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Centripetal Force

Today you are going to study an object
that moves in a circle.

An object that moves in circular motion
must have a force acting on it that is
directed toward the center of the
circle.

This could be something as simple as a
string pulling a ball into circular motion.


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The string is pulling on the ball.
Strings cannot push.
The circular motion could be a road
forcing a car to turn a curve.

The road continually pushes toward the
center of the curve.
Even in a vertical loop amusement park ride,
when a car is at the top of the loop,
the track is actually pushing it downward
toward the center of the circle
in which it is travelling at that moment.

Forces that make objects move in circular
motion are called
centripetal forces.

Centripetal means “center-seeking.”

This force should not be confused with
the psuedo force commonly known as
centrifugal.

Centrifugal means “center-fleeing,” and
centrifugal forces are not real.

Today you will measure the
centripetal force in a particular
circular motion and
show that it satisfies
Newton’s Second Law:
 F  ma .
The apparatus you will use is shown below.
Radius
Pulley
String
Bob
Slotted
Masses
Index
Spring
When viewed from above the hand-turned
apparatus looks like this
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The acceleration in this circular motion
is one associated with a change in the
direction of the velocity vector, not the
length of the velocity vector.

It, just like the centripetal force, also
points toward the center of the circle.
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To calculate the acceleration you have
to determine the angular velocity.
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Angular velocity is an angle measurement
divided by time.
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For example if you make one full spin in 2
seconds of time, then your angular velocity
would be 3600 divided by 2 seconds which
reduces to 1800/s.

Many of you have heard about 33 and a 1/3
rpm phonographic records that your parents
or grandparents had when they were young.
The rpm stands for revolutions per minute,
and it is an angular velocity measurement.

In lab today you will determine an
angular velocity based on an angular
measurement of radians instead of
degrees.
One radian is the angle subtended at the
center of a circle by an arc equal in length to
the radius of the circle.
2
3
1
57.30
4
6 segments gets
to here.
2p segments gets
completely around.
6
5
1 rev = 3600 = 2p radians (rad)
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To get the angular velocity measured in
terms of rad/s, you will make the
following measurements.

Count the number (N) of cycles the
apparatus makes, and measure the time
(T) to make these N turns.
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Repeat until you have three different
time measurements involving N turns
each time.

Take the average of the three T’s.
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Divide this average T by N to get
the average time (t) for one
rotation. In other words
t = T/N .
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Then the angular velocity (w) is
w = 2p/t .

Though it is not shown here, it is
not difficult to show that the
centripetal acceleration (a) is given
by
a=
2
w R
where R is the radius of the circle.

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Once you have a, you will multiply it by the
mass of the swinging object (the bob). (The
value will be on the blackboard.)
You will then compare this force to the force
necessary to position the bob at a distance R
from its rotation axis when the apparatus is
not spinning.
Radius
Pulley
String
Bob
Slotted
Masses
Index
Spring
For your lab exam, you
must know this method of
determining the
centripetal force.