Clarification on angular momentum

[tryingtolearn1]

Homework Statement

Conceptual clarification between two questions

Relevant Equations

Angular momentum

I am confused with the following two questions:

1. A particle moves under the influence of a central force directed toward a fixed origin $O$. Explain why the particle's angular momentum about $O$ is constant.

2. Consider a planet orbiting the fixed sun. Take the plane of the planet's orbit to be the $xy$ plane, with the sun at the origin, and label the planet's position by polar coordinates $(r,\phi)$. Show that the planet's angular momentum has magnitude $l = mr^2\omega$ , where $\omega =\dot{\phi}$ is the planet's angular velocity about the sun.

These two questions both have a particle that moves under the influence of a central force but conceptually why is the first question a constant but the second question is not a constant?

 

[PeroK]

Homework Statement:: Conceptual clarification between two questions
Relevant Equations:: Angular momentum

I am confused with the following two questions:

1. A particle moves under the influence of a central force directed toward a fixed origin $O$. Explain why the particle's angular momentum about $O$ is constant.

2. Consider a planet orbiting the fixed sun. Take the plane of the planet's orbit to be the $xy$ plane, with the sun at the origin, and label the planet's position by polar coordinates $(r,\phi)$. Show that the planet's angular momentum has magnitude $l = mr^2\omega$ , where $\omega =\dot{\phi}$ is the planet's angular velocity about the sun.

These two questions both have a particle that moves under the influence of a central force but conceptually why is the first question a constant but the second question is not a constant?

The second equation involves the constant angular momentum $l$. This tells you that, although $r$ and $\dot \phi$ separately are not constant, their product $r^2 \dot \phi$ must be constant.

The argument expressed in points 1 and 2 is fundamental to physics.