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EEJ MAIN Physics QUESTION #7067
Question 1
A planet of mass $m$ moves in a circular orbit around the Sun. If its angular momentum about the center of the Sun is $L$, determine its areal velocity.
  • $\frac{L}{m}$
  • $\frac{4L}{m}$
  • $\frac{L}{2m}$✔️
  • $\frac{2L}{m}$
Correct Answer Explanation

Areal velocity is defined as the area swept by the position vector per unit time: $\frac{dA}{dt}$.

In polar coordinates, $dA = \frac{1}{2} r^2 d\theta$.
So, $\frac{dA}{dt} = \frac{1}{2} r^2 \frac{d\theta}{dt} = \frac{1}{2} r^2 \omega$.

Since angular momentum $L = m r^2 \omega$, we can substitute $r^2 \omega = \frac{L}{m}$.

Therefore, $\text{Areal Velocity} = \frac{1}{2} \left( \frac{L}{m} \right) = \frac{L}{2m}$.