Question

Which one of the following is equivalent to the law of conservation of angular momentum ?

• A. Kepler's first law
• B. Kepler's second law
• C. Kepler's third law
• D. Newton's first law

Hint:

Central forces (like gravity or electrostatic force) always conserve angular momentum because the force vector always passes through the center of rotation, creating no torque.

Answer 1

The Correct Option is B

Concept: Kepler's Second Law (The Law of Areas) states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

Step 1: Relate Areal Velocity to Angular Momentum.
The areal velocity $\frac{dA}{dt}$ is given by: \[ \frac{dA}{dt} = \frac{L}{2m} \] Where $L$ is the angular momentum and $m$ is the mass of the planet.

Step 2: Apply Conservation.
Since gravity is a central force, the torque acting on the planet with respect to the Sun is zero ($\vec{\tau} = \vec{r} \times \vec{F} = 0$). Because torque is zero, angular momentum $L$ must be conserved (constant). If $L$ is constant, then $\frac{dA}{dt}$ is also constant, which is exactly what Kepler's Second Law describes.