Textbooks state: conservation of energy, conservation of momentum, and conservation of angular momentum are equal in status.
They arise from Noether’s theorem, corresponding respectively to the symmetries of time translation, space translation, and spatial rotation.

In my view, they possess a clear hierarchy:
Energy > Angular Momentum > Momentum.

This is not a mathematical derivation, nor an experimental conclusion. It is a worldview.
I lay it out not to persuade others, but because I have seen it, and so I write it down.

 

I. Momentum: One‑dimensional, the lowest level

Momentum corresponds to spatial translation. Push an object, and it moves in a direction—that is momentum.

But it tells only so much.
It does not care whether the object is rotating, whether it vibrates internally, whether it moves straight or curves.
High momentum means the center of mass moves fast; low momentum means it moves slowly. That is all.

From the perspective of energy flow, momentum describes the net flux of energy flow—how much energy is transported from one place to another per unit time, and in which direction.

It is one‑dimensional. It governs only a straight line.
This is the most basic level of information.

 

II. Angular Momentum: Two‑dimensional, the intermediate level

Angular momentum corresponds to spatial rotation.
A spinning top, Earth orbiting the Sun, an electron circling an atomic nucleus—angular momentum is at work.

Why is it one level higher than momentum?
Because it inherently involves two dimensions.

The formula for angular momentum is position cross momentum.
The cross product does not exist in a one‑dimensional line.
You must have a plane, a line revolving around a point, for angular momentum to exist.

Angular momentum also has a geometric character: it describes the area swept per unit time.
Kepler’s second law, stating that a planet sweeps out equal areas in equal times, is exactly conservation of angular momentum.

From the perspective of energy flow, angular momentum describes the curvature of energy flow.
The same energy flowing straight is momentum; flowing in a curve is angular momentum.

It is two‑dimensional.
It adds a geometric constraint and an extra structure.

 

III. Energy: Scalar, the highest level

Energy corresponds to time.
In my definition, time itself is the flow of energy, so energy occupies the highest level.

Why?

You can ignore momentum—the center of mass of a system can be completely stationary, with zero momentum.
You can ignore angular momentum—it may not rotate at all, with zero angular momentum.

But you cannot ignore energy.
As long as the system exists, as long as time passes, energy must be undergoing local transfer.
Or rather, the very fact that energy is transferring is time itself.

In an isolated system, energy is conserved, but momentum can be zero and angular momentum can be zero.
Energy is always the nonzero foundation.

From the perspective of energy flow:
Energy is the substance of the flow; momentum and angular momentum are merely modes of the flow.

This is my hierarchy.
It will not appear in physics textbooks, but it belongs in my worldview.