L23 Circular motion on level road - Laws of motion, Physics, Class 11

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going ahead with part 23 a very
important application of circular motion
is to study the motion of a car on a
level road and then compare the motion
of a car on a curve road or on an
incline road or sometimes we call it as
a banked road the first of all will see
the motion of a car on a level road if
you look at this diagram you could see
that a car is moving on in a circular
path that is what we told is a circular
motion now what we'll try to do here is
we will imagine that at a car is moving
or it is taking a turn on a level road
that means the road is straight the road
is somewhat like this it is a straight
road and the car is moving somewhat like
this and it is taking a turn I mean
however it is moving in a circle but the
level of the road is plain it is a
straight road there is no curve in the
roads I mean I'm sorry it is a curved
road however but the level or the
horizontal plane of the road is straight
so this is how the car is moving on it
so what are the various forces that are
acting on this car obviously
mg downwards the normal reaction force
vertically upwards and the force of
friction in this direction right now let
us apply the law of I'm sorry let us
write the equation of motions along the
vertical direction it would be n is
equal to mg now in this scenario in such
a scenario you would say if this car is
moving in a circular path like this that
means there is a centripetal force so
from where is that centripetal force is
coming if there is a centripetal force
that means there is a centripetal
acceleration so from where is the car
getting that centripetal acceleration in
this case
static frictional force this frictional
force provides the centripetal
acceleration to the car towards the
center which helps it to move in a
curved part or which helps it to take
this turn let us suppose the car
activates this turn so how is it taking
that turn because there is a force which
is helping it to move in a curved path
that force comes from centripetal
acceleration and that acceleration comes
from the force of friction that means
the force of friction acts somewhat like
this just try to visualize the figure in
this way this is what I have drawn this
is the direction of centripetal force
right so you imagine that the car has
been moved in this way I mean I have
drawn the figure from this point of view
so this is the centripetal force normal
reaction would be something which is
acting upward that means which is upward
from here and mg is something which is
acting downwards towards the ground so I
hope you can visualize the feggin all
right so we say that the static
frictional force provides the
centripetal acceleration right that
means this static frictional force would
provide the centripetal acceleration and
we know that the static frictional force
according to the law of static friction
this is always less than equal to MU s
into n and from the very first equation
which we wrote there we found n is equal
to mg so we can write F s is less than
equal to MU s into mg now since F s is
providing the centripetal acceleration
right so what we can write F SF s is
nothing but the centripetal force so
this F s would give rise to the
centripetal force that is generally
denoted by F C so instead of F s we can
write it as capital F C that eccentric
little force which is equal to mV square
by r this is less than equal to MU s
into mg correct so this M and
em gets cancelled so we get V square is
less than equal to mu s into R into G so
V is less than equal to root over mu s
ad G so what does the same this same is
that if a car is moving in a circular
path on a level road level Road means
that this road is a plain road it
doesn't have any inclination with the
horizontal so if a car is moving so this
is the direction of the friction now if
a car is moving on a plain road the
maximum velocity of the car while moving
in a circular path would be this that
means the velocity of the car would be
either less than or equal to this value
so this is the maximum velocity of the
car so we say that this is the maximum
velocity in circular motion on a level
road now please understand this scenario
very carefully the most important part
here to understand is to visualize it
practically this car is moving on a
circular path so the frictional force
will act along this direction when it
takes this turn this frictional force
will provide the centripetal force and
there will be a normal reaction acting
in the proper direction you can imagine
it coming outward from this page from
the screen and there would be a mg which
would be acting downwards just opposite
to n so that is how I have taught it it
n is upward mg is downwards and this is
the direction of frictional force I mean
if you think that you were standing
somewhere here and trying to visualize
this car if you were standing somewhere
here and visualizing this path then you
would see it somewhat like this so I
hope it is clear to you now please
remember this value of velocity because
now we are going
studying in the next slide the motion of
a car on a banked road and we will have
a comparison of the BAM throat with this
Leben road so let's proceed to the next
slide thank you
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