Mistake 1 — Applying the perpendicular axis theorem to 3D bodies. The perpendicular axis theorem ($I_z = I_x + I_y$) is valid only for planar (flat, 2D) objects. Never use it for a solid sphere, hollow sphere, or cylinder. If you see a sphere in the question and reach for this theorem, stop.

Mistake 2 — Forgetting to add $Md^2$ in the parallel axis theorem. When computing I about a tangent or any off-CM axis, students often write down $I_{cm}$ and stop. Always add the $Md^2$ displacement term. Example: $I_{tangent,\,disc} = MR^2/4 + MR^2 = 5MR^2/4$, not $MR^2/4$.

Mistake 3 — Assuming the fastest rolling body has the largest mass or radius. The incline acceleration $a = g\sin\theta/(1 + K^2/R^2)$ is completely independent of mass $M$ and radius $R$. Only the shape (via $K^2/R^2$) matters. This is one of the most frequently exploited traps in NEET MCQs.

Mistake 4 — Confusing kinetic energy conservation with angular momentum conservation. When a skater pulls in her arms, angular momentum $L$ is conserved but kinetic energy increases (from muscular work). Never say "energy is conserved" in an angular momentum problem unless explicitly told the system is closed and no work is done.

Mistake 5 — Using $v = \omega R$ when rolling is not specified. The constraint $v_{cm} = \omega R$ holds only for rolling without slipping. If the problem says "slides without rolling" or does not specify, you cannot use this relation.

Mistake 6 — Wrong CM position for semicircular bodies. Semicircular ring: $2R/\pi$ (about 0.64R). Semicircular disc: $4R/3\pi$ (about 0.42R). These are different — confusing them is a common error. Both are measured from the centre of the full circle.