Question

Диск радиусом 80 см равномерно вращается вокруг своей оси. Скорость точки, находящейся на расстоянии 20 см от центра диска равна 2 м/с. Определите скорость крайних точек диска. ​

Answer 1

Ответ:

8 м/с

Объяснение:

составим пропорцию

0,8 м-х

0,2 м-2 м/с

х=0,8×2/0,2=8м/с

Answer 2

Problem Analysis

We are given a disk with a radius of 80 cm that is rotating uniformly around its axis. The speed of a point located 20 cm from the center of the disk is given as 2 m/s. We need to determine the speed of the points at the edges of the disk.

Solution

To solve this problem, we can use the concept of linear velocity and angular velocity. The linear velocity of a point on a rotating object is given by the product of its distance from the axis of rotation and the angular velocity.

Let's denote the linear velocity of a point on the disk as v, the distance of the point from the center of the disk as r, and the angular velocity of the disk as ω.

We are given that the linear velocity of a point located 20 cm from the center of the disk is 2 m/s. Therefore, we have the following equation:

v = r * ω

We can rearrange this equation to solve for ω:

ω = v / r

Substituting the given values, we have:

ω = 2 m/s / 0.2 m = 10 rad/s

Now, we can calculate the linear velocity of the points at the edges of the disk. The linear velocity of a point at the edge of the disk is equal to the product of the radius of the disk and the angular velocity:

v_edge = r_edge * ω

Substituting the given value of the radius (80 cm = 0.8 m) and the calculated value of ω, we have:

v_edge = 0.8 m * 10 rad/s = 8 m/s

Therefore, the speed of the points at the edges of the disk is 8 m/s.

Conclusion

The speed of the points at the edges of the disk is 8 m/s. This is calculated using the formula v = r * ω, where v is the linear velocity, r is the distance from the center of the disk, and ω is the angular velocity. The given linear velocity of a point located 20 cm from the center of the disk is used to calculate the angular velocity, which is then used to calculate the linear velocity at the edges of the disk.