### by Saulius Pakalnis

Gyroscope

A gyroscope is a spinning device demonstrating the principle of conservation of angular momentum, in physics.
The traditional mathematical definition of the angular momentum of a particle about some origin is:

where L is the angular momentum of the particle, r is the position of the particle expressed as a displacement vector from the origin.
p = m*v is the linear momentum of the particle (more correct expression is ).  m - mass of the particle.
If a system consists of several particles, the total angular momentum can be obtained by adding (integrating) all the angular moments of the constituent particles. Angular momentum can also be calculated by multiplying the square of the distance to the point of rotation, the mass of the particle and the angular velocity.

Precession of Gyroscope
The device, once spinning, tends to resist changes to its orientation. If external force F1 is applied to some point which is at radius r from rotation axis of gyroscope, the spinning device begins to rotate. The motion "seems to be strange" as it does not follow the applied force direction, but moves in a perpendicular one. This rotation of spinning plane is called precession.
The simplest explanation of the phenomenon is shown below.

The gyroscopic precession is fundamental phenomenon which explains why boomerang returns. See boomerang model in next chapter.
Examples:

 . Exercise: get precession with disk sander by moving your wrist up and down The angular momentum of turning bicycle wheels makes them act like gyroscopes to help stabilize the bicycle. This gyroscopic action also helps to turn the bicycle. Stability of free-hand biking: see by yourselves how front wheel turns to the left/right when you shift your center of mass (and bend the bike) to the left/right side of a bicycle.