Types of MotionIf you had to think consciously in order to move your body, you would be severely disabled. Even walking, which we consider to be no great feat, requires an intricate series of motions your cerebrum would be utterly incapable of coordinating. The task of putting one foot in front of the other is controlled by the more primitive parts of your brain, the ones that have not changed much since the mammals and reptiles went their separate evolutionary ways. The thinking part of your brain limits itself to general directives such as “walk faster,” or “don’t step on her toes,” rather than micromanaging every contraction and relaxation of the hundred or so muscles of your hips, legs, and feet.
Physics is all about the conscious understanding of motion, but we are obviously not immediately prepared to understand the most complicated types of motion. Instead, we will use the divide-and-conquer technique. We will first classify the various types of motion, and then begin our campaign with an attack on the simplest cases. To make it clear what we are and are not ready to consider, we need to examine and define carefully what types of motion can exist.
Rigid-body motion distinguished from motion that changes an object’s shape
Nobody, with the possible exception of Fred Astaire, can simply glide forward without bending their joints. Walking is thus an example in which there is both a general motion of the whole object and a change in the shape of the object. Another example is the motion of a jiggling water balloon as it flies through the air. We are not presently attempting a mathematical description of the way in which the shape of an object changes. Motion without a change in shape is called rigid-body motion (the word “body” is often used in physics as a synonym for “object”).
Center-of-mass motion as opposed to rotation
A ballerina leaps into the air and spins around once before landing. We feel intuitively that her rigid-body motion while her feet are off the ground consists of two kinds of motion going on simultaneously: a rotation and a motion of her body as a whole through space, along an arc. It is not immediately obvious, however, what is the most useful way to define the distinction between rotation and motion through space. Imagine you attempt to balance a chair and it falls over. One person might say that the only motion was a rotation about the chair’s point of contact with the floor, but another might say there was both rotation and motion down and to the side.
It turns out there is one particularly natural and useful way to make a clear definition, but it requires a brief digression. Every object has a balance point, referred to in physics as the center of mass. For a two-dimensional object such as a cardboard cutout, the center of mass is the point at which you could hang the object from a string and make it balance. In the case of the ballerina (who is likely to be three-dimensional unless her diet is particularly severe), it might be a point either inside or outside her body, depending on how she holds her arms. Even if it is not practical to attach a string to the balance point itself, the center of mass can be defined.
Why is the center of mass concept relevant to the question of classifying rotational motion as opposed to motion through space? It turns out that the motion of an object’s center of mass is nearly always far simpler than the motion of any other part of the object. The ballerina’s body is a large object with a complex shape. We might expect that her motion would be much more complicated than the motion of a small, simply-shaped object, say a marble, thrown up at the same angle as the angle at which she leapt. But it turns out that the motion of the ballerina’s center of mass is exactly the same as the motion of the marble. That is, the motion of the center of mass is the same as the motion the ballerina would have if all her mass was concentrated at a point. By restricting our attention to the motion of the center of mass, we can therefore simplify things greatly.
We can now replace the ambiguous idea of “motion as a whole through space” with the more useful and better defined concept of “center-of-mass motion.” The motion of any rigid body can be cleanly split into rotation and center-of-mass motion. By this definition, the tipping chair does have both rotational and center-of-mass motion. Concentrating on the center of mass motion allows us to make a simplified model of the motion, as if a complicated object like a human body was just a marble or a point-like particle. Science really never deals with reality; it deals with models of reality.
Note that the word “center” in “center of mass” is not meant to imply that the center of mass must lie at the geometrical center of an object. A car wheel that has not been balanced properly has a center of mass that does not coincide with its geometrical center. An object such as the human body does not even have an obvious geometrical center.
It can be helpful to think of the center of mass as the average location of all the mass in the object. With this interpretation, we can see for example that raising your arms above your head raises your center of mass, since the higher position of the arms’ mass raises the average.
Jete-illusion
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Center-of-mass motion in one dimension
In addition, there are cases in which the center of mass moves along a straight line, such as objects falling straight down, or a car that speeds up and slows down but does not turn.
Note that even though we are not explicitly studying the more complex aspects of motion, we can still analyze the center-of-mass motion while ignoring other types of motion that might be occurring simultaneously. For instance, if a cat is falling out of a tree and is initially upside-down, it goes through a series of contortions that bring its feet under it. This is definitely not an example of rigid-body motion, but we can still analyze the motion of the cat’s center of mass just as we would for a dropping rock.Which of the following could fit the missing paragraph?（）
A、Ballerinas and professional basketball players can create an illusion of flying horizontally through the air because our brains intuitively expect them to have rigid-body motion, but the body does not stay rigid while executing a grand jete or a slam dunk. The legs are low at the beginning and end of the jump, but come up higher at the middle. Regardless of what the limbs do, the center of mass will follow the same arc, but the low position of the legs at the beginning and end means the torso is higher compared to the center of mass, while in the middle of the jump it is lower compared to the center of mass. Our eye follows the motion of the torso and tries to interpret it as the center-of-mass motion of a rigid body. But since the torso follows a path flatter than we expect, this attempted interpretation fails, and we experience an illusion that the person is flying horizontally.
B、Linear motion, sometimes more broadly called translational motion, is simply the shifting of an object from one point in space to another. Schematically, on a typical graph with x- and y-axes, if a point shifts from the origin at (0, 0) to the point (3, 4), the Pythagorean theorem may be used to show that the point has undergone 5 units of linear motion (the square root of 32 + 42 is 5). An arrow shot from a bow undergoes linear motion.
C、When something rotates, roughly speaking, it spins around in a circle. A child standing in one spot on a playground and spinning in a circle until she reaches her original starting point has undergone rotational motion, but she need not complete the circle for this to be true; they key point is that her body has rotated about a well-defined geometric axis – in this case, one running from the top of her head to the ground at her feet.
D、Things that move in a reciprocating manner, but with elements of rotational motion like swinging, are said oscillate. A pendulum, which swings from a fixed point of attachment and traces an arc, is a classic example. A sprinkler or oscillating fan does the same thing, except that these oscillate in a horizontal plane rather than a vertical plane and are powered by motors rather than gravity.
【正确答案】：A
【题目解析】：由文章题目可知本文是在讲不同类型的运动，缺失段落前有一个黑色的标题：Jete-illusion，其中jete是芭蕾舞小跳。可知缺失段落讲的是在做类似于芭蕾舞小跳动作时产生的错觉。四个选项中符合该标题的是A选项。
