2.1 Systems and Center of Mass
- Syllabus
- 2024
- Topic
- 2.1
- Level
- —
Learning objectives
2.1A—Describe the properties and interactions of a systemDescribe 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.2.1B—Describe the location of a system’s center of mass with respect to the system’s constituent partsDescribe 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.
2.1.A—Describe the properties and interactions of a system
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.
2.1.B—Describe the location of a system’s center of mass with respect to the system’s constituent parts
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.