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 why a spinning body has kinetic energy even when its centre of mass is at rest and its momentum is zero. (Guide: “Kinetic energy with the centre of mass at rest”)
- I can explain why ½Iω² for a fixed axis is the sum of the ordinary kinetic energies of all the pieces, not extra energy. (Guide: “From ½v² dm to ½Iω²”)
- I can explain why rotational kinetic energy is a scalar that is never negative, and why opposite spins add. (Guide: “A scalar, never negative”)
Calculation
- I can derive K = ½Iω² by integrating ½v² dm with v = rω. (Guide: “From ½v² dm to ½Iω²”; Practice Q7(a))
- I can find the kinetic energy of a rod with non-uniform density by integration. (Guide: Worked example 1; Practice Q4)
- I can find ω from θ(t) by differentiating and then calculate K, with ω in rad/s. (Practice Q1)
- I can calculate the total kinetic energy of a body that moves and spins, using I about the centre of mass. (Guide: Worked example 2; Practice Q5)
- I can show that ½I_pivot ω² equals ½Mv_cm² + ½I_cm ω² using the parallel axis theorem. (Guide: “A fixed axis that is not through the centre of mass”; Practice Q2)
Reasoning
- I can prove that the translation-plus-rotation split has no cross term, for a dumbbell or in general. (Guide: “Why the split works”; Practice Q5)
- I can sketch K against ω, t or θ for a rotating body and explain each shape. (Guide: Figure 2 and “Graphs and comparisons”; Practice Q3)
- I can compare the kinetic energies of two bodies, such as a hoop and a disc, and say when “more mass far from the axis” means more energy. (Practice Q7)
- I can analyse falling-mass data to find a rotational inertia and say how friction biases the result. (Practice Q6)
All ticked? Move on to Topic 6.2, Torque and Work, or return to the course roadmap.