Inertia and mass Video Lecture - Class 9

in your study of physics you will often
encounter the idea of mass and you will
also might encounter the idea of inertia
and what I want to do in this video is
think about what is the similarity or
the difference between these two
concepts or these two ideas and physics
and I'm going to give you a little bit
of time to do it I encourage you to ask
people and search the web and look at
textbooks whatever you can do to figure
out the similarities and differences
between mass and inertia so from a
historic perspective if you've asked for
someone what is mass mean or what does
it represent they'll say it means what
it represents how much stuff an object
is made up of or how much matter how
much matter actually constitutes an
object and if you were to ask them well
what is inertia then they'll say well
inertia describes an inertia is a
property of an object that's really how
hard is it to accelerate that object how
hard is it to change that object's
velocity so we could call this maybe a
resistance resistance to acceleration so
on this first this first glance right
over here you might say okay well these
are two different ideas and they seem
like two different ideas until we start
thinking about a couple of things one
Newton's second law and also how you
would actually go about measuring mass
so how would you actually measure this
right over here how would you measure
mass because you might say well maybe
you just look at this the size of the
object but the size by itself doesn't
tell you how much stuff there is you
could have a very large object that's
not very dense but means let's say
cotton candy or a hot air balloon and
you could have a very small object
that's very very dense you could take a
lead weight or something even denser a
teaspoon of the material from a neutron
star incredibly incredibly dense very
very high mass so you couldn't just look
at the the size or the volume of an
object but lucky for us Newton's second
law does give us a tool for figuring out
the mass of an object Newton's second
law tells us that the force that acts on
an object is equal to the mass of that
object times the acceleration of that
object and the acceleration and the
force are going to go in the
exact same direction or if you want to
think only about the magnitudes you can
say the magnitude of the force on a on a
not on a object is going to be equal to
its mass its mass its mass times the
magnitude of the acceleration they say
well how does this allow me to measure
an object's mass well I can apply some
force to it I can apply some force a
certain magnitude and then I can measure
how much that object is accelerated and
then I could just solve for MU divide
both sides of this equation by a you get
F over a is equal to M but what am i
measuring so I will actually solve for a
mass here I could you know I'll get my
proper units of mass depending on what
my units of force and acceleration are
right over here but what am i implicit
ly measuring as well well I'm applying a
force on something and I'm seeing how
much it's accelerating I'm seeing what
is its resistance to accelerating so I'm
really trying to also determine its
inertia so when you think about mass in
this way we now think about this is
actually inertial mass inertial inertial
mass one way to think about is that the
mass is actually quantifying that
object's inertia so we can split hairs
over the definitions but in this way of
viewing mass mass and inertia are really
the same thing and it's actually very
hard to just directly measure how much
stuff or matter there is that's why I
put it in quotes right here the more
pure definition of what mass even is is
or one of the more pure definitions of
what mass even is is how resistant is
that object to acceleration because
especially once you start getting into
the subatomic domains the quantum
domains the idea of how much stuff there
is starts to become very abstract and
all we can do is measure how does how
does that that entity or that particle
how does that respond to force how
resistant is that to acceleration and
that will and that is essentially what
we're describing is mass or inertial
mass but you might say wait wait that's
not the only way to measure mass you
have Newton's law of gravitation I could
have some object that has a known mass
so let's say this is some object with a
known mass let's call it m1 and let's
say that there's some other object with
an
unknown mass let's call it m2 and this
is the mass that we are trying to
measure and we know that they're going
to exert they're going to they're going
to pull on each other Newton's law of
gravitation and everything we're talking
here we're talking about classical
mechanics that's the world we're going
to deal with we're not going to talk
about we're not going to talk general
relativity or anything like that right
now well we know if we know this mass
and if we know the distance between them
we know the distance between their
center of masses so just like that and
if we can measure their respective pulls
on each other so we know that if m2 is
pulling on m1 with some force so I'll
draw that as a vector like this m1 will
pull on m2 with an equal and opposite
force so a force with the same magnitude
but just the opposite direction and so
we can measure what that force is we can
we know what m1 is we know the distance
between them and from that we can figure
out what m2 needs to be and from and and
when you measure mass when you think
about mass in this way you're actually
referring to gravitational mass me right
this way this right over here is
gravitational gravitational
gravitational mass now lucky for us it
has been verified that these two things
these two things are actually measuring
the exact same thing that inertial mass
is equivalent to gravitational mass so
you can debate on the definitions and it
might be a little different in different
contexts sometimes people want you to
think of more in classical terms inertia
as resistance to acceleration mass is
how much matter there is but essentially
they're talking about the same thing
mass is a measure of how resistant
something is to acceleration or mass is
a measure of inertia