Question 219 of 223

If the angular momentum of a planet of mass $m,$ moving around the Sun in a circular orbit is $L,$ about the center of the Sun, its areal velocity is:

A$\dfrac{L}{m}$B$\dfrac{4L}{m}$C$\dfrac{L}{2m}$D$\dfrac{2L}{m}$

Show answer and solution▾

Answer: (C) $\dfrac{L}{2m}$

$\vec{dA}=\dfrac{1}{2}\vec{r}\times \vec{v}dt$

$\dfrac{d\vec{A}}{dt}=$ areal velocity $=\dfrac{1}{2}\vec{r}\times \vec{v}$

$=\dfrac{1}{2}\dfrac{\vec{r}\times m\vec{v}}{m}=\dfrac{1}{2m}L$

$\dfrac{dA}{dt}=\dfrac{L}{2m}$

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