The number of coordinates in the phase space of a single particle is 6.

The phase space of a particle refers to the space in which all possible states of the particle can be represented. Each state is defined by a set of coordinates that describe the position and momentum of the particle. In classical mechanics, these coordinates are usually represented by three position coordinates (x, y, z) and three momentum coordinates (px, py, pz). Therefore, the total number of coordinates in the phase space of a single particle is 6.

Position coordinates:
- The position of a particle in three-dimensional space can be described by three coordinates: x, y, and z. These coordinates represent the displacement of the particle along the x, y, and z axes, respectively. Each coordinate can take any real value, allowing for continuous positioning of the particle in space.

Momentum coordinates:
- The momentum of a particle is a vector quantity that describes the motion of the particle. It is defined as the product of the mass and velocity of the particle. In classical mechanics, momentum is often represented by three coordinates: px, py, and pz. These coordinates represent the momentum of the particle along the x, y, and z axes, respectively. Similar to position coordinates, each momentum coordinate can take any real value.

Interpretation of the phase space:
- The phase space of a single particle can be visualized as a six-dimensional space, where each point represents a unique state of the particle. The position coordinates determine the location of the point in three-dimensional space, while the momentum coordinates determine the direction and magnitude of the velocity vector at that point.

Phase space volume and conservation:
- In classical mechanics, the phase space volume is conserved for an isolated system. This means that as the particle moves through its phase space, the volume it occupies remains constant. This conservation is related to the principle of conservation of energy, where the total energy of the system is constant.

Conclusion:
- In summary, the number of coordinates in the phase space of a single particle is 6. These coordinates include three position coordinates (x, y, z) and three momentum coordinates (px, py, pz). These coordinates describe the position and momentum of the particle in three-dimensional space and allow for the representation of all possible states of the particle.