2.1 Systems and Center of Mass

• 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
• $\vec{r}_{CM}$ 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