High School Physics Wheel Bottom Speed Problem Physics Master Comes Down 100

All plane motion can be described in terms of translational (translation) and rotation, and velocity is synthesized from translational velocity and rotational speed. Translational has reference, and rotation is absolute, just like one end of a rod around the other end of the fixed axis rotation, all the speed on the rod is different due to the distance from the center of rotation, but the rotation speed of each point on the rod is the same, the formula v=w*r (v is the linear velocity, w is the angular velocity, r is the distance from the point of motion to the center of rotation) is this principle. In the concept of instantaneousness, a point can always be found on a moving object with zero relative velocity to the frame of reference, that is, the velocity of the center is zero.

In the problem you described, the point of contact between the tire and the ground is the velocity transient of the tire (how to find the specific transient center: the perpendicular focus of any two points in the direction of the velocity on the object. The velocity is the resultant velocity of translation and rotation).

With the instantaneous center as the reference point, any point on the object can be regarded as rotating around the instantaneous center (no translation) just like the above-mentioned rod rotates around the fixed end, and the velocity of any point on the tire can be calculated by the formula v=w*r. In the problem, the distance from the center of the wheel to the center of the wheel is r, so the velocity is v, and the distance from the top of the wheel is 2r, so the velocity is 2v. Then analyze the force of the tire, the wheel and the ground are subjected to the friction force of the ground on it, so that the motion state of the contact point changes, you should know that the force parallel to the direction of velocity changes the velocity, and the force perpendicular to the direction of velocity changes the direction of velocity (just like in uniform circular motion, the force on the object, the velocity does not change, but the direction changes all the time, and the force direction of the object should be perpendicular to the direction of motion).

As a result, the point of contact gains maximum acceleration at one moment and velocity at the next moment. The speed at the top of the wheel is the largest, and the centripetal acceleration obtained is also the largest (a=v2 r), which changes the direction of motion at the fastest speed, and it can be seen from the whole that the wheel is completing a cycle of motion. (You can also try to analyze that in fact, the ground provides forward power to the front wheels of the car, while the rear wheels provide frictional resistance, and the concept of instantaneous center mentioned above is a concept in university theoretical mechanics).

The instantaneous center of rotation of the rigid body motion is the bottom of the wheel, so the velocity is 0, and the distance between the top and the center is 2; 1. According to the angular velocity, the velocity ratio is 2; 1. Because the center of the wheel is the same as the speed of the vehicle, the conclusion can be drawn.

I just studied physics in my second year of junior high school. I think it's because the velocity synthesis puts the assuming car forward, the velocity direction of the point at the bottom is backward and the velocity direction of the point at the top is forward, so the synthesis is 0 and the other is the 2v you said, but this seems to contradict the linear velocity of each point. To put it simply, there is translation.

The speed is the same as the axle, so the speed is not 0

In fact, the velocity on the wheel can be as follows v+vcos(x), where x is the angle to the longitudinal axis

Of course, this is only a numerical velocity, not a vector, and the direction of velocity needs to be found separately. Do you need it? This physics question is not too difficult, you can ask me again if you need it

<> derivation process uses a vector synthesis formula for velocity.

For details, see the High School Physics Competition Book.

I really haven't learned it.

I won't take the college entrance examination. You're going to participate in the contest

Since, as you said, the upper part has a speed of 2v, then it will also move forward due to inertia.

Similarly, the actual motion of the vertex can also be regarded as the combined motion of the rotation of the wheel and the horizontal motion forward, and the velocity is v wr=2v;

The bottom point velocity is v-wr=0, so v wr is both the rotational speed of the wheel and the speed at which it moves horizontally.

Less than a little next to the top, the speed of the wheel depends on the specific height: vo = v+wh h is the height relative to the axle.

In short, it will be v vo 2v

Hehe, let's talk about speed, what is the premise of our description of speed? is the frame of reference.

The speed is different in different frames of reference. So when we talk about what the velocity is, we have to understand what the frame of reference is chosen.

So what is the frame of reference for the speed of the wheel at the bottom of the wheel with a speed of 0 and the top speed of the car at 2? It's all ground. The bottom of the wheel is well understood.

Because the bottom of the wheel does not slide relative to the ground, otherwise it is skidding. Since there is no relative motion, and we are using the ground as a frame of reference, the velocity is, of course, 0. So why is the speed at the top 2 by the car?

Because velocity in the center of the wheel = speed of the car, why? Because the center of the wheel is fixed to the axle of the car.

Above. We know that the edge of the wheel is moving in a circular motion relative to the center of the wheel.

The linear velocity is equal everywhere, and the velocity of the bottom of the wheel with respect to the center of the wheel and the velocity of the top of the wheel with respect to the center of the wheel are equal and in opposite directions. Then the conclusion of 2 times the speed of the car is obtained.

It only makes sense to study the speed of reference if the frame of reference is clear. The reason why the car can move forward is because the speed of the bottom relative to the ground is 0, so the axle has speed relative to the ground, and the car has speed. If the velocity of the bottom relative to the ground is the linear velocity of the wheel, then the velocity of the center of the wheel relative to the ground is 0.

That is, the speed of the car is 0The car skidped.

The rate is, which means that the linear velocity v=12m liquid collapses

Angular velocity =v group tung r=20 rad mega buried tans rotational speed n= 2 =20 2