A particle with position vector $\overrightarrow{\mathrm{r}}$ has a linear momentum…
A particle with position vector $\overrightarrow{\mathrm{r}}$ has a linear momentum $\overrightarrow{\mathrm{p}}$. Which one of the following statements is true in respect of its angular momentum ' $\overrightarrow{\mathrm{L}}$ ' about the origin?
$\overrightarrow{\mathrm{L}}$ acts along $\overrightarrow{\mathrm{P}}$
$\overrightarrow{\mathrm{L}}$ is maximum when $\overrightarrow{\mathrm{P}}$ is perpendicular to $\overrightarrow{\mathrm{r}}$
$\overrightarrow{\mathrm{L}}$ acts along $\overrightarrow{\mathrm{r}}$
$\overrightarrow{\mathrm{L}}$ is maximum when $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{r}}$ are parallel
Solution
The angular momentum of the particle is given by $\overrightarrow{\mathrm{L}}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}}$
Its magnitude is $\mathrm{L}=\mathrm{rp} \sin \theta$
$\mathrm{L}$ will be maximum when $\theta=90^{\circ}$