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physical laws of kinematics and dynamics in exercises
and practical classes.
A small rotating disc marked with an angular scale
supports a transversely mounted beam to which
weights can be attached. The disc rests on an air-
cushion so that it can rotate virtually without friction
and the axis of rotation is preset by adjusting the
centre. The weight of a driving mass hanging on a
thread is transmitted to the disc via one simple pulley
and a multiple pulley.
Because the frictional drag is minimal, even very small
torques are enough to start the rotational motion.
Consequently, the effect of the inertia contributed by
the accelerating weight on the thread is less than one-
thousandth of the total, even for the smallest moment
of inertia that an be investigated. Moreover,
measurement of the angular distance covered in a
period of several seconds can be made very easily by
the unaided eye and a hand-operated stopwatch.
For precise measurements it is possible to use a digital
counter, which can be started by the built-in start/stop
unit and stopped by a signal generated when the zero
point of the scale passes through a light beam from a
laser reflection sensor.
The air-flow generator for the rotating apparatus is
designed to operate with a mains voltage of either 230
V ±10 % (U8405680-230) or 115 V ±10 % (U8405680-
115).
A set of accessories is available for the rotating system
on air bed (U8405690) that allows for experiments on
frictionless rotational oscillations and on frictionless
rotational motion with a larger rotating disc.
3. Equipment Supplied
1 Rotational air-cushion bearing unit
1 Rotating disc with transverse beam
1 Multiple pulley
1 Start/stop unit
3 S-shaped hooks (2x 1 g, 1x 2 g)
1 Set of additional weights (2x 12.5 g, 2x 25 g, 2x 50 g)
1 Air-flow generator with mains adapter
1 Silicone-rubber tube with valve
1 Pulley
1 Stand rod, long
1 Stand rod, short
1 Stainless steel rod, 250 mm
1 Levelling washer
1 Reel of cotton-thread
4. Technical Data
Angle scale:
Scale divisions:
Length of transverse beam:
Radial distance to holes in beam:
Space between holes:
Multiple pulley radii:
Moment of inertia of rotating disc
and transverse beam:
Max. moment of inertia:
Min. driving torque:
Max. driving torque:
5. Basic Principles
In analogy to Newton's law of motion for translational
motion, the relationship between the torque M that is
applied to a rigid body with a moment of inertia J,
supported so that it can rotate, and the angular
α
acceleration
is as follows
= J
α ⋅
(1)
M
.
If the applied torque is constant, the body undergoes
a rotational motion with a constant rate of angular
acceleration.
In a time t from the start, the body rotates through
the following angle:
1
ϕ
=
α ⋅
t ⋅
(2)
2
This leads to the following expressions for the angular
α
acceleration
:
ϕ ⋅
2
α
=
(3)
2
t
and, for the special case
π
α
=
(4)
.
2
t
The torque M results from the weight of an
accelerating mass m
axis of rotation of the body, and is therefore:
=
⋅
(5)
M
r
m
M
M
2
where g = 9.81 m/s
constant.
If two additional masses m
transverse beam of the rotating system at a fixed
distance r
from the axis of rotation, the moment of
J
inertia is increased from the initial value J
added masses) to:
=
+
⋅
⋅
2
(6)
J
J
2
m
r
0
J
J
2
0 – 360°
1°
≈ 440 mm
30 – 210 mm
20 mm
5/10/15 mm
≈ 0.9 g m
≈ 7.1 g m
≈ 0.05 mN m
≈ 0.60 mN m
2
.
ϕ
o
= 90
,
acting at the distance r
M
⋅
g
, the gravitational acceleration
are attached to the
J
2
2
from the
M
(without
o
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