3B Scientific Torsion Axle - Manual (Page 2)

2
5. Accessories
Set of Test Bodies for Torsion Axle U20051
Fig. 1 Set of Test Bodies for Torsion Axle
1 Wooden sphere, 2 Mounting plate, 3 Solid cyl-
inder, 4 Wooden disc, 5 Hollow cylinder
The accessories for the torsion axle (U20050) consist
of two cylinders with nearly identical weights but
different weight distributions, a mounting plate for
the cylinders, a wooden disc and a wooden sphere.
Hollow cylinder (metal):
External diameter: 90 mm
Height: 90 mm
Mass: approx. 425 g
Solid cylinder (wood):
Diameter: 90 mm
Height: 90 mm
Mass: approx. 425 g
Mounting plate:
Diameter: 100 mm
Mass: approx. 122 g
Wooden disc:
Diameter: 220 mm
Height: 15 mm
Mass: approx. 425 g
Moment of inertia: 0.51 kgm 2
Wooden sphere:
Diameter: 146 mm
Mass: approx. 1190 g
Moment of inertia: 0.51 kgm 2
6. Theory
To determine various moments of inertia for differ-
ent test bodies, these objects are placed on a ball-
bearing supported shaft which has a coiled spring
attached. The coiled spring is subjected to restoring
torque D. The oscillation period
T of the torsion
pendulum results in the moment of inertia J.
D
J
T
π = 2 2
2
4
T
D
J
⋅
π
=
The values determined experimentally confirm the
findings theoretically postulated for a body of the
mass m, whose mass elements
Δm rotate at a dis-
tance r
z
around a fixed axis:
∫ ∑
= ⋅ Δ =
=
dm r r m J
2
z
n
1 z
2
z
7. Operating notes
• Mount the torsion axle in a tripod stand and
align it horizontally using the spirit level.
• Do not adjust the screws that press the securing
spheres to the rod. (They are adjusted so that the
weights can be moved along the rod but are not
forced outwards by centrifugal forces.)
• Always arrange the experiment so that the spring is
compressed and not extended.
• Start the oscillation by turning the rod 180°
(max. 360°).
• Determine the oscillation period from several
measurements by forming the mean value out of
e.g. 5 oscillations.
• Note down the exact value of the restoring torque
D on the torsion axle or in the operating manual.
This value is used to determine the moment of
inertia J from the oscillation period T.
8. Experiments
To perform the experiments the following apparatus
are required (recommended):
1 Stand Base Tripod, 185 mm U13271
1 Digital Stopwatch U11902
1 Precision Dynamometer 1 N U20032
1 Set of Test Bodies for Torsion Axle U20051
8.1 Determination of the restoring torque D
• Insert the rod without weights onto the torsion axle.
• Attach the 1 N dynamometer to the rod so that it
acts perpendicularly to it.
• At distances of r = 10 cm, 15 cm and 20 cm from
the centre of the rod measure the force F needed
to rotate the rod from its state of equilibrium by
about
α = 180°.