Nano PHYSICS . MECHANICS . MOMENTUM AND COLLISIONS . EXPLOSIONS AND RECOIL

Center-of-Mass Analysis

The center-of-mass frame simplifies breakup problems and highlights symmetry. Use COM velocity before and after, total momentum zero in the COM frame, and vector momentum in 2D breakups.

Physics · Mechanics · Momentum and Collisions · Explosions and Recoil · Center-of-Mass Analysis
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: center-of-mass analysis
Free
Establish explosions and recoil as internal-force interactions where momentum can remain conserved.
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Goal: define explosion and recoil using system momentum, internal forces, and released internal energy.
STEP 2
Conceptual grounding: build the explosion-and-recoil model
Free
Build a workflow for systems, external impulse, signs, mass ratios, kinetic-energy changes, and COM motion.
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Goal: use conservation of momentum to analyze breakups and recoil when external impulse is negligible.
STEP 3
Real-world connection: interpret fragment motion and COM motion
Free
Apply explosion and recoil reasoning to springs, skaters, rifles, fragments, fireworks, and projectile breakups.
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Goal: explain fragment motion, recoil speed, kinetic-energy increase, COM motion, and two-dimensional breakup in physical contexts.
STEP 4
Check your understanding: diagnostic mini-quiz
Paid
Attempt each question before revealing the explosion-and-recoil reasoning.
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Goal: identify and correct internal-force, external-impulse, recoil-sign, mass-ratio, COM-frame, and vector-component errors before they become calculation errors.
STEP 5
Practice: solve increasingly rich explosion and recoil situations
Paid
Apply the model to situations that grow in complexity.
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Goal: write concise, physically justified explosion and recoil calculations and explanations.
STEP 6
Summary & reflection + explorations
Paid
Consolidate the model and explore changing masses, stored energy, frames, dimensions, and external forces.
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🔒 ▶ Explore interactive simulation
Goal: carry the model forward into collision reversal, center-of-mass frames, two-dimensional momentum, recoil systems, and realistic breakups.