Couple - System of Particles & Rotational Motion Video Lecture - Class 11

hello friends this video on system of
particles and rotational motion fat16 is
brought to you by exam prom no move here
from exam let now when we are talking
about this equilibrium of rigid body let
us talk about couple in order to
understand rotational equilibrium a
little better so what is a couple it is
a new terminal couple is a pair of equal
and opposite forces with different lines
of action this was the example which I
was mentioning right you have equal and
opposite forces because of which the net
force is zero but these two forces are
acting along different lines as a result
there is a rotation which is happening
so this results in rotation without
translation so it results in rotation
without translation let us look at the
same example which I mentioned before
you have this rod you apply equal and
opposite forces on both ends of the rod
so what will happen this force will try
to take it up this force will try to
take it down and as a result the rod
will start moving in anti-clockwise
direction so the rotation will happen
right that is what happens so the rod
will start moving in this fashion so
these kind of forces is known as a
couple that is a pair of forces couple
is always a pair of horses which are
equal and opposite but they are acting
along different lines of action right
now the same thing in case of this is
applicable and some of the practical
examples of couple is your dual why do
you have this door opener on this end
and this fixation on this end so that a
couple can be formed so when you push
the door from this end you are applying
a force here and since it is fixed on
the other end there is another Force
which is operating here so two equal and
opposite forces will help the door to
rotate right so have you ever seen that
the door has this door opener at this
end no right so
similarly when you open a bottle not
only to get the bottle opener but also
when you try to open up the cap of a
bottle with your hand you just move it
how do you move your fingers if this is
the top of your bottle on this side you
apply force in this direction and in
this side you apply force in this
direction and that is how you open it it
- these are some of the practical
examples of couple now because of this
couple so the publicly is a very
important tool because because of this
couple thought comes into picture and as
a result rotation takes place so let us
look at the principle of movements for a
liver
now when I say principle of moments
what do I even refer to when I talk
about moment moving here refers to
moment the force and moment the force is
nothing but talk right so let us take
the example of a seesaw which you often
see in children Park and all those stuff
where you have and straight rod length
structure where you have to see tails on
the two ends and there is at some point
there is a fixed point between the truth
right now this point is known as fulcrum
so well club is the point around which
or about which the two ends move with
respect to each other right so now let
us suppose that a force f1 acts at this
end and there is neither force f2 which
acts on this end right let us a cool I
mean when two children sit on the both
hands like suppose this is the force
applied on this end and this is the
force applied on the skin now because of
this fulcrum there would be a reaction
force in the opposite direction that is
giving us our let us suppose the
distance of this is d1 and the distance
of the other end is d2 right now in
order for this lever to be in
equilibrium so for mechanical
equilibrium we have to ensure that there
is translational equilibrium as well
rotational equilibrium so when I talk of
translational equilibrium I mean that
the net force should be equal to zero so
what is the net force here ad is the
force which is acting upward right so I
minus f1 plus f2 which is acting
downwards so this is the net force
acting in this system so this should be
equal to zero so this implies that R
minus f1 minus f2 should be equal to
zero also it should be in rotational
equilibrium that means the net torque
should be equal to zero now water store
torque is given by R cross F what is our
R is the position from the origin so
here fulcrum is considered as the origin
so that means the torque at this end
will be equal to d1 f1 and the torque on
the other end will be equal to d2 F
those but in this case that direction of
the torque in this case what is the
direction of the torque R cross F that
means R cross F so if you curl your
fingers in this fashion you get the
direction of the torque as your thumb
pointing towards yourself whereas in the
other case when in point ready to cross
F do you see your thumb pointing in the
downward direction that is opposite
direction so therefore here d2 my F 2
will have the negative sign because if
this is torque is in the opposite
direction right so this will be equal to
this should be equal to zero right so
now this equation is a very important
equation so in this equation we call f1
as load so f1 is known as load f2 is
known as effort so this is my load this
is my effort so therefore this distance
the distance of the load from the
fulcrum is known as load R and the
distance of the effort from the fulcrum
is known as effort arm right so
therefore we can write this equation as
d1 f1 is
- D - f D or this can be written as so
this can be written as load arm into
load is equal to effort arm into effort
and this is this defines the principle
of moments for a leaver so to ensure
rotational equilibrium in case of a
leaver we should ensure that the load R
multiplied by load should be equal to
the effort R multiplied by the effort so
we often define another term known as
mechanical advantage which is
abbreviated as ma so this mechanical
advantage is the ratio of load in effort
that is f1 by excellence which is also
equal to DP by D 1 so this is how we
define mechanical advantage of a leaver
so mechanical advantage of a levite is
the ratio of the load to the effort
right so using how this mechanical
advantage helps us because if the
mechanical advantage if the value of
mechanical advantage is very high that
means F 1 is very very greater than F 2
that means a large amount of load is
required in in order to get a small
amount of effort whereas if the
mechanical advantage of a leave word is
very small and that means that F 1 by F
2 is very small that means F 1 is very
very less than F 2 that means a small
amount of load can give you a huge
amount of effort right so this is how we
define mechanical advantage or funding
works
so when mechanical advantage is very
very greater than 1 that's what I
mentioned just now right so when it is
very very greater than 1 that means F 1
by F 2 is very greater than 1 which
means F 1 is
an f2 similarly here when it is less
than 1 this means f1 by f2 is less than
1 which implies F 1 is less than F 2 so
here it implies that large load will
give rise to small effort and here it
implies that small load will give rise
to large effort right okay thank you
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