Pure Rolling

v_cm = ωR.

Concept

Pure Rolling is a foundational idea in this chapter. The defining relationship is:

$v_{\rm cm} = \omega R, \quad a_{\rm cm} = \alpha R$

Total KE = ½mv² + ½Iω²; for incline: a = gsinθ/(1+k²/R²).

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 $v_{\rm cm} = \omega R, \quad a_{\rm cm} = \alpha R$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.