Question

ДАЮ 30 Б СУПЕР СРОЧНО Шкив диаметром 1 м делает 720 оборотов за 3 минуты. Каковы угловая, линейная скорс Шкива и период вращения шкива?​

Answer 1

Ответ:

Период вращения T=(5*60)/300=1 сек.

Угловая скорость

< var > \omega=\frac{2\pi}T=6,28\ c^{-1} < /var ><var>ω=

T

2π

=6,28 c

−1

</var>

Линейная скорость на ободе шкива

< var > v=\omega R=0,628 < /var ><var>v=ωR=0,628</var> м/с

Answer 2

Calculation of Angular Velocity, Linear Velocity, and Period

To calculate the angular velocity, linear velocity, and period of the pulley, we can use the given information:

- Diameter of the pulley: 1 meter - Number of revolutions made by the pulley: 720 - Time taken for these revolutions: 3 minutes

Let's calculate each of these values step by step.

1. Angular Velocity:

Angular velocity is the rate at which an object rotates around a fixed axis. It is measured in radians per second (rad/s). To calculate the angular velocity, we need to convert the number of revolutions to radians and divide it by the time taken.

The formula for angular velocity is:

Angular Velocity (ω) = (2π * Number of revolutions) / Time taken

In this case, the number of revolutions is 720 and the time taken is 3 minutes. We need to convert the time to seconds, as the formula requires the time in seconds.

Time taken in seconds = 3 minutes * 60 seconds/minute = 180 seconds

Now, we can calculate the angular velocity:

Angular Velocity (ω) = (2π * 720) / 180 = 8π rad/s

So, the angular velocity of the pulley is 8π rad/s.

2. Linear Velocity:

Linear velocity is the rate at which an object moves along a circular path. It is measured in meters per second (m/s). To calculate the linear velocity, we need to know the circumference of the pulley and the angular velocity.

The formula for linear velocity is:

Linear Velocity (v) = Angular Velocity (ω) * Radius

The radius of the pulley is half of its diameter, which is 1/2 meter.

Linear Velocity (v) = 8π * (1/2) = 4π m/s

So, the linear velocity of the pulley is 4π m/s.

3. Period:

The period of an object in circular motion is the time taken for one complete revolution. It is measured in seconds (s). To calculate the period, we need to know the angular velocity.

The formula for the period is:

Period (T) = 2π / Angular Velocity (ω)

Using the angular velocity calculated earlier:

Period (T) = 2π / (8π) = 1/4 s

So, the period of the pulley is 1/4 second.

In summary: - The angular velocity of the pulley is 8π rad/s. - The linear velocity of the pulley is 4π m/s. - The period of the pulley is 1/4 second.

Please let me know if there's anything else I can help you with!