Question

Точка А, которая расположена на ободе колеса, двигается со скоростью v. Линейная скорость движения точки В, которая расположена на расстоянии R от центра колеса, вдвое меньше, чем скорость точки А. Какое расстояние преодолеет колесо за 1 период?

Answer 1

Я сама не знаю , я как пень

Answer 2

Calculation of Distance Traveled by the Wheel

To calculate the distance traveled by the wheel in one period, we need to consider the relationship between the linear velocities of points A and B on the wheel.

Let's denote the linear velocity of point A as v and the linear velocity of point B as v/2. We also know that point B is located at a distance R from the center of the wheel.

The linear velocity of a point on the wheel is given by the formula v = ω * r, where ω is the angular velocity of the wheel and r is the distance of the point from the center of the wheel.

Since point B is located at a distance R from the center of the wheel, we can write the equation as:

v/2 = ω * R

To find the distance traveled by the wheel in one period, we need to find the circumference of the wheel. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

In this case, the radius of the wheel is R. Therefore, the circumference of the wheel is:

C = 2πR

Since one period of the wheel corresponds to one complete revolution, the distance traveled by the wheel in one period is equal to its circumference:

Distance = C = 2πR

Now, let's substitute the value of C in terms of R into the equation for v/2:

v/2 = ω * R

Solving for ω, we get:

ω = v / (2R)

Substituting this value of ω into the equation for Distance, we get:

Distance = 2πR

Therefore, the distance traveled by the wheel in one period is 2πR.

Please note that the above explanation assumes that the wheel is rolling without slipping.