When the position vector $\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$ changes sign as $-\vec{r}$, which o

Question

When the position vector $\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$ changes sign as $-\vec{r}$, which one of the following vector will not flip under sign change?

Professor PC Thomas Classes · Answer

Under a parity inversion or sign change where $\vec{r} 	o -\vec{r}$, vectors like velocity ($\vec{v} = \frac{d\vec{r}}{dt}$), acceleration ($\vec{a} = \frac{d\vec{v}}{dt}$), and linear momentum ($\vec{p} = m\vec{v}$) also change their signs. However, angular momentum is defined as a cross product $\vec{L} = \vec{r} 	imes \vec{p}$. Under the transformation, $\vec{L}' = (-\vec{r}) 	imes (-\vec{p}) = \vec{r} 	imes \vec{p} = \vec{L}$. As a pseudovector, angular momentum does not flip its sign.