Gravitational Torsion Balance
012–06802B
10
The torsion constant can be determined by observing the period
(
T
) of the oscillations, and then using the equation:
T
2
=
4
π
2
I/
κ
(1.6)
where
I
is the moment of inertia of the small mass system.
The moment of inertia for the mirror and support system for the
small masses is negligibly small compared to that of the
masses themselves, so the total inertia can be expressed as:
(1.7)
Therefore:
(1.8)
Substituting equations 1.5 and 1.8 into equation 1.4 gives:
(1.9)
All the variables on the right side of equation 1.9 are known or
measurable:
r =
9.55 mm
d
= 50 mm
b
= 46.5 mm
m
1
= 1.5 kg
L
= (Measure as in step 1 of the setup.)
By measuring the total deflection of the light spot (
Δ
S
) and the
period of oscillation (
T
), the value of
G
can therefore be
determined.
Procedure
1.
Once the steps for leveling, aligning, and setup have been
completed (with the large masses in Position I), allow the
pendulum to stop oscillating.
2.
Turn on the laser and observe the Position I end point of
the balance for several minutes to be sure the system is at
equilibrium. Record the Position I end point (
S
1
) as
accurately as possible, and indicate any variation over
time as part of your margin of error in the measurement.
G
=
π
2
Δ
S b
2
(
d
2
+
2 5
2 5
r
2
)
T
2
m
1
Ld
I
= 2
m
2
(
d
2
+
2 5
2 5
r
2
)
κ
= 8
π
2
m
2
d
2
+
2 5
2 5
r
2
T
2
Summary of Contents for AP-8215
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