Question

Механическое движение от калеса 1 к колесу 2 передается с помощью ремня. Если угловая скорость колеса 2 равна 100 πc-1, и радиусы колес соответственно 30 и 10 см, сколько оборотов в минуту совершает колесо 1?

Answer 1

Объяснение:

Возможно так:

R₁ = 30 см = 0,3 м

R₂ = 10 см = 0,1 м

W₂ = 100 πc-¹

W₁/W₂ = 30/10

W₁/100 πc-¹ = 3

W₁ = 3 * 100 πc^-1 = 300 πc-¹

W₁ = 2·π·n

300 πc-¹ = 6,28 * n

n = 300 / 6,28 = 48

48 * 60 = 2 880

Answer 2

I can answer your question in detail. Mechanical motion from wheel 1 to wheel 2 is transmitted by a belt. If the angular velocity of wheel 2 is equal to 100 πc-1, and the radii of the wheels are 30 and 10 cm respectively, how many revolutions per minute does wheel 1 make?

To solve this problem, we need to use the following formula:

$$v = \omega r$$

where $v$ is the linear velocity, $\omega$ is the angular velocity, and $r$ is the radius of the wheel.

Since the belt is tight and does not slip, the linear velocity of both wheels is the same. Therefore, we can write:

$$v_1 = v_2$$

$$\omega_1 r_1 = \omega_2 r_2$$

where the subscripts 1 and 2 denote the wheels 1 and 2 respectively.

We are given the values of $\omega_2$, $r_1$, and $r_2$. We need to find the value of $\omega_1$, which is the angular velocity of wheel 1. We can rearrange the equation above to get:

$$\omega_1 = \frac{\omega_2 r_2}{r_1}$$

Substituting the given values, we get:

$$\omega_1 = \frac{100 \pi \times 10}{30}$$

$$\omega_1 = \frac{1000 \pi}{30}$$

$$\omega_1 \approx 104.72 \text{ rad/s}$$

This is the angular velocity of wheel 1 in radians per second. To convert it to revolutions per minute, we need to use the following conversion factor:

$$1 \text{ rad/s} = \frac{60}{2 \pi} \text{ rpm}$$

where rpm stands for revolutions per minute.

Multiplying the angular velocity of wheel 1 by this factor, we get:

$$\omega_1 \times \frac{60}{2 \pi} \approx 104.72 \times \frac{60}{2 \pi}$$

$$\omega_1 \times \frac{60}{2 \pi} \approx 999.87 \text{ rpm}$$

Therefore, the answer is that wheel 1 makes about 999.87 revolutions per minute.

I hope this explanation was clear and helpful. If you want to learn more about mechanical motion, you can check out some of the web search results I found for you . Have a nice day!