Glossary
Center of Mass (COM)
The average position of all the mass in a system, representing the point where the entire mass of the system can be considered to be concentrated for analyzing its motion.
Example:
When a gymnast performs a flip, their body rotates around their center of mass, even as their overall trajectory follows a parabolic path.
Center of Mass Calculation Formula
A mathematical equation used to determine the position of the center of mass for a system of discrete particles or a continuous object.
Example:
Using the center of mass calculation formula, you can find the balance point of a barbell by considering the masses and positions of its weights.
Emergent Properties
Properties of a system that arise from the interactions of its individual parts, rather than being properties of the parts themselves.
Example:
The collective 'wave' created by fans in a stadium is an emergent property of individual fans standing and sitting in sequence.
Energy and Mass Transfer (in Systems)
The exchange of energy (e.g., heat, work) and/or mass between a system and its surrounding environment.
Example:
A boiling pot of water demonstrates energy and mass transfer as heat moves from the stove to the water, and steam (mass) escapes into the air.
External Variables
Factors outside a system that can influence its internal structure, dynamics, and overall behavior.
Example:
The temperature of the room is an external variable that can affect the rate at which ice melts in a glass.
Individual vs. System Behavior
The concept that the behavior of individual components within a system can be different from the collective behavior of the system as a whole.
Example:
While individual water molecules in a river move chaotically, the river as a system exhibits a smooth, directed flow.
Internal Structure Effects
The principle that the arrangement and connections of a system's components significantly influence its overall properties and behavior.
Example:
The strength and flexibility of a bridge are highly dependent on its internal structure effects, such as the design of its trusses and the materials used.
Macroscopic Modeling
A simplification technique where a complex system is treated as a single object, ignoring its internal details, when those details are not crucial for understanding its overall behavior.
Example:
When calculating the trajectory of a thrown football, we often use macroscopic modeling by treating it as a single point mass, ignoring the complex air currents around its surface.
Symmetrical Objects (COM)
For objects with uniform density and geometric symmetry, the center of mass is located precisely on their lines or planes of symmetry.
Example:
The center of mass of a perfectly balanced, uniform meter stick is exactly at its 50 cm mark due to its symmetry.
System
A collection of objects or particles that are grouped together for the purpose of analysis, often interacting with each other and their environment.
Example:
A car, its engine, and its wheels can be considered a system when analyzing its overall motion on a road.
Systems as Single Objects
The analytical approach of representing a complex system as a single point mass located at its center of mass, simplifying the analysis of its overall translational motion.
Example:
When analyzing the flight path of a rocket, physicists often treat it as a system as a single object located at its center of mass to simplify trajectory calculations.