Moment of Force on a Rigid Body Video Lecture | Engineering Mechanics - Civil Engineering (CE)

welcome to electron line now that we
understand what a vector product is we
can multiply two vectors together using
the vector product methodology now we
can start talking about the moment of a
force now the moment of a force can also
be can can also be expressed as the
torque now in physics we tend to talk
about the torque in engineering we tend
to talk about the moment of a force so
what is the moment of a force well
here's the symbol that we use we use the
letter M and sometimes we use a little
subscript and yes it is indeed a vector
and it turns out the moment of the force
is the cross product of the position
vector multiplied times the force acting
on the object now in fact that by itself
doesn't really mean anything yet
so let's say we have a region here on a
planar planar format we have an object
that is able to rotate about this point
right there so we're going to call this
point the origin or the Oh point we can
call any point and that is where this
little symbol came from this indicates
the location where the object can rotate
or pivot so that's this point right
there and so we indicate that on the
symbol M standing for the moment R is
the position vector it is the vector
that's drawn from the point of rotation
or pivot from the pivot point to the
point where the force actually acts so
here we're going to draw the vector R
like that so there's our vector R and
that goes into our equation right there
and then we apply a force at that
location in any direction so in this
case the force is in the plane that
we've drawn here so that both the R
vector and F vector is in the plane it
doesn't have to be of course but just to
make it visually easier to see we've
done that and then notice if we draw a
line that continues in the same
direction as the R vector the position
vector we have this line right here and
the force vector then makes an angle
with the direction of the position
vector we'll call that angle theta and
so we then claim that the moment is
equal to the R vector times the F vector
the position vector times the force
vector and of course since it's a
product we can use our right hand rule
point your fingers in the direction of
the R vector the
vector curl your fingers in direction of
the force vector which is still in the
same plane as that object and then your
thumb will point perpendicular way from
both our vector and the F vector which
means perpendicular away from the plane
so let's try to draw that here so here
we have therefore what we call the
moment about point O right there so
that's that way we say it
it's the moment about this rotation or
pivot point in this case at point O or
the origin also notice that it's upward
away from the plane so this is
perpendicular both to the R vector and
perpendicular to the effect of the force
vector now well of course if we do R
cross F we'd have a vector say magnitude
in the opposite direction now since
that's a cross product we can say we can
calculate also the magnitude of this
vector of the moment so what would be
the magnitude of that so the magnitude M
the magnitude of the moment would be
equal to the magnitude of the position
vector times the magnitude of the force
times the sine of the angle between the
two now what is the angle between the
two it's of course this angle right
there notice if we draw our vector over
here you can clearly see that theta then
becomes the angle between the two and
you can see as the angle gets bigger as
the angle reaches 90 degrees the moment
will be the largest as the angle becomes
zero the moment will then go down to
zero sometimes we also want to look at
the moment in a different way so what
we're going to do now is draw what we
call the line of action of the force so
if we take the direction of the force
and we continue forward like this and
backwards like this we now have drawn
what we call the line of action the
force the line along which the force
acts if we now draw another line let me
use a different color for that a line
from the pivot point to the line of
action of the force in such a way that
that line reaches the line of action of
force perpendicular to the line meaning
at 90 degree angles let's do that right
here so that this is a right angle and
this is a right angle right there
then this is called the shortest
distance from the pivot point to the
line of action of the force and we call
depth D now let's find an equation or
let's find a way to express D now we
have a triangle right here and notice
that this angle here must be the same as
this angle over here so I can duplicate
the angle on the other side these are
opposite angles theta and then D becomes
the opposite side to this angle and
let's see here and then R is the
hypotenuse so therefore we can then
write that D D is equal to the
hypotenuse R times the sine of the angle
theta now if we come back over here
notice you have an R and a sine of theta
if I then rewrite this I could say this
is equal to F times R sine theta and
then if I replace this portion of the
equation by D that's the shorter
distance from the pivot point to the
line of action of the force then we can
say that this is equal to the force
times that distance so either way we can
find the magnitude of the moment by
multiplying the force times the shortest
distance from the pivot point to the
line of action of the force or simply we
can find the magnitude of the moment by
multiplying the magnitude of the
position vector times the magnitude of
the force times the sine of the angle
between them either way we'll get to the
exact same result that's what we mean by
the moment now you may say well what
does the moment really mean well the
moment has to do with a force applied at
the distance away from an object that
can rotate for example this may help us
let's say that I draw a bolt this is an
eight-sided bolt let's say that I put a
wrench on that bolt because I want to go
ahead and either tighten it or loosen it
so there's my wrench and let's go like
this so let's say I want to tighten the
bolt I want to turn it like this and
tighten the bolt well if I apply a force
over here I will apply a moment to that
bolt and so the ball of course can
rotate
like this and so this here would be the
distance from the point of rotation to
the line of action of the force there's
the line of action of the force and then
here would be the force that's applied
and then the moment applied to the bolt
would be simply be the product of our
times F now of course we already know
that sometimes it's very hard to tighten
bolts very hard to loosen bolts then
then pull in the push in the opposite
direction I cannot try to loosen bolts
what can I do if I just can't tighten or
just can't loosen the bolt well I can
increase the moment by moving that fours
over to a large larger distance away
because remember the moment is in a way
the force that you apply to rotational
motion and so if you then move the force
over here that you have a larger
position position vector then D also
becomes larger the moment comes large it
becomes easier to tighten or loosen the
belt the bolt so it is kind of a way to
look at the moment is a force applied to
an object to make it rotate and either
you can increase the moment by making
the force larger or by making the moment
arm as we call it larger the position
vector distance from the point of
rotation to where we're applying the
force and so hopefully that gives you a
better idea of what a moment of a force
is and this is the best way to look at
it