It's professor Dave, let's discuss
uniform circular motion.
We've examined a lot of linear motion up to
this point, whether horizontal, vertical
or at some angle, but there are a lot of
objects that follow circular paths of
motion. This type of motion is
accompanied by an entirely different set
of equations, so we have to learn these
if we want to approximate the motion of
the planets, as well as a wide variety of
earthbound objects. Consider a ferris
wheel. As the wheel turns the cars
exhibit circular motion because they
revolve around a single axis of rotation
which runs through the center of the
wheel perpendicular to the plane that
contains it. The cars move around this
axis with a constant radius so they
trace a circle as they move, since a
circle is the set of all points
equidistant from some central point.
To describe the speed of the car it is
common to discuss the tangential speed
because the inertia of an object causes
it to try to maintain a straight line
path. This is the speed of the car along
the tangent line at a particular instant.
If this tangential speed is constant we
will call this uniform circular motion.
The tangential speed will depend on the
distance of the car from the axis of
rotation. If you place a sticker on the
wheel very close to the center it will
complete one revolution in the same
amount of time as one of the cars.
But the sticker will travel just a short
distance that you could trace with your
finger, while the car travels much
farther, all the way along the edge of
the wheel. Since speed is distance over
time, a shorter distance covered in the
same amount of time must mean a slower
tangential speed. This seems
counterintuitive, since the wheel is one
object, but that's why we can also
discuss angular velocity, which we will
learn about later. The uniform circular
motion of the car happens because of a
constant centripetal acceleration
towards the center of the wheel. At any
given moment the car has a velocity
vector that is tangent to the wheel and
while the magnitude of this velocity
will not change, the direction is
constantly changing, and any such change
in velocity can only happen due to some
acceleration. The centripetal
acceleration will always point towards
the center of the wheel, which will in
turn continually pull the direction of
the velocity vector towards the center
of the wheel. This is what produces the
circular motion, as though the car is
always trying to move towards the center
of the circle but never makes it there
because of its tangential speed.
Centripetal acceleration is given by
tangential speed squared over the radius
of the path, so this value would increase
if the car were to move faster and if it
were to sit closer to the center. We know
from Newton's second law that if an
acceleration occurs there must be some
force present to produce it, and
centripetal acceleration is generated by
the centripetal force. Centripetal force
is simply centripetal acceleration times
the mass of the object, since F equals ma.
So we can describe centripetal force by
simply adding the subscript C on force
and acceleration or it can be given by m
times tangential speed squared over the
radius of the path. This represents the
force that must be applied to produce
the circular motion, like the amount of
force that must be applied to spin a
ball on a string in a circle around your
head. If this centripetal force that
points towards the center perpendicular
to the tangential velocity were to
suddenly vanish, in the event that you
were to let go of the string, then the
object would simply move along the
tangent line at the precise moment of
release, since there would no longer be
any force pulling the object towards the
axis of rotation. So centripetal force is
the force pulling an object inwards
towards the axis of rotation during
circular motion, and it can take the form
of tension from a string, gravity exerted
by massive objects, or static friction
from the road when a car navigates a
curve. But when you are on a rotating
object like a merry-go-round, you feel
yourself getting pushed outwards. This is
often referred to
as the centrifugal force, implying
that it is the reactionary force to the
centripetal force, but in actuality this
is not a real force. The sensation that
is produced on the merry-go-round is
simply due to the inertia of your body
attempting to maintain a straight line
path of motion. Inertia is not a force, it
is just a result of Newton's first law.
You are not physically part of the
merry-go-round, but if you hold on tight
enough, the resulting frictional force
will cause you to follow the same
circular path without any problem. If you
are seeking a thrill and decide to let
go, inertia will outweigh the centripetal
force and you will fly off the side
hopefully onto some soft grass.
Let's check comprehension.
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