EXPERIMENT NO 10
Objective:
The object of the experiment is to study
gyroscope and the angular moment.
Apparatus:
The TM 630 Gyroscope Apparatus.
Theory:
A gyroscope (from
Ancient Greek γῦρος gûros, "circle" and σκοπέω skopéō, "to
look") is a spinning wheel or disc in which the axis of rotation is free
to assume any orientation by itself. When rotating, the orientation of this
axis is unaffected by tilting or rotation of the mounting, according to the
conservation of angular momentum. Because of this, gyroscopes are useful for
measuring or maintaining orientation.
A gyroscope is a wheel
mounted in two or three gimbals, which are a pivoted supports that allow the
rotation of the wheel about a single axis. A set of three gimbals, one mounted
on the other with orthogonal pivot axes, may be used to allow a wheel mounted
on the innermost gimbal to have an orientation remaining independent of the
orientation, in space, of its support. In the case of a gyroscope with two
gimbals, the outer gimbal, which is the gyroscope frame, is mounted so as to
pivot about an axis in its own plane determined by the support. This outer
gimbal possesses one degree of rotational freedom and its axis possesses none.
The inner gimbal is mounted in the gyroscope frame (outer gimbal) so as to
pivot about an axis in its own plane that is always perpendicular to the
pivotal axis of the gyroscope frame (outer gimbal). This inner gimbal has two
degrees of rotational freedom.
The axle of the spinning
wheel defines the spin axis. The rotor is constrained to spin about an axis,
which is always perpendicular to the axis of the inner gimbal. So the rotor
possesses three degrees of rotational freedom and its axis possesses two. The
wheel responds to a force applied to the input axis by a reaction force to the
output axis.
The behavior of a
gyroscope can be most easily appreciated by consideration of the front wheel of
a bicycle. If the wheel is leaned away from the vertical so that the top of the
wheel moves to the left, the forward rim of the wheel also turns to the left.
In other words, rotation on one axis of the turning wheel produces rotation of
the third axis.
A gyroscope flywheel
will roll or resist about the output axis depending upon whether the output
gimbals are of a free or fixed configuration. Examples of some
free-output-gimbal devices would be the attitude reference gyroscopes used to
sense or measure the pitch, roll and yaw attitude angles in a spacecraft or
aircraft.
The centre of gravity of
the rotor can be in a fixed position. The rotor simultaneously spins about one
axis and is capable of oscillating about the two other axes, and, thus, except
for its inherent resistance due to rotor spin, it is free to turn in any direction
about the fixed point. Some gyroscopes have mechanical equivalents substituted
for one or more of the elements. For example, the spinning rotor may be
suspended in a fluid, instead of being pivotally mounted in gimbals. A control
moment gyroscope (CMG) is an example of a fixed-output-gimbal device that is
used on spacecraft to hold or maintain a desired attitude angle or pointing
direction using the gyroscopic resistance force.
In some special cases,
the outer gimbal (or its equivalent) may be omitted so that the rotor has only
two degrees of freedom. In other cases, the centre of gravity of the rotor may
be offset from the axis of oscillation, and, thus, the centre of gravity of the
rotor and the centre of suspension of the rotor may not coincide.
Experimental Verification of Gyroscopic Laws:
In the experiment, the
slider weight is set to various radii (r=25,50, 75,95 mm). the mass of the
slider weight (m=65.6), the acceleration due to gravity, and the radius r of the
slider weight produce the moment Mw dictated by the balance bar:
Mw =m.g.r = 0.0656 kg . 9.81 m/s2 .r =
0.6435 N. r
This moment Mw is counteracted by the
gyroscopic moment, causing the balance bae to be lifted to the horizontal
position.
The theoretical gyroscopic moment Mk is
calculated from the rotational speed of the frame nf , the
rotational speed of the gyro ne and
the mass moment of inertia of the gyro Jz (Jz =
375cm2g) as follows:
Mk=
ωf ωe Jz =
2л/60.nf . 2л/60 ne . 0.0000375 kg/m2
Procedure:
·
Place the protective hood in the retaining ring.
·
Turn the two speed potentiometers to zero.
·
Switch on the motor for the gyro.
·
With the speed potentiometer run upto the desired rotational speed.
·
Switch on the motor for the frame (gyroscope).
·
With speed potentiometer increase the rotational speed until the balance
bar is horizontally aligned.
·
Make a note on both rotational speed.
Data and Observations:
Radius r
(m)
|
Moment Mw
(Nm)
|
Rotational speed ne
(rpm)
|
Rotational speed nf
(rpm)
|
Moment Mk
(Nm)
|
Derivation
(%)
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Graphical Representation:
Conclusion:
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