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| | | date = July 3, 2006 | | | date = July 3, 2006 |
| | | title = Centrifugal Force | | | title = Centrifugal Force |
| − | | image = centrifugal force.png | + | | image = centrifugal_force.png |
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| | | titletext = You spin me right round baby, right round, in a manner depriving me of an inertial reference frame. Baby. | | | titletext = You spin me right round baby, right round, in a manner depriving me of an inertial reference frame. Baby. |
| | }} | | }} |
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| | ==Explanation== | | ==Explanation== |
| − | [[Black Hat]] has strapped {{w|James Bond}} to a centrifuge and claims that the {{w|Centrifugal force|centrifugal}} force will be lethal. Bond objects that there is no such thing, but just {{w|Centripetal force|centripetal}} force. The notion of centrifugal force is a common one, as we experience it whenever we turn. Teachers will initially teach Newtonian mechanics in an inertial frame, and in inertial frames, the centrifugal force is zero. Instead, a body that moves in a circle does so because of a centripetal force (acting towards the center of the rotation). This is a reasonable (and correct) view, but it is a subtle point that many students find hard to grasp, as it seems to contradict their personal experience of centrifugal forces. For the sake of exposition, teachers may claim that "There is no such thing as centrifugal force." This, however, is also a misconception, which is addressed in the explanation below:
| + | In this comic, Black Hat has strapped {{w|James Bond}} to a centrifuge and claims the centrifugal force will be lethal. Bond objects that there is no such thing, but just centripetal force. |
| − | ;Observers' point of view (Black Hat, us, etc.)
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| − | :James Bond is moving in a circle, and is therefore accelerating. The force keeping him there is an inward force of contact against the centrifuge, a centripetal force. Via Newton's {{w|Newton's laws of motion#Newton's third law|third law}}, since the centrifuge is pushing Bond inward, Bond is pushing the centrifuge outward. The centrifuge's material is strong enough not to break under this force, however.
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| − | ;James Bond's point of view
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| − | :In James Bond's frame of reference, Bond is at rest. He is kept there by two forces: the above-mentioned inward force of contact against the centrifuge, and an ''outward centrifugal force''. He feels both forces.
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| − | As mentioned in the explanation, as the centrifuge rotates faster, the forces needed to keep him in motion get larger, so the force he feels gets larger. This will eventually kill him. The conclusion will be the same regardless of which frame of reference is chosen.
| + | Issac Newton was the first to announce that any body will be in a stable state of motion iff ([[1033: Formal Logic|if and only if]]) no force is applied. No motion at all is a stable state, as is constant translation. Imagine yourself on a bicycle: if you are going fast and do not brake, only the friction of the air, tires and internals of the bike will slow you down if you are not going uphill. |
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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.
| + | Now ride your bike on a circular track, at considerable speed. You will feel the "centrifugal" force, which is actually a centripetal force that you are applying to leave your straight course. That is what moving along an orbit really is: constantly changing the direction of movement, which needs a constant force. |
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| − | 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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| − | 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}}."
| + | Black Hat argues that within a spinning inertial system, "centrifugal" force is real. Here is why: to transform equations to a subsystem, everything inherent to the system as a whole must be subtracted, including the centripetal forces, which leaves a centrifugal force on the other side of the equation. Wikipedia hints that while the centripetal force is universal, the centrifugal force is bound to the specific inertial system. |
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| − | 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.
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| − | 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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| − | "Furthermore, if you're on the equator, you're being flung outward by a centrifugal force<sup>1</sup>."
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| − | <br><sup>"1</sup>Yes, centrifugal. I will fight you."
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| − | <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.)
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| | ==Transcript== | | ==Transcript== |
| − | :[James Bond, drawn as Cueball, is strapped to a giant wheel suspended from the ceiling. Black Hat is standing next to two levers.] | + | ::[James Bond is strapped to a giant wheel suspended from the ceiling. Black hat is standing next to two levers.] |
| − | :Black hat: How do you like my centrifuge, Mister Bond? When I throw this lever, you will feel centrifugal force crush every bone in your body. | + | :Black hat: How do you like my centrifuge, mister Bond? When I throw this lever, you will feel centrifugal force crush every bone in your body. |
| − | :[Same scene, but a closer shot.] | + | ::[Same scene, but a closer shot.] |
| | :Bond: You mean centripetal force. There's no such thing as centrifugal force. | | :Bond: You mean centripetal force. There's no such thing as centrifugal force. |
| − | :Black hat: A laughable claim, Mister Bond, perpetuated by overzealous teachers of science. Simply construct Newton's laws in a rotating system and you will see a centrifugal force term appear as plain as day. | + | :Black hat: A laughable claim, mister Bond, perpetuated by overzealous teachers of science. Simply construct Newton's laws in a rotating system and you will see a centrifugal force term appear as plain as day. |
| − | :[Closer shot, only Bond's head is visible.] | + | ::[Closer shot, only Bond's head is visible.] |
| | :Bond: Come now, do you really expect me to do coordinate substitution in my head while strapped to a centrifuge? | | :Bond: Come now, do you really expect me to do coordinate substitution in my head while strapped to a centrifuge? |
| − | :Black hat: No, Mister Bond. I expect you to die. | + | :Black hat: No, mister Bond. I expect you to die. |
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| − | ==Trivia==
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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].
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| − | * 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]].
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| | {{comic discussion}} | | {{comic discussion}} |
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| | [[Category:Comics featuring Black Hat]] | | [[Category:Comics featuring Black Hat]] |
| − | [[Category:Physics]]
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| − | [[Category:Comics featuring Cueball]]
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| − | [[Category:Footer comics]] <!-- in footer staring around Oct 13, 2006 -->
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| − | [[Category:Comics with xkcd store products]]
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| − | [[Category:Fiction]]
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