reference that you are in, then
you could conclude that you are in an inertial
frame of reference. So, the essential criterion
that I would like to highlight is that in
this frame of reference, motion is determined
entirely by initial conditions alone.
This is particularly useful as a pose to some
of the other criteria, which are invoked to
reference what an inertial frame of references
or to point out what an inertial frame of
references is? This question of course was
important for Galileo, it was important for
Newton. The early idea that Newton envisaged
was that in an inertial frame of reference
is situated in deep space, amidst distant
stars.
Now, this is in a certain sense a very romantic
idea, it is almost poetry. That the inertial
frame of references situated in deep space,
then to a greats Newton's romance, it sort
of distance on earth and it reminds me of
this song from the movie [fl] in which, he
says that [fl]. It is like a frame of reference,
it is situated deep amidst stars and then
it distance on earth just to address Newton's
needs or Galileo's needs to have an inertial
frame of reference, but there is move to this
than just poetry in romance and that is what
we need to talk about.
We have agreed that we will recognize an inertial
frame of reference as one in which motion,
the evolution of a system, the temporal evolution
and the time evolution of the mechanical straight
of a system is completely determined by initial
conditions. Let us consider this red frame
of reference, this is a Cartesian frame of
reference X, Y and Z and this carries a subscript
I to tell us that this is the frame of reference
that we will regard as the inertial frame
of reference.
Let us now talk about another frame of reference,
whose origin, O prime moves with respect to
the origin of this inertial frame of reference,
which is O I and this moves at a constant
velocity. So, the displacement vector between
the two origins is equal to this u t, where
u or u subscript c is the constant velocity
of the frame F prime with respect to F.
Now, how will these two observers; the observer
in the red frame which we have identified
as an inertial frame of reference as one,
in which motion is determined entirely by
initial conditions.
How do the observations of an observer in
the inertial frame, which is the red frame,
which is the frame F compared with the observations
made by another observer in the frame F prime?
The observer look certain object, whose position
vector in his frame of reference is r t and
this object has got at different position
vector, which is r prime in the frame F prime.
You can use this triangle law of addition,
you know that these two vectors are r prime
and related to each other through this displacement
vector O O prime, which is u c times the time
that has elapsed. Since, the frame of reference
F prime crosses the point O I, so that is
the model we have in mind.
Now, for simplicity, we assume that the frames
of references have their coordinate accesses,
which are mutually parallel to each other.
So that the X prime is along X, Y prime is
along Y and so on, but the only thing is that
at, what we will call as time 0, which is
the reference time, from which we start observing
the system evolution. O prime get separated
from O I and it starts moving at a constant
velocity u c, so that is our conjecture.
If you differentiate this with respect to
time, this is within the realm of what we
call as Galilean relativity. In Galilean relativity,
this time has got an absolute significance
in both the frames of references; you do not
need to modify the perception of time in the
blue frame as it is in the red frame. This
is anticipation or what we shall discuss in
the next unit, which is unit 6, in which we
will discuss the special theory of relativity.
In which we will make use of the Lorentz transformations,
in which time itself needs to be modified
as you go to another frame of reference.
So that idea is not involved over here, this
is the pre-relativistic transformation; this
is what we call as the Galilean transformation.
In this, time is same for both the observers;
you take the derivative with respect to time
to get the corresponding velocities, you get
a relationship between the velocities as will
be observed by an observer in the frame F.
Compare it with the velocity of the same object
as the scene by the observer in the frame
F prime.
Now, obviously, you see that the first derivative
is different; the two velocities are different
and the differences by this constant velocity
u, this comes from a simple differentiation
with respect to time.
The velocity is a different, but what is a
big deal? If the velocity is a different,
it does not change the perception of equilibrium
in the two frames of references, because we
already learnt from Galileo's law of inertia
that the state of rest and of uniform motion
are completely equivalent to each other and
these do not require any calls. In these states,
motion is determined completely by initial
conditions, a cause will be required only
when equilibrium is disturbed. The detection
of the change in equilibrium will be in terms
of the second derivative of the position like,
not the first.
The first derivative is what gives you the
velocity. If the two velocities are different,
no big deal about it, but to see if there
is any departure from equilibrium, we must
look at the second derivative.
We now look at the second derivative, which
is d 2 r by dt 2, this which is the acceleration
perceived by an observer in the frame of reference
F. He finds that it is exactly the same as
it is for an observer in the blue frame, which
is moving at a constant velocity, the two
accelerations are exactly the same.
Which really means that it is the departure
from equilibrium - if this is what interests
the two observers, then they will not have
to invoke different laws, because what they
measure for acceleration that in the respective
frames of references is essentially the same.
Acceleration in the red frame, in the inertial
frame, is exactly equal to the acceleration
in the blue frame, which is moving with respect
to the red frame at a constant velocity, a
is equal to a prime.
Which necessarily means that if you just scale
it by a scalar, which is inertia, which is
the mass, then the equation f equal to m a
and m a prime equal to f prime, each of these
terms is exactly equal to any of the other
terms. So, F is equal to m a, which is equal
to m a prime, which is equal to F prime. All
the four quantities that you see, the two
forces F and F prime, the two accelerations
a and a prime, scaled by the same mass, which
of course remains invariant, when you go from
one frame to another. A mass is excellent
scalar; it is completely invariant, which
means that the laws of mechanics are exactly
the same in these two frames of references.
You can therefore call the frame of reference
F prime also as an inertial frame of reference,
because the same law of physics is to be invoked
in explaining the acceleration.
This is what justifies the high school definition
that an inertial frame of reference is 1,
which moves with respect to another inertial
frame of reference at the constant velocity.
This definition by itself does not mean very
much, but it makes perfect sense, once you
understand that the laws of mechanics are
turn out to be the same in such frames of
references, which are moving with respect
to each other by a constant velocity alone.
Because, the linear response, which Newton
invoked or rather Newton invented, this is
really very fascinating, because we are making
use of calculus, we are talking about the
first derivative, the second derivative and
calculus, they really did not exist before
Newton.
Newton was just about 21, 22 years old, when
he was observing planetary motion, to understand
the angular orientations of these planets,
he needed geometry, he needed trigonometry,
then he needed the some idea of the rate at
which these positions change with time. The
idea of rate, which is what we are so familiar
with because they teach us derivative in our
mathematics classes, so we know what a derivative
of a function, is.
We know that this can be defined only when
you construct a function, you need the function
to be continuous, so you need the idea of
a limit. Then, you take the change in the
value of the function at two neighboring points,
divided by the independent parameter difference.
Then, take the limit that the independent
parameter difference goes to 0.
Now, these ideas of limits and derivatives
really did not exist before Newton, but Newton
invented this, he invented calculus. Then,
he explained that when there is a departure
from equilibrium, it will result as acceleration,
which is the second derivative of the position
vector. This is then the result of some reason,
this is where you need to look for a reason,
as long as you do not find acceleration, you
do not find that the second derivative is
non-zero, you are looking only at equilibrium
that does not seek a cause at all, because
it is completely determined by initial conditions,
you do not have to look for any cause. But,
when there is a departure from equilibrium,
you must look for a cause, this then results
in the acceleration. So, acceleration is then
the effect of a certain cause, you must look
for this cause; it is this cause which Newton
called as force. Newton went on to tell us
that the result, which is acceleration, is
linearly proportional to the cause, which
is the force, so this is a linear response
theory.
You got a stimulus which is the force; in
modern language, we call this as an interaction.
So, this is the stimulus, to this stimulus
the mechanical system response by changing
its state of equilibrium, which manifest as
acceleration. This acceleration is linearly
proportional to the stimulus, the proportionality
is the inertia. So, F equal to m a, which
is the linear equation, m being the mass,
which is what we also call as inertia of the
system. This is a complete statement of the
linear response mechanism, which takes place
between the stimulus, which is the physical
interaction or the force and the response,
which is observed as an acceleration of the
mechanical system.
Now, what is fascinating is that the same
linear response mechanism F equal to ma or
F prime equal to ma prime. Exactly the same
relationship holds in both of these frames
of references, namely the blue frame of reference,
which moves with respect to the red frame
of reference at a constant velocity. So, the
same cause effect relationship, this is the
meaning of the statement that the physics
is the same in all inertial frames of references,
because the same physical interaction explains
the dynamics, it explains the departure from
equilibrium.
Galileo's understanding of inertia of course
was fundamental. Galileo came before Newton;
Newton was born the year Galileo died in 1642,
Galileo had recognized that the state of rest,
all of uniform motion are completely equivalent,
he did it by carrying out these experiments
by rolling, these spherical wooden objects
on incline planes or by dropping objects from
the top of a mast of a ship. Whether, you
drop it when the ship is in motion or if it
is duct or if it is anchored at some place,
it falls at the same relative place.
By observing this, Galileo recognized the
law of inertia, which is really very fascinating,
because it is completely counter intuitive.
Galileo recognize this and Newton factored
it in, his understanding of how a mechanical
system evolves with time. If it is in a state
of equilibrium, then the initial conditions
alone determine the evolution. If there is
a departure from equilibrium, then Newton
recognizes that there must be a cause, which
will generate the effect that is observed
is acceleration. This effect is directly proportional
to the cause in this stimulus linear response
mechanism. This is the principle of causality
or determine is in classical mechanics.
Now, this immediately tells us that mass and
weight are different things, mass is actually
the proportionality, which goes into the stimulus
response relationship. When the response is
provoked by a cause, which happens to be gravity,
then the interaction or the force is called
as the weight. The response, which is acceleration,
this is due to gravity, so it is called as
acceleration due to gravity.
This is the relationship between mass and
weight, it turn which we had used left, right
and center, because every time people want
to point out to me for good reasons that I
have grown fat, they always tell me that your
weight seems to have increased. What they
really mean is that the mass has increased;
mass is the actual quantity of matter.
It is not a bad idea to quickly do couple
of lunatic exercises, we will ask if lifting
a cow is easier on the moon, it looks like
a totally crazy idea, lifting a cow on the
earth is crazy enough and lifting it to the
moon is even more, so I would think. Actually
a cow can be lifted there, are this commercial
cow cradles which are available, one can actually
purchase it. You know the answer, but I raise
this question not to discuss them in the class,
but just to highlight the difference between
mass and weight, because in the moon the gravity
would be a little weaker.
Here, you see this lady lifting the cow, but
I am afraid, she is not lifting, she is probably
preventing the cow from flying off, because
is probably filled in with some gas that you're
put in a balloon. So, she is not just lifting
it, so these are fun lunatic exercises as
we call them.
Let us do one more, if it is easier to stop
a charging bull on the moon; this is a lovely
painting by Russian painters Sorokin. It is
beautiful painting, the question here is,
is it easier to stop a charging bull on the
moon? I let you think about it.
Now, we are in a position to understand what
exactly is meant by a physical cause, what
is meant by an interaction? A causes the physical
agency, which generates an effect, simple.
The effect is measured in terms of departure
from equilibrium, because the state of equilibrium
seeks no cause, it is self-sustaining and
it is determined completely by initial conditions
that is a first law of inertia.
It is only the departure from equilibrium,
only when the momentum changes as long as
the object continues to move at a constant
momentum; you seek no cause, it is completely
determined by initial conditions. Then, you
may seek a cause only when you observe a departure
from equilibrium, this cause is what we will
call as a force or a fundamental interaction.
This can belong to only one of the four fundamental
categories, it can be either way in electromagnetic
interaction or a gravitational interaction
or a nuclear strong or a nuclear weak. Of
course, modern physics aims at unification
of these forces, which is an attempt to understand
that all of these forces are different expressions,
different manifestations of the same fundamental
interaction, which is what is meant by unification.
The cause which will go into this stimulus
response theory will have to be a physical
interaction; it will have to be one of these
four fundamental forces. If you do not want
to call them as 4, because electromagnetic
and weak interaction has already being unified
that depending on the level of unification,
the number would be less than 4 - anything
from 1 to 4, but it cannot exceed 4.
These fundamental forces can be understood
only in terms of this idea, which we learn
very easily in our high schools, but it really
has a very Deeping impact on physics. Of course,
quantum theory makes the discussion quite
complex, so it is no more in terms of the
stimulus response in the kind of the differential
equation that you see from Newtonian dynamics.
But, the basic idea of fundamental interactions
still remains the same, which is part of the
reason that this idea really needs careful
discussion in college physics as well.
Now, we understand the meaning of this statement
that in inertial frame of reference is one,
in which Newton's laws hold, because this
statement is caused in the context of this
entire discussion that we have just had. All
that discussion goes in the background or
it provides a platform for developing what
is a very simple statement that is inertial
frame of references is one in which Newton's
laws hold, but without this discussion, this
statement really does not tell us very much,
it is just like a definition.
Now, in the previous frame of reference, in
the previous case, we compared observations
in two frames of references: the red frame
and the blue frame. The blue frame was moving
with respect to the red frame at a constant
velocity. Now, we will let the second frame
move not at a constant velocity, but we will
let it undergo acceleration with respect to
the inertial frame. So that brings us to discussing
physics in an accelerator frame of reference.
At the question that we are going to have
to rise is what will happen to the cause effect
relationship? Will causality in determinism
survive? Do these ideas survive in an accelerator
frame of reference? The answer is both yes
and no. I will explain why it is yes and why
it is no when we discuss it further?
Let us now construct a frame of reference,
which is this green frame, this frame F double
prime, this move with respect to the frame
O. Let us say, at t equal to 0, which is just
when you start the clocks in the two frames
of references, these clocks are Galilean clocks,
these are not Lauren's clocks. These - the
Lauren's relativity is what we will discuss
in the next unit, which is unit 6 .
We are now in the realm of Galilean relativity,
the two clocks, they remain synchronized in
Galilean relativity. When you start the clock,
the green frame and the red frame, let say
that they are on top of each other. At t equal
to 0, the green frame shouts of with a certain
initial velocity u i and the constant acceleration,
which is not 0 now, in the previous case it
was 0, now it is not; so F is some constant
acceleration.
The displacement vector between O and OO double
prime is obviously equal to u i t minus half
f t square, this comes from elementary kinematical
equations. Now, you consider motion seen by
an observer in the red frame, in the inertial
frame of a certain object, which is here,
whose position vector in the inertial frame,
is r. In the accelerator frame, this position
vector is r double prime; the two are related
to each other by the triangle law of edition.
So, r of t is equal to OO prime, which is
this vector from O to OO double prime plus
this green vector. So, OO double prime plus
r double prime is equal to r, so this is the
relationship that we get. OO double prime
- this is the displacement vector, which is
already seen to be u i t plus half f t square,
so this is our basic construct.
Now, to get the velocity, you take the first
derivative with respect to time. This is a
simple differentiation, on the left hand side
u get d r by dt, from differentiating u i
t, you get u i, by differentiating half f
t square, you get f times t. The factor two
will cancel in the denominator and this one
and then you get the velocity as seen in the
double prime frame of reference, which is
d by dt of r double prime.
If you now take the second derivative, you
will get the acceleration and that is what
will be a measure of departure from equilibrium,
this is where you are going to look for a
cause. You take the second derivative, so
here you have the second derivative on the
left hand side; on the right hand side, the
derivative of u i vanish, because it is just
the initial velocity, which is some constant
number, so its derivative with respect to
time will vanish. From the derivative of f
t, you get f and then you get the second derivative
as seen in the double prime or the accelerator
frame of reference.
In other words, the acceleration in the frame
red is not equal to the acceleration in the
accelerated frame. The acceleration of the
object under investigation, which is this
object we have, this is the object, whose
mechanical state is being observed by two
observers. The acceleration of this object
is different in two frames of references,
a is not equal to a double prime, the relationship
between them is a is equal to a double prime
plus f. Now, the observer in this green frame,
which is the accelerated frame, what is he
thinking? He measures acceleration in his
frame, which is a double prime and it is equal
to a minus f.
So, m a double prime, if you just multiply
this by the inertia of the system, which is
the mass of the system, ma double prime is
equal to ma minus mf. This is what the observer
in the green frame will recognize as the force,
so his idea of force is not the same as the
idea of force in the inertial frame of reference.
In other words, if m a which is the mass times
acceleration, is what we regarded to be equal
to the physical interaction from Newtonian
dynamics, in the inertial frame of reference.
This is what gave us several idea of force;
if this is what gives a several idea of force,
no matter what it form as electromagnetic,
nuclear strong, weak or gravity, it cannot
be anything else, it has to be one of these.
If this is what is recognized as force, then
this quantity over here is obviously not a
fundamental force, because the idea of fundamental
force was developed in the inertial frame
of reference. But, to the observer, in this
double prime frame of reference, which is
what we call as the accelerator frame of reference,
to this observer, the acceleration of a double
prime is a completely real phenomenon. It
is a measurable thing; it is what he measures
in his own frame of reference as the departure
from equilibrium.
He finds that it is equal to mass time's acceleration
in the inertial frame, less and a constant
quantity, which is m times the little f. If
this has already been identified as the fundamental
interaction, then this is obviously just a
mathematical art effect of the fact that this
frame of reference is accelerated with respect
to this; there is no physics in it.
It is not the result of a physical interaction;
it is a result of carrying out observations
in a frame of reference which is not in an
inertial frame of reference. So, whenever
you do that you will find that the mass times
acceleration in an accelerated frame of reference,
will not be equal to the physical force, but
it will be different. The difference in this
case is what I have written as F with the
subscript pseudo, because it is not a real
force.
What happens to the principle of causality?
The cause effect relationship, which was linear
response equation, acceleration was proportional
to the cause and the proportionality was the
inertia.
Now, that relation has to be modified, you
can sort of modify that relationship by inventing
this F double prime, which is the difference
between F and this mf, which is F pseudo.
This difference is what you can call as the
net pseudo force, which includes the real
interaction to a certain extent, but it also
includes a mathematical construct of the fact
that the observations are being carried out
in an accelerated frame of reference.
The same cause effect relationship, which
explained dynamics in the inertial frame of
reference, does not do so any more in the
accelerated frame of reference. Which also
means, the losses of mechanics are not the
same in these two frames of references, this
is the meaning of the statement that the inertial
frame of reference is one in which the laws
of mechanics hold. Now, we see what that statement
really means? Because, we find that the laws
of mechanics cannot be stated in the same
form, they must be modified if you have to
recast them in an accelerated frame of reference.
So, this is what we called as the real effects
of a pseudo force, because the observation
a double prime is very much real to the observer
in the accelerated frame of reference. You
can write F double prime equal to m a double
prime, in which this is now your idea of the
physical interaction, but this idea of the
physical interaction includes the real force
F less a force, which is not a physical interaction.
F pseudo cannot be reduced to any fundamental
force like electromagnetic or gravity or nuclear
strong or weak.
I will invite you to read this article, which
some of my students have written. In particular,
Gopal Pandurangan was the first want to do
this; subsequently this work was done also
by Chaitanya and Srinivasa Murthy. This article
is available at this link, this is the title
of this paper that what you see are really
facts of pseudo forces; the effects are real,
the cause is not.
You can sort of restate the deterministic
cause effect relationship, which really holds
only in an inertial frame of reference. It
is this relationship which generates in our
mind an intuitive perception of fundamental
forces. Once we recognize this idea of a fundamental
force, then we only study its form, whether
it is electromagnetic or nuclear or gravity
or some unification there off, these are different
forms. But, the idea of a fundamental interaction
comes essentially from the perception of an
inertial frame of reference.
If you want to somehow force causality in
frame of reference, which is accelerated,
because you always like to reason out in classical
mechanics, the entire domain of classical
mechanics is inspired by causality that you
look for causes. You think that there is a
cause, which explains the result.
If you seek similar relations in an accelerated
frame of reference, then you can do so only
by inventing causes do not exist, so these
are the pseudo forces. You can invent the
pseudo forces, these are fictitious forces
and obviously Newton's laws are not designed
for these fictitious forces. So, they can
be used in some sort of Newtonian formulation
of mechanics, but they will include these
pseudo forces, which are forced into our thinking
by the fact that we are explaining observations
in an accelerated frame of reference.
There are related issues like people talk
about weightlessness, you experience this
all the time. Means, if you carry away in
machine with you in the elevator, when you
come to this floor, we are now on the third
floor. This experiment is more interesting,
when the elevator is accelerated rapidly or
while going down, it is again accelerated,
but the direction of acceleration is different.
In one case, when the elevator is going up,
the acceleration exits against gravity, when
it is going down, it is in the same direction
as gravity. If you weigh yourself on a weighing
machine, you are going to record different
weights.
The idea of weightlessness is connected to
the fact that observations in an accelerated
frame of reference, it will not be explicable
in terms of the same fundamental interactions,
which are invoked in inertial frame of reference.
This is in fact very nicely exploited by sport
speaking. Here is a picture of Sergei Bubka,
who is retired, but one of the most famous
pole vaulters of all times.
Now, look at the allegiance with which he
goes over the bar. By flexing his body, means
he has got his arms and limb, which he can
position. I can hold my hand here, I can hold
it here, I can hold it here, but where I am
holding it will determine where my centre
of mass is. Unfortunately, it will not reduce
my mass, but at least it can change the position
of the centre of mass and that can be done
simply by changing the position of my limbs.
What he manages to do is by flexing his body
he can led the centre of mass, go a little
bit lower, then where he otherwise has to
raise the entire body to that point, if he
wants to clear a certain point. He can in
principle allow the centre of mass to actually
go below the bar, let the body go above the
bar, as long as he can flex his body suitably.
The energy he needs to raise a centre of mass
above the bar is obviously much more that
what is required to raise it to a point below
the bar.
Now, I do not know if he where his centre
of mass actually goes by, does it go below
the bar or above the bar that is a matter
of detail, but it is quite clear from this
discussion that it is not necessary to raise
it to the highest point, you can let it go
at a lower point. This becomes possible, because
his control on his limbs is so easier in this
state, because he is in a state of what we
call as weightlessness.
He is in a state of free fall, all parts of
his body are falling at acceleration due to
gravity at j. So, what he has to overcome
is just the inertia of this part of his body
by his muscle power and not the weight of
this. That is a difference between mass and
weight. He has to manipulate just the mass
and not the weight, because the entire body
it is in a state of weightlessness, it is
in a straight of free fall.
We can exploit it, athletes do it a very nicely.
Sergei Bubka is one of the best known pole
vaulter, so I had his picture, but may be
you are familiar with some of the modern pole
vaulters. This is the one who got the Olympics
gold medal in 2008 Yelena Isinbayeva, how
do you pronounce it? Vivek, do you know how
to pronounce it? I do not either. This is
the Russian name; she cleared 5.05 meters
in the 2008 Olympics, exactly the same thing.
In the kind of agility these athletes have
in manipulating the limps, is what distinguishes
them from ordinary people.
So, I guess we will take a brake here, if
there is any question I will be happy to take
it, otherwise we will take a break, we will
continue from this point. In the next class,
we will continue the discussion on real effects
of pseudo forces.
