Principle of Moments Video Lecture | Engineering Mechanics - Civil Engineering (CE)

hello everyone and welcome to another
simple science video in this video we
are going to be looking at the principle
of moments now following up from our
moments of a forest video we know that
when a force acts from a distance from a
pivot then there is going to be a
rotational effect or a turning effect
but what if we were to counterbalance
this turning effect with another force
which produces in this case an
anti-clockwise moment to counterbalance
its clockwise moment and therefore it
produces no net moment and we therefore
attain a state of rotational equilibrium
so when we were looking at this in a
mathematical way then we realize that
for an object to attain rotational
equilibrium the sum of its clockwise
moments must be equal to the sum of its
anti clockwise moments and in this
diagram that is numerically equal to F 1
times x1 equals to the F 2 times x2 this
is needed to for this rod to be in
rotational equilibrium now when we look
at an example let's look at the total
clockwise moment of the force for
Newtons and that is for Newton's times 2
meters which gives you 8 Newton meters
and if you were to look at the
anti-clockwise moments the
anti-clockwise moments is equal to 8
Newton meters and therefore the sum of
the clockwise moments is equal to the
sum of the anti-clockwise moments and
therefore this object has retained
attained rotational equilibrium and
similarly if you were to fit it on a
seesaw like beam where the center of
mass is right through the center and you
placed a pivot right on it maybe it's
not the scale but the well the total
anti-clockwise moment we calculated as 4
is FX and that should give you 4
Newton's times 2 meters that's the force
on the Left gives you 8 Newton meters
and it's
clockwise moment with which is caused by
the two Newton force on the right which
is equal to FX is equal to two Newton's
times four meters which gives you eight
Newton meters so similarly some of the
clockwise moments is equal to the sum of
the anti clockwise moments therefore the
object has attained rotational
equilibrium but the more common example
is when you're asked to find what a
certain force in the system is so in
this question you ask if this rod was in
rotational equilibrium find f2 so if
this rod is any rotation equilibrium
rule says that the sum of the anti clock
the sum of clockwise moments is equal to
the sum of the anti clockwise moments
and that should give you f 1 x 1 equals
F 2 X 2 that's just a general formula
for one force per moment direction and 2
and for the clockwise moments two meters
have 6 Newton's gives us 12 Newton
meters which is equal to 4 meters
multiplied by F 2 now we can then
calculate F 2 to be 3 Newton meters from
12 divided by 4 now similar thing
looking at a seesaw you might be asked
to find F 2 and if this rod is in
rotational equilibrium we know that some
of the clockwise moments is equal to the
sum of the anti clockwise moments so
therefore F 1 X 1 is equal to X 2 X 2
and we can equate to F 2 is equal to 6
Newton's times 3 meters to give us F 2
of 9 Newtons sorry that was not in the
right order but if we were looking now
that now let's look at the seesaw
equilibrium now if the rod was in
rotational equilibrium we were going to
find F 2 and if it is in rotational
equilibrium then the sum of the
clockwise moments should be equal to the
sum of the anti-clockwise moment so we
can equate it as f1 x1 is equal to F 2 X
2 except in this case X 2's are X 1 is a
little different in that x1 is no longer
a purple 3 meter distance it's a
distance of three meters cost 60 because
it's the perpendicular distance of the
line of action from the pivot
okay so that's a little different now we
can equate to F 2 is equal to 6 Newton's
times 3 meters times cost 60 which gives
us 2 F 2 of 9 Newton meters and
therefore an F 2 of 4.5 Newton's now
that is the end of the video now thank
you very much for watching my video