123: Centrifugal Force - Revision history

92.23.2.208: Moving that to Trivia, as the easiest way to correct the issue of this "third-level sub-section" continued into the "James Bond was almost killed by a centrifuge..." bit without ''any'' regard for why it was now part of a description of Lagrangians, etc.

2026-01-10T02:05:27Z

Moving that to Trivia, as the easiest way to correct the issue of this "third-level sub-section" continued into the "James Bond was almost killed by a centrifuge..." bit without ''any'' regard for why it was now part of a description of Lagrangians, etc.

TV4Fun: Add explanation of rotating systems

2026-01-10T01:18:46Z

Add explanation of rotating systems

Lettherebedarklight: /* Trivia */ add Category:Comics with a Spanish translation

2025-12-15T09:01:07Z

‎Trivia: add Category:Comics with a Spanish translation

CalibansCreations: /* Explanation */

2025-02-26T13:32:26Z

‎Explanation

172.68.205.135: /* Explanation */

2024-09-19T13:06:33Z

‎Explanation

PDesbeginner at 14:13, 17 June 2024

2024-06-17T14:13:51Z

172.69.195.184: /* Explanation */ Correcting the title ("local G" would be quite a bit more... interesting... than "local g") by also internalising the link how it perhaps would be intended.

2024-05-26T08:41:14Z

‎Explanation: Correcting the title ("local G" would be quite a bit more... interesting... than "local g") by also internalising the link how it perhaps would be intended.

172.68.22.153: /* Explanation */ Adding another comic about centrifugal force.

2024-05-25T23:42:49Z

‎Explanation: Adding another comic about centrifugal force.

FaviFake: /* Trivia */ Updated xkcd store link with Web archive link

2023-09-01T09:17:16Z

‎Trivia: Updated xkcd store link with Web archive link

FaviFake: Added trivia about footer comic

2023-07-26T10:17:08Z

Added trivia about footer comic

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 Teachers of mechanics are well aware of this; however, in introductory expositions, these ideas are often not taught. In theoretical mechanics, one describes the positions and velocities of the particles in a model relative to a frame of reference. This means that a time is chosen to be time 0, and positions are chosen to be (0,0,0), (1,0,0), (0,1,0), and (0,0,1). With these chosen, the position and time of any particle in the system can be described. It is an axiom of Newtonian Mechanics that there exist "Inertial Frames." In an inertial frame, a particle will remain at rest or at a constant speed unless acted on by an external force, and Newton's second law takes a simple form: F = ma. The surface of the Earth approximates an inertial frame. In a non-inertial frame, such as one rotating with a giant centrifuge, or moving with an accelerating vehicle, a particle will accelerate, relative to the frame. Newton's second law, when formed in such a frame, is much more complicated, as it has terms for the linear acceleration of the frame, the angular acceleration of the frame, the centrifugal force, and the {{w|Coriolis force}}. These extra terms are sometimes called "fictitious forces," as they result from the choice of the frame of reference. The mathematics required to describe problems in a non-inertial frame is more sophisticated, and all problems may be solved using an inertial frame. Thus is reasonable that teachers at school level "{{w|lie to children}}" and teach the mechanics in inertial frames.
 James Bond was almost killed by a centrifuge in {{w|Moonraker (film)|Moonraker}}. The final statement by Black Hat is that said by {{w|Auric Goldfinger}} in {{w|Goldfinger (film)|Goldfinger}} in response to James Bond's question "Do you expect me to talk?"
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 * This used to be one of the [[Footer comics|footer comics]] featured in the bottom segment of [https://xkcd.com xkcd.com].
 * This comic used to be [https://web.archive.org/web/20211215063004/https://store.xkcd.com/products/signed-prints available as a signed print] in the xkcd store before it was [[Store|shut down]].
 {{comic discussion}}

← Older revision		Revision as of 01:18, 10 January 2026
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	Teachers of mechanics are well aware of this; however, in introductory expositions, these ideas are often not taught. In theoretical mechanics, one describes the positions and velocities of the particles in a model relative to a frame of reference. This means that a time is chosen to be time 0, and positions are chosen to be (0,0,0), (1,0,0), (0,1,0), and (0,0,1). With these chosen, the position and time of any particle in the system can be described. It is an axiom of Newtonian Mechanics that there exist "Inertial Frames." In an inertial frame, a particle will remain at rest or at a constant speed unless acted on by an external force, and Newton's second law takes a simple form: F = ma. The surface of the Earth approximates an inertial frame. In a non-inertial frame, such as one rotating with a giant centrifuge, or moving with an accelerating vehicle, a particle will accelerate, relative to the frame. Newton's second law, when formed in such a frame, is much more complicated, as it has terms for the linear acceleration of the frame, the angular acceleration of the frame, the centrifugal force, and the {{w\|Coriolis force}}. These extra terms are sometimes called "fictitious forces," as they result from the choice of the frame of reference. The mathematics required to describe problems in a non-inertial frame is more sophisticated, and all problems may be solved using an inertial frame. Thus is reasonable that teachers at school level "{{w\|lie to children}}" and teach the mechanics in inertial frames.		Teachers of mechanics are well aware of this; however, in introductory expositions, these ideas are often not taught. In theoretical mechanics, one describes the positions and velocities of the particles in a model relative to a frame of reference. This means that a time is chosen to be time 0, and positions are chosen to be (0,0,0), (1,0,0), (0,1,0), and (0,0,1). With these chosen, the position and time of any particle in the system can be described. It is an axiom of Newtonian Mechanics that there exist "Inertial Frames." In an inertial frame, a particle will remain at rest or at a constant speed unless acted on by an external force, and Newton's second law takes a simple form: F = ma. The surface of the Earth approximates an inertial frame. In a non-inertial frame, such as one rotating with a giant centrifuge, or moving with an accelerating vehicle, a particle will accelerate, relative to the frame. Newton's second law, when formed in such a frame, is much more complicated, as it has terms for the linear acceleration of the frame, the angular acceleration of the frame, the centrifugal force, and the {{w\|Coriolis force}}. These extra terms are sometimes called "fictitious forces," as they result from the choice of the frame of reference. The mathematics required to describe problems in a non-inertial frame is more sophisticated, and all problems may be solved using an inertial frame. Thus is reasonable that teachers at school level "{{w\|lie to children}}" and teach the mechanics in inertial frames.
		+
		+	===Constructing Newton's Laws in a Rotating System===
		+	The simplest way to see the appearance of a centrifugal force term in a rotating system is by expressing quantities in polar coordinates. If we take a single point mass moving in a 2-dimensional plane with respect to some arbitrarily chosen center point, its position is completely described by its distance from the center, ''r'', together with its angle relative to the ''x''-axis in our coordinate system, ''θ''. It is possible to derive the force on the object in polar coordinates by taking Newton's first and second laws
		+	'''F''' = m d<sup>2</sup>'''r'''/d''t''<sup>2</sup>
		+	and transforming the objects linear motion into polar coordinates. However, we can arrive at this objective far more quickly by using the {{w\|Lagrangian mechanics\|Lagrangian}}
		+	''L'' = ''T'' - ''V''.
		+	Where ''T'' is the object's kinetic energy and ''V'' is its potential energy. If we assume there are no external forces acting on the object, then the potential energy ''V'' is just a constant that we can set equal to 0. This gives us the Lagrangian
		+	''L'' = ''T'' - ''V'' = ''T'' = ½''mv''<sup>2</sup> = ½''m''[(''r'' d''θ''/d''t'')<sup>2</sup> + (d''r''/d''t'')<sup>2</sup>] = ½m(''r''<sup>2</sup>''θ''<nowiki>'</nowiki><sup>2</sup> + ''r'''<sup>2</sup>)
		+	where ''θ'' is expressed in radians, we are using ''θ''<nowiki>'</nowiki> to express the angular velocity, and ''r''' to express the radial velocity. We can then apply Lagrange's equations
		+	∂''L''/∂''q''<sub>''i''</sub> - d/d''t'' ∂''L''/∂''q''<sub>''i''</sub>' = 0
		+	where each ''q''<sub>''i''</sub> is one of our coordinates, ''r'' and ''θ'' in our case, and each ''q''<sub>''i''</sub>' is the associated time derivative ''r''<nowiki>'</nowiki> and ''θ''<nowiki>'</nowiki>. Applying this with ''r'' gives us
		+	∂''L''/∂''r'' - d/d''t'' ∂''L''/∂''r''<nowiki>'</nowiki> = ''mrθ''<nowiki>'</nowiki><sup>2</sup> - d/d''t''(''mr''<nowiki>'</nowiki>) = ''mrθ''<nowiki>'</nowiki><sup>2</sup> - ''mr''<nowiki>''</nowiki> = 0
		+	⇒ ''mr''<nowiki>''</nowiki> = m d<sup>2</sup>''r''/d''t''<sup>2</sup> = ''mrθ''<nowiki>'</nowiki><sup>2</sup>
		+	Comparing this to the expression of Newton's laws from earlier, we see that this is saying precisely that in this reference frame, there is a centrifugal force that is proportional to ''rθ''<nowiki>'</nowiki><sup>2</sup>.

	James Bond was almost killed by a centrifuge in {{w\|Moonraker (film)\|Moonraker}}. The final statement by Black Hat is that said by {{w\|Auric Goldfinger}} in {{w\|Goldfinger (film)\|Goldfinger}} in response to James Bond's question "Do you expect me to talk?"		James Bond was almost killed by a centrifuge in {{w\|Moonraker (film)\|Moonraker}}. The final statement by Black Hat is that said by {{w\|Auric Goldfinger}} in {{w\|Goldfinger (film)\|Goldfinger}} in response to James Bond's question "Do you expect me to talk?"

← Older revision		Revision as of 09:01, 15 December 2025
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 The title text is inspired by {{w|Dead or Alive (band)|Dead or Alive's}} famous song from 1985, "{{w|You Spin Me Round (Like a Record)|You Spin Me Round}}."
-Randall feels very strongly that the centrifugal force is a real thing. He links to this comic in the first footnote of his ''[[what if? (blog)|what if?]]'' article [https://what-if.xkcd.com/92/ One-Second Day] and the 6th footnote of [https://what-if.xkcd.com/157/ Earth-Moon Fire Pole], stating that it is a real thing, and that he will go so far as to strap arguers to a centrifuge that he or someone he knows apparently owns. He also cites it in [[852: Local g]]
+Randall feels very strongly that the centrifugal force is a real thing. He links to this comic in the first footnote of his ''[[what if? (blog)|what if?]]'' article {{what if|92|One-Second Day}} and the 6th footnote of {{what if|157|Earth-Moon Fire Pole}}, stating that it is a real thing, and that he will go so far as to strap arguers to a centrifuge that he or someone he knows apparently owns. He also cites it in [[852: Local g]]
 As can also be seen in the [https://twitter.com/bohacekp/status/531500491180875776/photo/1 footnote on page 132] in his ''[[What If? (book)|What If?]]'' book, he will even fight you about it. From the book:<br>

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 <br><sup>"1</sup>Yes, centrifugal. I will fight you."
 <br>(The article itself is about what happens if you lose all your DNA, so it has not much to do with this "real" force... The sentence is just stating that the actual weight loss from losing all your DNA is similar to the weight loss you would experience by moving from the poles to the equator due to this force.)
 ==Transcript==

← Older revision		Revision as of 14:13, 17 June 2024
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 ==Trivia==
-*This comic is available as a signed print in the [https://store.xkcd.com/products/signed-prints xkcd store].
+* This used to be one of the [[Footer comics|footer comics]] featured in the bottom segment of [https://xkcd.com xkcd.com].
 {{comic discussion}}