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OBJECTIVE
To calculate the net force on an object moving in uniform circular motion and compare
with the expected value.
THEORY
A. Mass Rotating in Uniform Circular Motion
Consider the
Centripetal Force Apparatus
below.
The mass M
bob
is rotating in uniform
circular motion about the vertical rod in a radius R.
Diagram 1
Applying Newton’s 2
nd
Law in the radial direction gives a net force in the radial direction
given by
net
bob
r
FM
a
=
where
2
r
v
a
R
=
.
The speed of the mass M
bob
is given by
2
R
v
T
π
=
and thus
2
2
4
r
R
a
T
=
.
Therefore,
2
2
4
net
bob
R
T
=
.
CENTRIPETAL ACCELERATION

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B.
Mass in Equilibrium
Now let’s consider the case when the mass M
bob
is in equilibrium and the radius
R
is the
same as it was when it was rotating in uniform circular motion.
If this is the case, then
the tension force which equals the weight of the hanging mass W
hanging
, must be equal to
the net force in the radial direction
2
2
4
net
bob
R
FM
T
π
=
when the mass M
bob
was rotating in
uniform circular motion. We will be comparing these two values taking W

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