2.1 Systems and Center of Mass

Cards (21)

  • What is a physical system in the context of mechanics?
    A collection of objects studied
  • Why is defining the boundaries of a physical system important?
    To include relevant objects
  • Match the system with its center of mass location:
    Uniform rod ↔️ At the midpoint of the rod
    Uniform sphere ↔️ At the center of the sphere
    Uniform circular disk ↔️ At the center of the disk
  • The center of mass is the point around which a system's mass is evenly distributed.

    True
  • The center of mass is the point where a system's weight is concentrated.
    False
  • Match the system with its center of mass formula:
    Uniform rod ↔️ At the midpoint of the rod
    Uniform rectangular plate ↔️ At the geometric center of the plate
    Uniform sphere ↔️ At the center of the sphere
    Uniform circular disk ↔️ At the center of the disk
  • What formula is used to calculate the center of mass of a continuous system?
    \vec{r}_{CM} = \frac{1}{M} \int \vec{r} \, dm</latex>
  • The center of mass is the point where the system's mass is concentrated
  • The center of mass simplifies the analysis of a system's motion
  • Where is the center of mass of a uniform rectangular plate located?
    At the intersection of diagonals
  • What is a physical system in the context of mechanics?
    A collection of objects
  • What is the center of mass of a physical system?
    The point where mass is concentrated
  • For a uniform rod, all the mass can be treated as if it is concentrated at its midpoint
  • rCM\vec{r}_{CM} in the center of mass formula represents the position vector of the center of mass.

    True
  • For a uniform rod, the center of mass is located at its midpoint.

    True
  • The center of mass of a uniform sphere is at its surface.
    False
  • For a uniform circular disk, the center of mass is at the center of the circle
  • Defining the boundaries of a physical system is important because it determines which objects and forces are included in the analysis
  • For a uniform rod, the center of mass is located at the rod's midpoint
  • Where is the center of mass of a uniform circular disk located?
    At the center of the circle
  • To find the total mass of a non-uniform rod, we integrate its mass density over its length