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.