Axis Theorems

Parallel axis & perpendicular axis.

Concept

Axis Theorems is a foundational idea in this chapter. The defining relationship is:

$I_d = I_{\rm cm} + Md^2; \quad I_z = I_x + I_y$

Perpendicular axis theorem applies only to planar bodies.

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 $I_d = I_{\rm cm} + Md^2; \quad I_z = I_x + I_y$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.