Nano PHYSICS . MECHANICS . MOMENTUM AND COLLISIONS . CENTER OF MASS

COM for Continuous Systems

For continuous systems, replace sums with integrals. Learn the density idea, line, area, and volume mass distributions, and the setup strategy.

Physics · Mechanics · Momentum and Collisions · Center of Mass · COM for Continuous Systems
Access for this nano-lesson
Unsigned visitors can show & copy prompts for Steps 1-3. Signed-in free accounts can also Run with AI for Steps 1-2. Paid accounts unlock everything (Steps 1-6 + Help prompts + AI).
Steps 1-3 Free Steps 4-6 Paid
STEP 1
Orient: com for continuous systems
Free
Establish center of mass as a mass-weighted vector position for a chosen system.
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Goal: define center of mass using mass weighting, vector position, and physical intuition.
STEP 2
Conceptual grounding: build the center-of-mass model
Free
Build a workflow for discrete particles, continuous objects, coordinates, components, density, and symmetry.
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Goal: choose the correct discrete, continuous, or symmetry-based setup.
STEP 3
Real-world connection: interpret mass distributions and symmetry
Free
Apply center-of-mass reasoning to particles, rods, plates, composite objects, and balance intuition.
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Goal: explain component methods, density integrals, composite objects, and symmetry shortcuts in physical contexts.
STEP 4
Check your understanding: diagnostic mini-quiz
Paid
Attempt each question before revealing the center-of-mass reasoning.
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Goal: identify and correct ordinary-average, coordinate, component, density, and symmetry errors before they become calculation errors.
STEP 5
Practice: solve increasingly rich center-of-mass situations
Paid
Apply the model to situations that grow in complexity.
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Goal: write concise, physically justified center-of-mass calculations and explanations.
STEP 6
Summary & reflection + explorations
Paid
Consolidate the model and explore changing masses, positions, symmetry, density, and system choices.
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🔒 ▶ Explore interactive simulation
Goal: carry the model forward into system motion, collisions, momentum conservation, and extended-body reasoning.