Video Angular Momentum Video Lecture - Physics for JEE Main & Advanced

hi it's mr. Andersen and this is ap
physics essentials video 54 it's on
angular momentum momentum remember is a
product of the mass times the velocity
of an object so any object moving with
mass has momentum the only difference in
angular momentum is it's rotating or
spinning objects and so if you were to
try to get on this bicycle and balance
without the kickstand out you're
probably going to fall over but as you
start to bike as these wheels pick up
angular momentum they're going to resist
changes and it makes it easier for you
to remain upright and so angular
momentum is a vector so there's a clear
direction in which it acts and in AP
Physics you should be able to understand
the angular momentum of either a point
object so a point object is going to be
an object accelerating around a point so
it could be for example an object
attached to a spring or a planet
orbiting around the Sun and the equation
is very simple L is equal to our angular
momentum again it's a vector which is
equal to R that's going to be the radius
from the center to the object so that's
the distance times its linear momentum
which would be the mass times the
velocity in a line you also should be
able to calculate the angular momentum
of an extended object so the whole
object is rotating around a point so to
figure that out all we say is that
angular momentum is equal to I where
that's rotational inertia times the
angular velocity of the object and again
that inertia is going to change
depending on what that object is now to
figure out the direction of this vector
you'll use the right hand rule so if we
look at this one right here the object
is spinning like that so if you move
your fingers in the direction of that
spin then we should have angular
momentum that's moving in the upward
direction whereas on this one since it's
rotating in the other direction we're
going to have it acting in the downward
direction now we learned when we were
dealing with impulse that if you apply a
force for a given period of time that's
going to equal the change in momentum of
the object well the same applies here so
the change in angular momentum is equal
to not the impulse but rather the torque
times the change in time so that net
torque times the change in time
is going to give us a change in that
angular momentum so angular momentum of
this gyroscope since we're spinning it
in this plane that's going to keep it
spinning in that plane and so it's able
to resist changes due to gravity they're
really neat things we'll do in future
videos so you can take a wheel and give
it a certain amount of angular momentum
like that and so it's conserved but it
can be transferred some of that angular
momentum as we change the angle at which
that force is actually acting and so on
the two things you should be able to do
in AP physics is calculate the angular
momentum of a point object again that's
an object that's moving or rotating
around a given point so this could be an
object attached to a string or the moon
orbiting around the earth and so the
formula is pretty easy
it's simply R which is the radial
distance here times the linear momentum
so linear momentum is going to be in
this direction so it's the mass times
the velocity and so if you have these
three bits of information the velocity
of the object the mass and the radius
all we do is simply multiply those
together so let's say we had an object
one point one kilogram mass traveling at
3.2 meters per second and then we've got
about twenty eight centimeter here
distance between the two all we're going
to do is multiply those values out and
then we're going to get an angular
momentum of 0.99 kilogram meters squared
per second now the one thing I should
have included here is that this is a
vector value so we have to add a
direction to it how do we figure out the
direction well since the rotation is
like this we use the right hand rule to
show that that angular momentum is going
to be acting in the upward direction you
also should be able to calculate the
angular momentum of an extended object
like this rotating cylinder here all we
do is multiply the rotational inertia
times the angular velocity of that
object so if it's given let's say we
have an inertia of fifteen kilogram
meters squared we multiply that times
our angular velocity like that and we're
going to get one point seven times ten
to the second kilogram meters squared
per second now this again is a vector
and so what direction is that acting
again looking at my right hand rule it's
going to be acting in the upward
direction now how do we measure this in
the physics lab a good way to play
around with this is using a turntable so
you can use a turntable that's attached
to a desk as
certain amount of mass on it and what
you can do is you can give it a spin so
if we spin it in that direction we try
to make it as frictionless as we can
it's just going to keep spinning in that
direction these are generally pretty
heavy so they have a large amount of
rotational inertia you can also attach a
photo gate to it so we can measure that
angular velocity or the speed at which
is turning in radians per second and so
you can do calculations of rotational
inertia we can also do collisions let's
say or to take another object as the
bottom object is spinning with a certain
angular velocity we could simply drop
the top object on it so what's going to
happen is that angular momentum is going
to be conserved and so we're going to
have to see a decrease when we put both
of these together in its angular
velocity also you should understand how
a change in torque or net torque over a
given period of time it's going to
change the angular momentum this is just
like impulse in regular translational
motion and so here we've got an object
and we're going to apply a force to it
in this direction
remember if we apply a force
perpendicular to the lever arm we're
going to get a torque and so the torque
is going to be in this direction so I'm
going to start the animation and watch
what happens to the angular momentum so
as I add a force in that direction we're
getting an angular momentum in this
direction what's what's causing that
angular momentum again it's the lever
arm now times the momentum in that
direction so as we apply a torque it
takes awhile but we're building up
momentum in that direction now watch
what happens if we change the torque in
the other direction so again it's
already has some movement or momentum in
this direction but now we've reversed
the torque so it's going to be applying
a force in this direction so the torque
is down watch what happens we're going
to see a decrease in angular momentum
and then it goes in the other direction
and so again as we apply a torque
against that angular momentum what do we
get at this point we can bring it to a
standstill like that so how could we
model this well imagine we have this
turntable right here and I had Rockets
on either side and they're going to
apply a torque so they're going to apply
a force perpendicular to the lever arm
and as they do that over time what's
going to happen to the angular momentum
it's going to start to speed up in that
direction now how could you actually
measure that without using rockets you
could use a set up like this so we're
using that turntable again we could have
a little bit of a wheel
down on the bottom where we can apply a
force to it and so I'm having an object
go off the table now we can apply a
constant force in this direction so
that's going to be a torque over a given
period of time and that's going to give
me my change in angular momentum so did
you learn to predict the behavior of
objects in a collision as they conserve
angular momentum could you calculate the
angular angular momentum of both a point
object and an extended object and also
could you use torques and changing
torques to see that how that impacts the
angular momentum the object-- I hope so
and I hope that was helpful