PURPOSE/ OBJECTIVES
The purpose of this experiment is to study uniform circular motion and to compare the observed value
of the centripetal force with the calculated value.
APPARATUS/EQUIPMENT
1.
Centripetal force apparatus
2. Motor with coupler and means for counting turns
(Procedure A only)
3. Stopwatch or stop clock
4. Supporting rods, hook, right-angle clamp, and bench clamp (Procedure A only)
5. Weight hanger and weights
6. Vernier caliper (Procedure A only)
7. Level (Procedure B only)
8. Triple-beam balance (Procedure B only)
THEORY
If a body moves with constant speed in a circle, it is said to be moving with uniform circular motion. Even
though the speed is constant, the velocity is continuously changing because the direction of the motion
is continuously changing. Thus, such a body has an acceleration. It can be shown that the direction of the
acceleration is always toward the center of the circle (because it is only the direction and not the
magnitude of the velocity that is changing) and that its magnitude is given by
r
v
a
2
where
v
is the speed of the body in meters per second and
r
is the radius of the path in meters.
A force is necessary to produce this acceleration. Because it must be in the same direction as the
acceleration-namely, toward the center of the circle as noted above-it is called
centripetal force.
Newton's second law now requires that the magnitude of this force be equal to the mass times the
acceleration produced, so that in our present case

r
v
m
F
2
where
F
is the force in newtons,
m
is the mass of the rotating body in kilograms, and
v
and
r
are the
same as before. But by Newton's third law of motion, an equal and opposite force is exerted by the body
on the restraining medium. This reaction is called
centrifugal force.
The centripetal force can also be expressed in terms of the angular speed, since
v = rω and
ω=2πf
where
v
is the linear speed and
r
the radius of the path as
before,
is the angular speed in radians per
second, and
f
is the number of revolutions per second. Thus,
F
=
mrwω
2
or
F
=
4π
2
f
2
m
where
F
is the centripetal force in newtons as already described.
Figure
()
Centripetal force apparatus, manual form
Apparatus for the experiment is shown in Fig. (). A stretched string provides the centrifugal force to
keep the rotating mass moving in a circle, but the complete assembly is mounted on a horizontal bar (the
rotating platform) mounted on a vertical shaft carried in very good bearings. A knurled portion of the
shaft provides a convenient grip for the experimenter's fingers, and you'll find with a little practice that
you can keep the assembly rotating at a constant speed quite accurately. Note that at the bottom of the
spring there is a small pink disk, and because the spring and disk are at the center of rotation, the
position of the latter is easily observed even with the apparatus in motion. The mass to be kept rotating
at a particular radius is suspended by threads from a post mounted on the rotating platform at that