Rolling

A rolling object has kinetic energy in two places at once: its forward motion ($K_\text{trans}$) and its spin ($K_\text{rot}$). For pure rolling, $v_\text{cm} = R\,\omega$ ties them together, and static friction does no work because the contact point is instantaneously at rest. Get those three facts right and incline-race problems collapse to one equation: $v_\text{cm} = \sqrt{2gh / (1 + \beta)}$, with the shape factor $\beta$ doing all the work.

Three traps wait here. One: treating $v_\text{cm} = R\,\omega$ as if it always holds. It's a condition, not a law, and it fails the moment the wheel slips. Two: computing a rolling object's kinetic energy as $\tfrac{1}{2}Mv^2$ and forgetting the rotational piece. For a solid sphere, that misses about 29% of the total. Three: assuming static friction always drains energy. In pure rolling, it does no work, because the point where it acts is instantaneously at rest.