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

hello friends this video on system of
particles and relational motion fact ed
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you from exam now that we have spoken
about the angular velocity and
acceleration it is time to introduce a
new quantity related to rotation of
objects that is known as torque so let
us see what is a torque so torque is
nothing but the rotational analog of
force so basically I mean now if we I
guess you have got the flow of the
lesson so what are we actually trying to
do in this lesson we are trying to study
a system of particles or a rigid body
where you have where we do not consider
a body as a single particle we will
consider considering the body as a
system of particles at the same time we
are considering the rotational motion of
that body till now we I am in other
previous lessons the initial lessons we
spoke about the linear motion in one
plane motion in motion in three
dimensions and all those steps right but
there we never considered the rotational
motion of an object so here whatever we
are talking about is analogous to the
linear motion so like how we have
angular velocity which was a rotational
analog of linear velocity we have
angular acceleration which is again a
rotational analog of linear acceleration
similarly we have thought which is a
rotational analog of force the way we
have force in case of linear motion here
we even have torque in case of
rotational motion it is also known as
moment of force the torque is also
called as moment of force it is denoted
by the letter the Greek letter tau when
to understand talk let us take this
example which will help you to
understand this let us suppose you have
a rod as you can see here this is a rod
it is the force a force is applied on it
from upwards right so what will happen
this rod will start moving
now you apply an equal and opposite
force on the rod from downwards so now
what happens
since equal and opposite forces are
applied therefore the net force is zero
and the door does not move there is no
movement of the rod because you are
applying equal and opposite forces at
the same point correct now look at this
scenario let us suppose you have the
same rod and you apply the same equal
and opposite forces but now you apply
the two forces on the two ends of the
rod so what happens if you want to try
it yourself you see that what happens in
this case in this case the rod starts
rotating correct so what does this show
this shows that it is not let every time
if you apply equal and opposite force to
an object the net force will be zero and
there will be no motion that is true
only when the equal and opposite forces
are applied along the same lines of
force that means they should be applied
along the same lines so in the previous
example the equal and opposite forces
were applied along the same lines
therefore they cancel each other but in
this case since they are applied along
different lines therefore this force
wanted this end to go down and this
force wanted this end to go up as a
result this end went up and this end
went down and this resulted in a motion
or a rotational motion in the
anti-clockwise direction right so this
kind of force in case of rotational
motion this force I mean the for this in
case of linear motion when you have some
object you have a ball you apply some
force and the ball moves so you see that
the force is applied on the ball which
caused a linear motion in it similarly
these kind of equal and opposite forces
applied along different lines which
causes the body to rotate is known as
moment of force or taut so this is known
as taut so taut is the cause of the
patient right so similarly we can also
take a practical example that is the
example of a do like have you ever
observed that when you try to open the
door this is your door now if you let us
suppose if you are inside if you want to
open this door and if you apply a force
at this point in that case and push the
door
it is easier to open the door but you F
if you apply a force at this point and
try to open the door are you able to
open the door no you are not so the same
effect is working here also right
because when you are applying a force
here in that case the net force gets
compensated but when you apply your
force here this end wants to go to that
side that means to move outwards
whereas this end is fixed as a result
the door is moving that's like but then
if you apply this force on the end which
is fixed then the door is not able to
move at all let's Oh God plays a role in
this case as well so it is not only the
force but how and where it is applied is
important in rotational motion right so
it is not worry that you apply a force
and the body will start rotating but you
have to apply the force in the correct
place you have to get the correct
rotation of that object so now let us
look at a mathematical expression for
thought so torque is defined as the
cross product of torque is a vector
quantity and it is defined as the cross
product of the radius vector and the
force so torque is defined as the cross
product of radius vector and force so
how do we define it so a cross B is
equal to a d sine-theta similarly R
cross F is our F sine theta where as is
the position vector of the point on
which the force is applied F is the
magnitude of the force and theta is the
angle between R and F so in very similar
to how we find out the direction of a
cross V similarly
find out the direction of torque so the
direction of torque should be such that
it is perpendicular to our it is also
perpendicular to F that is torque should
be in a direction perpendicular to the
plane containing R and F right now
torque is a vector quantity because it
is defined not only by magnitude but
also by direction SI unit is Newton
meter because because it is given by the
product of the position vector R and
force and the unit for forces Newton and
the unit for R that is the position
vector is meter therefore the SI unit
for thought is Newton meter dimension
for talks is ml to the power 2 T to the
power minus 2 that that again comes from
here because torque is equal to given by
force multiplied by the position vector
now for force it is nothing but mass
into acceleration and this is the radius
vector so mass is M acceleration is M T
to the power minus 2 and R is again n so
this becomes M L to the power 2 T to the
power minus 2 so this is how we get the
dimension for torque thank you please
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