Explicit physics instruction
Center of mass is a weighted average of position using mass as the weighting factor. For point masses on one axis, x_cm=Σm_ix_i/Σm_i.
The center of mass can lie between objects or, for extended/irregular systems, even in empty space. It is a system-level coordinate, not necessarily the location of any one particle.
For translational motion, the center of mass responds to net external force as if the system mass were concentrated there.
Vocabulary: center of mass; weighted average; system coordinate; external force; symmetry.
Worked example with reasoning
Two masses, 2 kg at x=0 m and 4 kg at x=6 m, have x_cm=(2·0+4·6)/(6)=4 m.
Guided question
Where is the center of mass for 1 kg at x=0 m and 3 kg at x=8 m? Explain why it lies closer to the heavier mass.
Independent work
- Solve four one-dimensional center-of-mass problems.
- Use symmetry to predict one answer before calculating.
- Draw a mass-position diagram for each.
Misconception check
Center of mass is not always the geometric midpoint; mass distribution matters.
Formative understanding check
What shifts center of mass toward one side?
Reveal response
More mass located on that side, or mass positioned farther in that direction.
Mentor evidence conference
Ask Archaemenes to challenge model choice, stage boundaries, and residual interpretation.
Teacher guidance
Foundation: Use a weighted-average organizer.
Core: Calculate and interpret center of mass.
Extended: Extend to three-object systems and compare with geometric center.