Centre of Mass

R_cm = Σm_i r_i / Σm_i.

Concept

Centre of Mass is a foundational idea in this chapter. The defining relationship is:

$\vec R_{\rm cm} = (1/M)\sum m_i \vec r_i$

External force = M a_cm.

Worked Application

Apply the formula to a typical problem from your textbook. Identify the knowns, plug into the equation, and check that the units work out. Always sanity-check the magnitude before accepting an answer.

Common Confusions

• Confusing the variables in the formula — re-read the symbol definitions in the chapter.
• Forgetting unit conversions (cm vs m, g vs kg).
• Ignoring sign conventions where direction matters.

Key Takeaways

• Master the formula $\vec R_{\rm cm} = (1/M)\sum m_i \vec r_i$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.