JEE Main 2026 — Rotational Motion Question with Solution

The transformation $\vec{r}\to -\vec{r}$ is known as a parity transformation (inversion through the origin).
Vectors that change sign under parity are called polar vectors, while those that do not change sign are called axial vectors (or pseudovectors).
Velocity is defined as $\vec{v}=\frac{d\vec{r}}{dt}$. Since $\vec{r}\to -\vec{r}$, we have $\vec{v}\to -\vec{v}$.
Acceleration is defined as $\vec{a}=\frac{d\vec{v}}{dt}$. Since $\vec{v}\to -\vec{v}$, we have $\vec{a}\to -\vec{a}$.
Linear momentum is defined as $\vec{p}=m\vec{v}$. Since $\vec{v}\to -\vec{v}$, we have $\vec{p}\to -\vec{p}$.
Angular momentum is defined as $\vec{L}=\vec{r}\times \vec{p}$.
Under the transformation $\vec{r}\to -\vec{r}$ and $\vec{p}\to -\vec{p}$, the cross product becomes:
${\vec{L}}^{\prime }=(-\vec{r})\times (-\vec{p})=\vec{r}\times \vec{p}=\vec{L}$.
Thus, angular momentum does not flip its sign under the transformation $\vec{r}\to -\vec{r}$.