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April 25
[edit]I always imagined that (fixed) velocity was relative but acceleration (change in velocity) absolute, and that rotation was absolute being just a case of acceleration, i.e. the parts of a rotating body are constantly changing (direction of) velocity, i.e. accelerating in the general sense. However the article Absolute rotation does not even mention the word acceleration, as far as I can see. Shouldn't it? Isn't this an "easy" explanation? 2A00:23C8:7B20:CC01:CC87:EAA5:618F:BEF8 (talk) 20:45, 25 April 2025 (UTC)
- It is true that the article Absolute rotation does not contain the word "acceleration". It also names Newton whose laws represent classical physics and states "From the necessary centrifugal force, one can determine one's speed of rotation;..." without explaining this use of Newton's 2nd law of motion. I agree that the article might be made more accessible if it did not assume that the general reader already knows classical Newtonian mechanics. Such improvement might be done by adding explanation as you suggest or by appropriate links to other articles. The place to propose your changes is Talk:Absolute_rotation. Philvoids (talk) 13:05, 26 April 2025 (UTC)
- Newtonian mechanic's accelerations are relative though, for the Galilean transformations preserve distances and time intervals, but, like the Lorentz transformations, these transformations do not preserve velocities and all accelerations. For example, consider a shipmate waving hello from a ship's bow to a beachcomber as their ship sails along the coastline and then the mate sprints to the ship's stern to wave goodbye. With respect to the ship's deck our mate first accelerated then decelerated, but from the stationary shore's reference frame they first decelerated to a slower speed and then accelerated (unless the ship slowed too) to match the ship's speed again. In short, all motion depends on reference frames, and this was true even in Newton's time when physicists speculated that motion could also be intrinsic and absolute, i.e. with respect to an absolute ether (e.g. Aether theories). Modocc (talk) 22:28, 30 April 2025 (UTC)
Graphical solution to conservation of linear momentum problems
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1. A 3 g ball moving south at 2 m/s collides with a 2 g ball moving northeast at √8 m/s. If the 2 g ball reverses course at half its initial speed, how is the 3 g ball deflected? If instead the collision were perfectly inelastic, how do the balls move?
2. Vectors representing each momentum is drawn by multiplying each mass and velocity, keeping the resultant momentum before and after the collision the same.
3. Dividing the magnitude of the vector by its mass gives the desired velocity: 2 m/s eastwards. A perfectly inelastic collision would make the balls move together as a 5 g mass in the direction of the resultant dashed purple arrow at 2√5/5 m/s.
I found a technique to solve conservation of linear momentum problems by drawing a diagram, as illustrated.
If the collision were instead elastic i.e. kinetic energy is conserved, is it possible to find all possible solutions graphically? Thanks, cmɢʟee⎆τaʟκ 22:17, 25 April 2025 (UTC)
- I'm not sure if there is a graphical approach to solving for area (ie v^2), I've never seen one. Greglocock (talk) 00:30, 26 April 2025 (UTC)
Thales's theorem - Can one conclude that if the two balls had the same mass m, one could use Thales's theorem to state that if AC is the resultant vector in the diagram, the constituent vectors are AB and BC for any B on the circle, so that |AB|² + |BC|² = |AC|² to conserve kinetic energy i.e. ½mv₁² + ½mv₂² = constant? Cheers, cmɢʟee⎆τaʟκ 12:12, 28 April 2025 (UTC)
- If the balls have the same mass, then isn't the solution quite simple for perfectly elastic collision? Velocity components along the line between the two centres swapped between the balls, and perpendicular components unchanged. (Someone please correct if this is wrong!) With balls of different mass, the solution algebraically most probably involves some multiplications, additions and divisions, all of which can in theory be done "graphically" using ruler and compass, but of course it could get very messy in practice. A neat graphical solution is a bigger ask. 2A00:23C8:7B20:CC01:DCDC:39AB:FED1:9A1B (talk) 18:27, 28 April 2025 (UTC)
- You're right, thanks. I hadn't considered it. cmɢʟee⎆τaʟκ 10:51, 29 April 2025 (UTC)
- If the balls have the same mass, then isn't the solution quite simple for perfectly elastic collision? Velocity components along the line between the two centres swapped between the balls, and perpendicular components unchanged. (Someone please correct if this is wrong!) With balls of different mass, the solution algebraically most probably involves some multiplications, additions and divisions, all of which can in theory be done "graphically" using ruler and compass, but of course it could get very messy in practice. A neat graphical solution is a bigger ask. 2A00:23C8:7B20:CC01:DCDC:39AB:FED1:9A1B (talk) 18:27, 28 April 2025 (UTC)
