Do you know what rolling means?

Do you feel too simple to see this topic? The problem on the surface is simple, but many people have not figured out, and even fully understand the mistake.

As a physical term, rolling is not simple. Understanding it needs to start with two basic forms of rigid movement, they are flat and rotating.

Tip: Because the mass point can only be flat, it is not considered, so the "object" in this article means "rigid body", that is, the object that is neglected.

Ping movement is that the object is only transferred or not; the rotation is that the object is unwavering.

What? It seems a bit dizzy.

It is really a bit messy, although that's right! But in fact, they all have strict definitions!

Translation: The connection between any two points inside the object is always parallel during the movement of the object, and the exercise is flat.

Such as like this.

Rotation: Any point on the object is doing a circular motion around a certain point.

It's simple, that's it.

The two of them are combined in different proportions to form a variety of different movements!

If this combination movement occurs on a certain surface (plane or curved), then it is used to rolling.

It looks simple, right?

We start from the most typical rolling -pure rolling, it refers to the rolling of Slipping or Skidding, or it is composed of a combination of rotation peace.

Maybe you are a bit embarrassed to the words "not slipping"?

In fact, you might think too much, you only need to understand it literally. If you don't slip, just don't move! Movement is relative. The movement here is relative to the ground, so not to slipping means relative to the ground -good guy, isn't it exercise? How can I not move the ground?

The "no movement" mentioned here refers to "the part of the part that is in contact with the ground is not moving on the ground." For example, when you walk, the feet you step on the ground are actually not moving to the ground, and the other leaving foot is moved.

Taking the wheel as an example, if it rolled purely on the ground, then it is not moving with the point (the lowest point of the wheel) that it comes to the ground! Let's analyze it carefully.

Before formal analysis, let's review the relative sexual relationship between classic mechanics.

There are three substances: A, B and C, so the relative relationship of their speed can indicate the meaning of the bidding here as "the former is relative to the latter", such as the speed of A relative to B.

The second letter of the bidding in the above speed symbol represents the reference object. For example, in the upper formula, "when choosing B as a reference, the speed of A".

The relative relationship of speed shows that any relative speed can always be regarded as multiple other relative speed.

Look at the speed of the wheel's lowest point now.

As shown in the figure below, the wheels are rolling, and the radius is set, and the angle speed of the center center is.

The speed of the wheel's minimum point, the speed of the minimum point relative to the center point, and the speed of the center point relative to the ground are represented, harmonious, respectively.

Obviously, the direction level of the direction is to the left, and the direction level is to the right. As for the direction of the direction, it is temporarily represented by the number of positive numbers. The relative relationship between these three speeds is to be right.

According to the relationship between the line speed and the angle speed, the lowest point of the wheels is relative to the center of the wheels, and the direction level is left to the left. Therefore, the upper formula can be written as the meaning of not slipping above. The lowest point of the wheels is zero, so there must be

This is the relationship between the center speed of the wheels and the wheel speed when the wheels are rolled purely.

In fact, not only does the center speed of the wheels meet this relationship, but for pure rolling wheels, any point to the ground is equal to the angle speed of the wheels multiplied by the distance between the point to the ground contact point. For example, the speed of the wheels is the speed of the wheel, and the speed of the front point is.

It is easy to understand this point. Since the lowest point of the wheels does not move, it is equivalent to the ground, and any relative speed on the wheel is its relatively low -point speed, and the relatively low -point movement is not at the corresponding distance as the corresponding distance as the corresponding distance as the corresponding distance. Does the radius turn?

That's right! Any point to the ground is the distance from the point to the lowest point.

But you may have a little doubt, is the angle speed of the wheel around the center?

Yes! It can be proved that no matter which point is on the wheels, the angle speed of the wheels is the same. This is called the absoluteness of the rigid angle speed. It will not be proved here. If you are interested, you can read the book yourself.

Speaking of which, do you realize a problem, the speed of each point on the rolling wheels is different?

That's right! Because the bicycle wheel is rolling, not rotating!

Experienced people will notice that the bicycle wheels during driving, the more the spokes above the top, the more blurred, which is caused by this.

Regarding the pure rolling of the wheels, a price saying is also mentioned earlier, which is "the movement of a combination of a combination of a combination of peace". What does this mean?

It means that any point on the edge of the wheels is the overall flat speed of the wheels and the rotation speed of its relative to the center of the wheels at a ratio of 1: 1.

This is obvious!

Because the wheels are flat with all points, the speed is, the direction level; the speed of any point on the edge of the wheels is the speed of the center, and the direction is cut along the direction. According to the relativity of speed, they are the speed of this point. The two have been proved before that the speed of the wheels is equal when the wheels are rolled. This shows that any point at any point on the edge of the wheels is always equal to the synthesis of the speed vector of two equal size! This is the meaning of 1: 1 ratio. In fact, pure rolling is not limited to wheels. Looking at the movement of these objects below, it is obviously a pure rolling -because they are zero with the speed of the ground contact point, and the speed of each point on the object is satisfied.

After talking about the pure rolling, look at the non -pure rolling.

It is very simple. Non -pure rolling means that the contact point is slippery, that is, the speed of the wheel's lowest point is so there is so on the non -pure rolling. The speed on the edge of the wheels is not based on the flat movement and rotation 1: 1 combination. For any point on any rigid body, non -pure rolling means.

If further analysis, non -pure rolling is greater than or less than divided into two cases.

The right situation often occurs when the car brakes, and is also called slippery, translated as slipping. In order to describe the degree of slippery, the definition of the definition of the sliding rate often occurs when the car is accelerated. It is also called sliding rotation. It is translated as SKIDDING. Similarly, the definition rotation rate is as unknown.

For example, when your luggage wheel is not turned, you can only drag hard. At this time Quick, but the car did not move at all. At this time, the slip rate was 100%.

There are so many about rolling.

If the movement of the rigid body is not limited to one side, it is not called rolling, but the general movement of the rigid body. The general exercise of the rigid body is relatively complicated, and it is not displayed here for the time being.

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Source: University Physics

Edit: yellow water machine

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