3B Scientific Torsion Axle - Manual (Page 3)

3
Torque: r F M
⋅ =
Restoring torque:
α
=
M
D
Fig. 2 Determination of the restoring torque
8.2 Dependency of the moment of inertia J on
the distance r, in which a mass m rotates
round a fixed axis
• Attach the rod without weights to the torsion axle.
• Determine the moment of inertia J(rod).
• Arrange the weights at symmetrical distances of
r = 5 cm, 10 cm, 15 cm, 20 cm and 25 cm from
the centre of the rod.
• Determine the moment of inertia J(rod + weights).
• Calculate the moment of inertia J(weights) =
J(rod + weights) – J(rod).
Fig. 3 Dependency of the moment of inertia J on the
distance r
8.3 Comparison of the moments of inertia of
cylinders of the same weight but with
different weight distribution
8.3.1 Wooden disc (WD)
• Attach the wooden disc (WD) to the torsion axle.
• Determine the moment of inertia J(WD).
Fig.4 Determination of the moment of inertia of a
wooden disc
8.3.2 Solid cylinder (SC) and hollow cylinder (HC)
• Attach the mounting plate (P) to the torsion axle.
• Determine the moment of inertia J(P).
• Place a cylinder onto the mounting plate (P).
• Determine the moments of inertia J(SC + P) and
J(HC + P).
• Determine the moments of inertia
J(SC) = J(SC + P) – J(P)
J(HC) = J(HC + P) – J(P) by subtracting.
Fig. 5 Comparison of the moments of inertia of cylin-
ders
8.4 Determination of the moment of inertia of a
sphere (S)
• Attach the sphere (S) to the torsion axle.
• Determine the moment of inertia J(S).
A comparison of the sphere with the wooden disc
(refer to 8.3.1.) reveals that they both have the same
moment of inertia. Spheres (S) and wooden discs
(WD) have the same moment of inertia if the follow-
ing holds true with regard to their mass
m and their
radii R:
2 2
) S ( ) S (
5
4
) WD ( ) WD ( R m R m
⋅ = ⋅
Fig. 6 Determination of the moment of inertia of a
sphere
8.5 Dependency of the moment of inertia J on
the distance a between the rotation axis and
the axis of the centre of gravity, verification
of Steiner’s theorem
• Attach the round disc to the torsion axle and
align it horizontally.
• Start the disc turning about its centre of gravity
(a = 0).
• Determine the moment of inertia J
0
.
• Determine the moments of inertia J
a
for different
distances of a = 2 cm, 4 cm, 6 cm......16 cm be-