Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain what rotational inertia measures and why it depends on both mass and the distribution of mass about the axis. (Guide: “Resistance to changes in rotation”)
- I can explain why a hoop has twice the rotational inertia of a disk with the same mass and radius. (Guide: “Why a hoop beats a disk”; Practice Q3)
- I can explain why I is smallest about an axis through the centre of mass. (Guide: “The parallel axis theorem”; Worked example 1)
Calculation and derivation
- I can calculate I = Σmr² for small objects, using the perpendicular distance to the axis. (Guide: Worked example 1; Practice Q1)
- I can derive I for a uniform rod about any perpendicular axis by integration, including ML²/12 and ML²/3. (Guide: “Deriving the standard results”; Practice Q4)
- I can derive I for a rod with a nonuniform λ(x), and find its centre of mass. (Guide: Worked example 2; Practice Q7)
- I can derive I for a thin cylindrical shell, a disk and an annular ring by adding coaxial rings, and check the limiting cases. (Guide: “Deriving the standard results”; Practice Q5)
- I can use I = I_cm + Md², always starting from the centre-of-mass axis. (Guide: Worked example 2; Practice Q2, Q7)
Graphs and reasoning
- I can compare rotational inertias of objects with the same mass but different mass distributions without calculating. (Guide: Figure 2, Worked example 3; Practice Q3)
- I can linearise data with a graph of I against r² and read the mass and the fixed part of I from it. (Guide: “Linking to experiments”; Practice Q6)
- I can explain why a mistaken use of the parallel axis theorem between two off-centre axes gives the wrong answer. (Practice Q7(d))
All ticked? Move on to Topic 5.5, Rotational Equilibrium and Newton’s First Law in Rotational Form, or return to the course roadmap.