Transcript Properties of Uniform Circular Motion

Properties of Uniform
Circular Motion
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Uniform circular motion - circular motion
at a constant speed - is one of many
forms of circular motion. An object moving
in uniform circular motion would cover the
same linear distance in each second of
time.
When moving in a circle, an object traverses a distance
around the perimeter of the circle. So if your car
were to move in a circle with a constant speed of 5
m/s, then the car would travel 5 meters along the
perimeter of the circle in each second of time.
if the circle had a circumference of 20 meters, then it
would take the car 4 seconds to make a complete
cycle around the circle.
Change the equation for average speed:
Avg speed =distance/time =circumference/time
and substitute 2**radius for circumference
to get the equation:
Avg Speed =
2**R
Where T = period of time to complete 1 revolution
Using this equation, it becomes clear that the
radius of the circle is directly proportional to
the average speed. For instance - if the
radius of the circle were doubled, but the
period to traverse the circumference remains
the same, then the speed must double.
Objects moving in uniform circular motion will have
a constant speed. But does this mean that they will
have a constant velocity? Recall that speed and
velocity refer to two distinctly different quantities.
Speed is a scalar quantity and velocity is a vector
quantity. Velocity, being a vector, has both a
magnitude and a direction.
Since an object is moving in a circle, its direction is
continuously changing.
As the object rounds
the circle, the direction
of the velocity vector is
different than it was the
instant before. So while
the magnitude of the
velocity vector may be
constant, the direction
of the velocity vector is
changing.
Acceleration is defined as a change in velocity over a
period of time, therefore an object with a change in
the direction of the velocity has an acceleration, even
if there is no change in speed, or the magnitude of the
velocity.
velocity
=
Avg Acceleration =
time
Vf - Vi
t
Remember the rules for adding or
subtracting vectors:
1.
2.
3.
the magnitude of the vectors does not
change
the directions of the vectors do not
change for addition, but one vector is
reversed for subtraction
vectors must be placed head to tail to
add or subtract
For example:
(Notice the direction of the acceleration.)
This inward acceleration can be demonstrated with a cork
accelerometer. The cork will move toward the direction of the
acceleration.
For an object moving in a circle, there must be an inward force
acting upon it in order to cause its inward acceleration. This is
sometimes referred to as the centripetal force
requirement. The word "centripetal" (not to be confused
with "centrifugal") means center-seeking. For objects moving
in circular motion, there is a net force towards the center
which causes the object to seek the center.
To understand the need for a centripetal force, it is
important to have a sturdy understanding of
Newton's first law of motion - the law of inertia.
The law of inertia states that ...
"... objects in motion tend to stay in motion with the
same speed and the same direction unless acted
upon by an unbalanced force.“
According to Newton's first law of motion, it is the
natural tendency of all moving objects to continue in
motion in the same direction that they are moving ...
unless some form of unbalanced force acts upon the
object to deviate the its motion from its straight-line
path. Objects will tend to naturally travel in straight
lines; an unbalanced force is required to cause it to
turn. The presence of the unbalanced force is
required for objects to move in circles.
Any object moving in a circle (or along a circular path)
experiences a centripetal force; that is there must
be some physical force pushing or pulling the object
towards the center of the circle. This is the
centripetal force requirement. The word
"centripetal" is merely an adjective used to describe
the direction of the force. The force could be a
tensional force, a gravity force, a contact force, or
even simply friction.
The Forbidden F-Word
When the subject of circular motion is discussed, it
is not uncommon to hear mention of the word
"centrifugal." Centrifugal, not to be confused
with centripetal, means away from the center or
outward. Have you ever felt a force pushing you
outward as you made a sudden turn in a vehicle?
Ask yourself the following questions:
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Does the sensation of being thrown outward from
the center of a circle mean that there was
definitely an outward force?
If there is such an outward force on my body as I
make a left-hand turn in an automobile, then
what physical object is supplying the outward
push or pull?
And finally, could that sensation be explained in
other ways which are more consistent with our
understanding of Newton's laws?