Rotational Motion Part 3

Concept:Vectors are classified into polar and axial types based on their behavior under coordinate inversion.Polar vectors (e.g., position, force) flip their sign: $\vec{A} \to -\vec{A}$.Axial vectors (e.g., angular momentum) do not flip under sign change.Explanation:Option A: Velocity is $\vec{v} = \frac{d\vec{r}}{dt}$.If the position vector changes sign to $-\vec{r}$, then velocity becomes $\frac{d(-\vec{r})}{dt} = -\vec{v}$.So it flips. It is a polar vector.Option B: Linear momentum is $\vec{p} = m\vec{v}$.Since $\vec{v}$ flips to $-\vec{v}$, momentum becomes $m(-\vec{v}) = -\vec{p}$.So it flips. It is a polar vector.Option C: Acceleration is $\vec{a} = \frac{d\vec{v}}{dt}$.Since $\vec{v}$ flips to $-\vec{v}$, acceleration becomes $\frac{d(-\vec{v})}{dt} = -\vec{a}$.So it flips. It is a polar vector.Option D: Angular momentum is $\vec{L} = \vec{r} \times \vec{p}$.Applying the sign change to both $\vec{r}$ and $\vec{p}$: $\vec{L}' = (-\vec{r}) \times (-\vec{p})$.The product of two negatives cancels out: $\vec{L}' = \vec{r} \times \vec{p} = \vec{L}$.So it does not flip. It is an axial vector.Answer:The correct option is (D), Angular momentum.