3B Scientific Gyroscope User Manual

3B SCIENTIFIC3B SCIENTIFIC
3B SCIENTIFIC®
3B SCIENTIFIC3B SCIENTIFIC
Instruction sheet
9/05 ALF
PHYSICSPHYSICS
PHYSICS
PHYSICSPHYSICS
Gyroscope U52006
bm
bl
9
8
7
6
1
2
1 Disc
2 Gyroscope axle
3 Bobbin
4 Set of accessories U52010
5 Tripod stand
6 Stand rod
7 Counterweight, large
8 Counterweight, small
9 Adjusting screw
bl Scale
bm Spirit level
5
The gyroscope is used for demonstration and experimen­tal quantitative derivation of the laws of gyrostatics. The following topics can be dealt with experimentally:
Moment of inertia of the disc
Turning moment/angular momentum
Precession
Nutation
1. Safety instructions
Make sure that the gyroscope is standing firmly on
the surface
Make sure no components of the gyroscope (disc,
weights) can fall down.
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2. Description, technical data
2.1 Gyroscope
The gyroscope includes a vertical stand rod 6 to which is attached a gyroscope axle 2 that can be rotated ver­tically and horizontally on its bearings. A disc 1 mount­ed on double ball bearings is fitted on one side of the axle. At the other end, there are two counterweights 7,
8 that can be moved to balance the axle. Fine adjust-
ments can be made at the end of the axle by means of an adjusting screw 9. To generate external turning mo­ments, a hanger with an additional weight is suspended from the axle. The angle of inclination of the axle is dis­played on a scale bl which is clear and easy to read. A spirit level bm is provided so that the gyroscope can be
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aligned to the horizontal. The disc can be made to rotate either manually or by means of a string. The double ball­race bearing guarantees almost frictionless rotation that goes on for an extended period of time. The open con­struction of the gyroscope facilitates excellent observa­tion of the gyroscopic phenomena. Scale: – 45° to +45° Scale divisions: 1° Disc: 250 mm Ø Mass of disc: 1500 g Mass of counterweights: 50 g, 1400 g Total mass: 4650 g
2.2 Accessories for the gyroscope
The set of accessories for the gyroscope U52006 consists of an additional disc and a counterweight. It is used to demonstrate the cancellation of gyroscopic forces when two discs rotate in opposite directions with the same rotational speed.
3. Theory
A gyroscope is a rigid body that rotates around an axis that is fixed at one point. If no external turning moment is applied, the axis of the gyroscope (being equivalent to the axis of its angular momentum) maintains its position in space. If, however, an external force is applied to the axis, then this turning moment effects a change in angu­lar momentum. As a result, the axis is laterally displaced. The gyroscope moves in a direction perpendicular to both its own axis and to the acting force. This motion is called precession. If an impulse is applied to the axis of the gyroscope when it is spinning normally, the resulting turn­ing moment causes an additional angular motion and the gyroscope starts to wobble. This wobbling motion is called nutation. In general, both motions are superim­posed on one another.
Stand rod U15002 and bosshead U13250 for fixing the
gyroscope.
Light barrier U18020 and digital counter U21005 for
measuring the period of rotation of the gyroscope disc.
5.1 Determining the moment of inertia I of the disc
Set up the gyroscope as shown in Fig. 1 and balance
it.
A known turning moment D is applied to the disc. The resulting angular momentum dω/dt is measured. The following equation applies:
ω
dD
=
dt I
To apply this turning moment, wind a string around the bobbin, suspend a weight from one end of the string and allow the weight to fall.
Turning moment D = mgr (m = mass of accelerating weight and r = radius of bobbin).
To determine the angular acceleration, measure the time t between releasing the disc and when the weight hits the floor.
Next determine the angular velocity ω
. To do so, use
E
the light barrier to measure the period of one disc revolution. Before starting the experiment, glue a thin strip of paper onto the rim of the disc.
The moment of inertia I is calculated using the equa- tion:
D t
ω
d
=
dt t
ω
E
I=
ω
E
4. Operation
Place the tripod stand 5 on a level, non-vibrating
work surface.
Insert and fix the stand rod 6 into the tripod stand.
Insert the gyroscope axle 2 into its bearing.
Align the device in a horizontal position by using the
spirit level bm.
Slide the disc 1 and the counterweights 7, 8
along the axle. Use the locking ring to securely fix the disc and balance the gyroscope. Use the adjusting screw 9 for making fine adjustments.
Rotate the gyroscope manually or with the help of a
string wound into the bobbin 3.
5. Examples of experiment
In order to conduct the experiments, the following addi­tional equipment is required:
Mechanical adding stopwatch U11901 for measuring
the precession and nutation frequencies.
Fig. 1: Determining the moment of inertia of the disc
5.2 Precession
The aim of the experiment is to demonstrate preces­sion and to study the interdependence of the period of precession and the frequency of rotation of the disc.
Set up the gyroscope as shown in Fig. 2 and balance it.
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