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.  

disk

FIGURE 1



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.

disc2

FIGURE 2

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 will increase.  



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