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  4. If A is the areal velocity of a planet of mass M , then its angular momentum about the centre of the circular orbit is

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Q. If $A$ is the areal velocity of a planet of mass $M$ , then its angular momentum about the centre of the circular orbit is

NTA AbhyasNTA Abhyas 2022

Solution:

Areal velocity is area swept per unit time.
$A=\frac{\frac{1}{2} r \left(r d \theta \right)}{d t}=\frac{1}{2}r^{2}\frac{d \theta }{d t}=\frac{1}{2}r^{2}\omega =\frac{1}{2}\frac{\left(M r^{2}\right) \omega }{M}=\frac{L}{2 M}$
$\Rightarrow L=2MA$