Table of Contents
Rotation, spin and revolution
Terminology
https://1notes1.blogspot.com/2022/08/rotation-and-revolution.html
- I reserve the word “rotation” for the rotation of a solid disk, or a spinning top, or a whirling sling. These are motions where all rotating points have the same angular velocity. Rotational motion obeys the radian rule.
- I reserve the word “revolution” for orbital motion. Since orbital motion obeys Kepler’s Rule (not the radian rule), objects revolving at different radii, have different angular velocities.
- This means that, a formula such as \[a=\frac{v^2}{r}\] which is valid for rotation will not be valid for revolutions.
- But Newton and his disciples assume that rotation and revolution are the same motion and they build their theory of orbital motion on this similarity. This is why they claim that orbital motion must be dynamical and forceful.
- But orbital revolution is circular inertia, as Galileo thought.
https://leanpub.com/densytics/read#leanpub-auto-how-did-newton-spin-rotation-into-orbits
Newton’s use of \(v^2/r\)
- \(v^2/r\) is the centrifugal acceleration, outward tendency of the rotating object.
- But \(v^2/r\) is simply \(r/t^2\)
in other words, \(v^2/r\) is simply half of Kepler’s Rule, \(r/t^2=1/r^2\). Half of Kepler’s Rule is not Kepler’s Rule. This means that rotation obeys half of Kepler’s Rule, which means that, rotation is not orbital motion. Orbital motion obeys Kepler’s Rule, \(t^2\propto r^3\) or \(r/t^2=1/r^2\).
=>THE ABOVE IS OBVIOUSLY WRONG<=
Rotation, revolution and spin
- Chatgpt explains it well
- The difference is where is the axis of rotation is located, inside the rotating object or outside
chatgpt
Yes, there are meaningful differences between spin, rotation, and revolution, although they all involve an object moving around an axis or a point. Here’s how they differ:
1. Spin
- Spin specifically refers to an object rotating around its own internal axis.
- The axis of spin is usually within the object, like the axis running through the Earth’s poles.
- Example: Earth spins on its own axis, causing day and night. Similarly, a basketball spinning on a finger is spinning around its internal axis.
2. Rotation
- Rotation is a more general term and can apply to any turning movement around an axis, which could be internal (like spin) or external.
- The term “rotation” is sometimes used interchangeably with spin, but it’s broader. For example, it includes cases where an object might rotate around an external point.
- Example: When discussing the Earth’s daily motion around its own axis, we sometimes refer to it as “rotation” (and specifically as a “spin” when emphasizing that it’s around an internal axis).
3. Revolution
- Revolution refers to the motion of an object around an external point or another object.
- It describes the path an object takes around something else, usually following a circular or elliptical orbit.
- Example: The Earth’s yearly path around the Sun is a revolution. Similarly, the Moon revolves around Earth. In both cases, they are moving around an external point rather than their own internal axis.
Summary of Key Differences
- Spin: Rotation around an object’s own axis (internal).
- Rotation: General term for turning around an axis, either internal or external.
- Revolution: Movement around an external point or object (often in an orbit).
Examples in Astronomy
- Earth’s spin: Earth spinning on its axis every 24 hours (internal axis).
- Earth’s revolution: Earth orbiting (revolving) around the Sun every 365.25 days (external point).
- The Moon’s motion: The Moon rotates (spins) on its own axis and revolves around the Earth.
So, while all three involve turning or movement along an axis, spin is specifically around an internal axis, revolution around an external point, and rotation is the general term that can refer to either.
Naming conventions for spin-type motion
chatgpt
We say “rotation-al” motion but we cannot say “spin-al” motion because “spinal” means related to spine. Suggest a word for spin-type motion
You’re right! “Spin-al” would indeed be confusing due to its association with the spine. Here are some alternative terms that could convey the concept of “spin-type motion”:
- “Axial motion” – Since spinning involves rotation around an internal axis, this term emphasizes the axis at the center of the object’s motion. It could be a clean and technical way to refer to spin-type motion.
- “Self-rotation” – This term highlights that the object rotates around its own axis, rather than around an external point.
- “Intrinsic rotation” – This conveys the idea that the rotation is inherent to the object itself, distinguishing it from external rotations or revolutions.
- “Gyro-motion” – Inspired by gyroscopes, which spin on their axes, this term could be adapted to refer to any spinning-type motion.
- “Spinward motion” – Borrowing from science fiction, “spinward” has sometimes been used to describe direction relative to a spinning object. It could also work as a term to describe spin-type motion.
Any of these terms could fit as an alternative to “spinal motion” for describing spin-type movements while keeping the focus on internal-axis rotation.
Gyroscope
- We also have this rotational motion that I need to check
- A gyroscope continues to rotate even when the input of energy is stopped
- And a gyroscope can rotate as if endlessly
Derivations of radial acceleration \(v^2/r\)
Descartes
Huygens
Newton
- Book 1, Proposition 4.
Vector method
Calculus method
Older textbooks
Two circles method
Everyone knows that spin and revolution are two different types of motion
- There are two types of rotational motion. One is spin where the axis of rotation is inside the rotating body. The sling motion is spin motion.
Figure 1: Spin
- We established that everyone agrees that spin and revolution are two different type of rotational motion.
- In spin the axis of rotation is insede the rotating body. The whole body rotates.
- As in the picture above the earth revolving around the sun describes an imaginary sphere. What is the volume of this sphere. I think I computed it. I need to find it. But what its relevance?
- But the axis \(AB\) and radius \(CD\) are imaginary also but when the earth rotates or spins the axis of rotation is inside the earth and it rotates and the radius of rotation is real too.
Figure 2: Radians motion
- You are forcing \(CE\) or \(C\) to cover more distance than \(B\). In unit distance \(B\) covers smaller distance than \(C\). So \(C\) must travel faster, right?
- So spin is forced motion because all points on the radius turn with different speed.
Figure 3: Rotation revolution
- Orbits are not spin motion because in orbital motion the integrity of the radius is not respected. This is because orbital motion obeys Kepler’s Rule.