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CENTRIPETAL FORCE
Purpose:
To investigate the relationship between the mass, velocity, radius of curvature and force when an
object moves in a circular path.
Apparatus:
Computer, Photo gate, interface box, stand, masses, string, metal rod, ruler.
Background:
We know that a force is required to change an object’s velocity. The force that is applied causes the object
to accelerate. In this experiment we would like to investigate the force that is necessary to keep an object
moving in uniform circular motion.
By uniform circular motion we mean that the object will execute a path that is a perfect circle at a constant
speed. Please remember that the speed of the object is equal to the magnitude of the velocity of the object.
Because the direction of the velocity vector is changing, the object is accelerating. This means a force is
exerted on the object.
v
v
v
v
R
Figure 1. Illustration of an object executing uniform circular motion.
The object executing uniform circular motion is accelerating. An acceleration that produces uniform
circular motion is called a centripetal acceleration because it always points toward the center of the circle.
It has been determined that the magnitude of the centripetal acceleration is a ratio of the square of the speed
that the object is moving at and the radius of the circular path being followed.
a
v
r
c
=
2
E
q
.
1
)
To reiterate, an important feature of centripetal acceleration is that the direction of the acceleration always
points toward the center of the circle no matter where the object is along its path. This indicates that the
acceleration vector is always changing even though the magnitude of the acceleration is constant.
From the understanding of the acceleration that an object possesses while executing uniform circular
motion we can now talk about the force that is involved in producing the acceleration of the object. From
Newton’s second law we know that the force exerted on the object will cause an acceleration that is
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proportional to the object’s mass. Because the object is executing uniform circular motion, the acceleration
can be described by the definition of centripetal acceleration.
Fm
am
v
r
==
∑
2
E
q
.
2
)
The force points toward the center of the circle, the same direction as the centripetal acceleration. The
centripetal force also changes direction so that it always points toward the center of the circle as the object
moves around the circular path. The centripetal force is made up of all the physical forces that act on the
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 Fall '09
 JohnJames
 Circular Motion, Force, Mass, Rotation, Velocity, Polar coordinate system

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