Glossary
Center of Mass
The unique point where the weighted average of the positions of all the parts of a system resides, representing the average position of the total mass.
Example:
When a diver performs a somersault, their center of mass follows a parabolic trajectory, even as their body rotates.
Closed System
A system that allows energy transfer but not mass transfer with its surroundings.
Example:
A sealed, uninsulated container of gas undergoing compression is a closed system as work (energy) can be done on it, but no gas (mass) enters or leaves.
Emergent Properties
Properties of a system that arise from the collective interactions of its individual components, which are not present in the components themselves.
Example:
The ability of a flock of birds to move as a coordinated unit is an emergent property that isn't present in any single bird.
External Variables
Factors or conditions outside a system that can influence its internal structure, properties, and behavior.
Example:
Increasing the ambient temperature is an external variable that can cause a metal rod to expand.
Isolated System
A system that does not exchange either energy or mass with its environment.
Example:
In an ideal scenario, the entire universe can be considered an isolated system since there's nothing outside of it to exchange energy or mass with.
Linear Mass Density (λ)
A measure of how much mass is contained per unit length along a one-dimensional object, often used for rods or wires.
Example:
For a non-uniform rod, the linear mass density might vary along its length, meaning some sections are heavier per meter than others.
Open System
A system that can exchange both energy and mass with its surroundings.
Example:
A boiling pot of water on a stove is an open system because heat (energy) is transferred to it, and steam (mass) escapes into the air.
Symmetrical Mass Distributions
Objects or systems where mass is distributed evenly around one or more axes or planes, causing the center of mass to lie on the lines of symmetry.
Example:
A perfectly uniform sphere has a symmetrical mass distribution, so its center of mass is exactly at its geometric center.
System
A defined collection of objects or components that interact with each other and potentially with their surroundings.
Example:
When analyzing the motion of a rocket, we can define the rocket itself, its fuel, and exhaust gases as a single system.
Volume Mass Density (ρ)
A measure of how much mass is contained per unit volume within a three-dimensional object, indicating the compactness of its mass.
Example:
The volume mass density of lead is much higher than that of aluminum, meaning a given volume of lead contains more mass.