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What are the steps to calculate the center of mass ($x_{cm}$) along an axis for discrete objects?
1. Identify the mass ($m_i$) and position ($x_i$) of each object. 2. Calculate the sum of ($m_i * x_i$) for all objects. 3. Calculate the sum of all masses ($m_i$). 4. Divide the sum of ($m_i * x_i$) by the sum of the masses.
What is the difference between individual component behavior and system behavior?
Individual components may behave differently from each other and the system as a whole. System behavior considers the collective interaction.
What is the difference between energy transfer and mass transfer in systems?
Energy transfer involves the exchange of energy with the surroundings (e.g., heat). Mass transfer involves the exchange of matter with the surroundings (e.g., evaporation).
What is the definition of 'center of mass'?
The average position of all the mass in a system.
Define 'system' in the context of physics.
A collection of objects whose interactions we are studying.
What are 'emergent properties'?
System properties that arise from the interactions of its parts.
What is macroscopic modeling?
Treating a system as a single object when internal details are unimportant.
Define 'lines of symmetry'.
Imaginary lines where if folded along it, the two halves of the object match exactly.