The Gyroscopic effect.
To understand a gyroscope we first need to understand vectors.
Adding vectors is easy. We are used to problems like determining
the direction of a boat moving at a fixed speed forward with a wind pushing
it to one side. It is easy to understand the resultant
force that will act on the boat. It is the result of adding the
two vectors for the wind and the motor.
To explain a gyroscope we need to multiply vectors. There
are two ways to multiply vectors. They are called the dot product
and the cross product. Here we will be concerned with the cross product.
In the cross product when two vectors perpendicular to each are
multiplied then the resultant is perpendicular to both. This however
does not tell us the direction of the resultant as two directions are
possible. The direction of the cross produce is predicted by
the right hand rule
If this was not enough a spinning disk is represented by it's angular
momentum w. This is a vector quantity. The
magnitude of this vector is equal to the produce of the moment
of inertia and rotational velocity of the disk. Now we need
to assign a direction to this spinning disk. To do this we draw a
line along the axis of the wheel. To choose it's direction we use
the right hand rule. We visualize grabbing the vector with our right
hand with our fingers pointing in the direction of rotation. Then
our thumb will point in the direction of the vector.
Figure 2 represents a spinning gyro mounted in gimbals. If
we try to turn it by applying a twisting force T to the gyro.
This twisting force is also represented by another vector. The
vector T (torque) represents this twisting force. The vector R is the
resultant of both T and W. R = T X W or R = the cross
product of T and W.
Now R as can be verified by this experiment represents the axis of the
resulting motion of the gyroscope. R however is a velocity. The
more torque T that is applied the faster R turns.
The best way to try to get an understanding of the gyroscope is to
get one and experiment with it. When this is done it is important to
devise some type of gimbals.
To demonstrate the above we can tie two strings to the posts on the ends
of the axle of a toy gyroscope. If the gyroscope is hung from one string,
and the axis is placed horizontal and started spinning the force of
gravity will cause to precess around it's hanging string. Furthermore
if a small force is applied to the hanging string the velocity of precession
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