Examining the principles of the gyroscope!
Since we are talking about instruments, and we still must discuss the attitude indicator, heading indicator as well as the turn coordinator, we shall start with the operating principles behind these instruments. These instruments are gyroscopic instruments. Let's first examine what a gyroscope is.
A gyroscope is a rotating mass that operates on the principle of "Rigidity in Space". What this means is that once the gyroscope is spinning, it tends to remain in its position and resists being moved. A good example is a bicycle wheel. If you were to hold a wheel by its axle and then spin it faster and faster, you would see this. As the wheel begins to spin, it is easy to tilt it back and forth, however as it gets spinning faster, it gets harder and harder to tilt it. This is what "rigidity in space" means. The greater the spinning mass and the closer that mass is located to the spinning axis, the better the gyro will be. Imagine the above illustration as that biclycle tire. Notice that as the gyro spins faster, it becomes harder and harder to deflect the gyro. Once the gyro is spinning, it can be used to show movements around a given axis. The illustration shows how the gyro can be used in an attitude indicator to show pitch and bank. This illustration shows a vertical gyro, not a horizontally aligned gyro as actually used in the attitude indicator. This is merely used to show the similarity between the bicycle tire and the spinning gyro that will serve to steady the attitude indicator. The gyro in the upper right that is paired with the attitude indicator's movements is actually the way the gyro is mounted.

Another valuable principle that the gyroscopic instruments use is "gyroscopic precession.

Gyroscopic Precession
When a force is applied to a spinning mass, the force is not noticed in the position that it was applied. The force will act 90 degrees from the point of application in the direction of rotation.
If you view the illustration above, you see that when a force is applied to the spinning gyro, the force acts 90 degrees in the direction of the rotation. This is the same principle used in riding a bicycle. When you turn the bicycle at higher speeds, you do not turn the handle bars you merely lean the bike. When you lean, you apply a force to the top of the wheel. The force acts 90 degrees and pushes the wheel in the direction of the turn.

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