The document provides an overview of gyroscopes, explaining their basic definitions, structural components, and principles of operation such as rigidity in space and precession. It details the mechanics behind gyroscopic motion and precession, including torque and angular momentum, and discusses the construction and failure modes of columns related to engineering stability. The content emphasizes applications of gyroscopes in maintaining orientation, particularly in aviation instruments.

2. 1.BASIC DEFINITION
2.NEUTAL ,UNSTABLE AND
STABLE EQUILLIBRIAM
3.STRUTS
(a) Introduction
(b) Types and applications
4.COLUMNS
(a) Introduction
(b) Designs
5.FAILURE OF COLUMN
6. FAILURE OF SHORT
COLUMN BY CRUSHING
7.FAILURE BY BUCKLING
8.EULER'S COLUMN
(a) Assumptions
(b) Sign conventions
(c) Various end conditions
9.RANKINE'S FORMULA
10.CONCLUDING POINTS

3. A gyroscope is a device for measuring or maintaining orientation,
based on the principles of angular momentum
Mechanical gyroscopes typically comprise a spinning wheel or disc in
which the axle is free to assume any orientation. This orientation changes
in response to an external torque and due to large angular momentum
associated with the disc's high rate of spin and moment of inertia

4. A conventional gyroscope is a
mechanism comprising a rotor
journaled to spin about one axis,
the journals of the rotor being
mounted in an inner gimbal or
ring; the inner gimbal is
journaled for oscillation in an
outer gimbal for a total of two
gimbals.
The outer gimbal or ring, which is
the gyroscope frame, is mounted
so as to pivot about an axis in its
own plane determined by the
support.
Inner gimbalis 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).

6. Gyroscope mainly function on basis of two
properties
1) Rigidity in space: the gyro has a tendency to
resist forces applied to it, it is stable on the axis it
spins. This is the principle behind which a
spinning top stays upright, and the incorporation
of gyroscopes in flight instrument have resulted in
instruments like the artificial horizon which by
maintaining rigidity in space allow for flight solely
by reference to the instruments.
2) Precession: when a force is applied
perpendicular to a spinning rotor the rotor will
resist the force where it is applied and the force
will manifest 90 degrees later in the direction the
rotor is spinning.
.

7. Torque-induced precession (gyroscopic precession) is the phenomenon in which
the axis of a spinning object (e.g., a part of a gyroscope) "wobbles" when a torque is
applied to it, which causes a distribution of force around the acted axis. The
phenomenon is commonly seen in a spinning toy top, but all rotating objects can
undergo precession. If the speed of the rotation and the magnitude of the torque are
constant, the axis will describe a cone, its movement at any instant being atright
angles to the direction of the torque. In the case of a toy top, its weight is acting
downwards from its centre of mass and the normal force (reaction) of the ground
pushing up on it at the point of contact with the support constitute two opposite and
equal forces producing a torque.

8. Fundamental equation describing precession is
τ
where and L are torque and angular momentum
It follows that torque is perpendicular to axis of rotation and perpendicular to L resulting in
motion perpendicular to both L and T.
This is called PRECESSION
Thus if gyroscope spin slows down, its angular momentum decreases and so precession
increases. This continues until
device is unable to rotate fast enough to support its own weight, when it stops and fall off
its support mostly due to friction because friction against precession cause another
precession that goes to cause the fall.

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