Meaning and Conservation of Angular Momentum

Consider a particle A having linear momentum and radius vector with respect to the origin as given in the figure. After a time Dt, the particle is at B and the radius vector becomes + D.

The velocity of the particle has a radial component v_r and an angular component v_f. So pr and p_q are the radial and angular momenta,

This is the geometrical significance of angular momentum.

Sub Topics

Illustration
Kepler's second law

Illustration

Kepler's second law

In the case of a planet, moving around the sun in an elliptical orbit with the sun at one of the foci of the ellipse, the gravitational force always acts along the line joining the planet with the sun. Thus, the force is always radial or the angular component

of the force is always zero.

L = Angular momentum = constant

Hence, if angular momentum remains constant, areal velocity should also remain constant. Kepler's second law states that, area swept by the radius vector of the planet in equal intervals of time is same or in other words, areal velocity of the planet is constant.