About gyroscopes

Graphic - gyroscopes

A gyroscope is a symmetrical mass, usually a wheel, mounted so that it can spin about an axis in any direction. A spinning gyroscope will resist changes in the orientation of its spin axis. Gyroscopes are used in ship stabilizers to counteract rolling, and a gyroscope is the nucleus of most automatic steering systems, such as those used in airplanes, missiles, and torpedoes.

Although the motion of a gyroscope can seem perplexing, some motions are easily analysed using Newton’s second law for rotation (Key Point 5.19).

Precession of a simple gyroscope

A simple gyroscope spinning fast enough, when suspended at one end on a piece of string, can appear to ‘defy gravity’ and hang horizontally, while rotating about the suspension point.
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Let’s look at the gyroscope from the side. The force of gravity acts on the center of mass to rotate it about the support point: i.e. there is a torque acting that is directed into the page
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Now looking from above. The torque vector is parallel to the rate of change of angular momentum (Key Point 5.16)

\[ \vec{\tau} = \frac{d \vec{L}}{d t} \]

So the angular momentum vector rotates about the suspension point in the horizontal plane: the gyroscope precesses

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The gyroscope does not defy gravity at all. It is gravity that is making the gyroscope precess, by providing the torque.

Same situation with a stationary gyroscope: a pendulum

It is instructive to look at what happens when the gyroscope has no initial angular momentum, but is released from the same position. The torque that acts is the same, and the angular momentum vector grows with time parallel to the torque. This describes a rotation in the vertical plane i.e. the gyroscope acts as a pendulum. The reason that a spinning gyroscope behaves differently is that it already has angular momentum
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