The minimum number of coordinates required to specify the motion of a particle or system of particles is known as the degrees of freedom (DOF). The DOF represents the number of independent parameters needed to describe the position and orientation of the system at any given time.
For a single particle moving in three-dimensional space, three coordinates (such as x, y, and z) are required to specify its position. Therefore, a single particle typically has three degrees of freedom.
In a system of multiple particles, the total number of degrees of freedom depends on the number of particles and the constraints acting on the system. Each particle contributes three degrees of freedom for its position. However, the degrees of freedom can be constrained due to inter-particle interactions, external forces, or geometric restrictions.
For example, if particles in a system are connected by rigid rods or are confined to move on a specific surface, these constraints can reduce the number of degrees of freedom. In such cases, the total number of degrees of freedom is given by 3N - C, where N is the number of particles and C is the number of constraints.
It's important to note that the concept of degrees of freedom becomes more complex in certain situations, such as when considering rotational motion or quantum mechanics. The above explanation provides a simplified understanding applicable to classical mechanics and basic systems of particles.