2.1 Systems and Center of Mass

Describe the properties and interactions of a system.

• System properties are determined by the interactions between objects within the system.
• If the properties or interactions of the constituent objects within a system are not important in modeling the behavior of the macroscopic system, the system can itself be treated as a single object.
• Systems may allow interactions between constituent parts of the system and the environment, which may result in the transfer of energy or mass.
• Individual objects within a chosen system may behave differently from each other as well as from the system as a whole.
• The internal structure of a system affects the analysis of that system.
• As variables external to a system are changed, the system’s substructure may change.

Describe the location of a system’s center of mass with respect to the system’s constituent parts.

• For objects or systems with symmetrical mass distributions, the center of mass is located on lines of symmetry.
• The location of a system’s center of mass along a given axis can be calculated using the equation .
• For a nonuniform solid that can be considered as a collection of differential masses, dm, the solid’s center of mass can be calculated using the equation
  • i. The linear mass density of a rod or other linear rigid body is the derivative of the rod’s mass with respect to the position of the differential mass element on the rigid body. Relevant equation:
  • ii. If a function of mass density is given for a solid, the total mass can be determined by integrating the mass density over the length (one dimension), area (two dimensions), or volume (three dimensions) of the solid. For example:
• A system can be modeled as a singular object that is located at the system’s center of mass.