Solution to problem 9.2.7 from the collection of Kepe O.E.

9.2.7 Winch drum 1 rotates with angular velocity? = 6 rad/s. Determine the angular velocity of the lifted pipe 2 if the radius ratio r/R = 2/3. (Answer 1.5)

The problem gives the value of the angular velocity of winch drum 1 (? = 6 rad/s) and the radius ratio r/R = 2/3. It is necessary to find the angular velocity of the lifted pipe 2.

To solve the problem, we will use the law of conservation of angular momentum, according to which the angular momentum of a closed system remains unchanged in the absence of external moments.

The angular momentum of the winch drum 1 is equal to the angular momentum of the pipe 2 after the start of their interaction. Let us denote the angular momentum of the drum and pipe as L1 and L2, respectively, and their radii as r1 and r2.

Since winch drum 1 and pipe 2 rotate around an axis passing through the centers of their bases, their linear velocities at the ends are equal. Therefore, we can write the equation for angular momentum:

L1 = L2

r1 * m1 * v1 = r2 * m2 * v2,

where m1 and m2 are the masses of the drum and pipe, respectively, v1 and v2 are the linear velocities at the ends of the drum and pipe, respectively.

Since the ratio of radii r/R = 2/3, we can write:

r1 = (2/3)R, r2 = R.

Then the equation for angular momentum will take the form:

(2/3)R * m1 * v1 = R * m2 * v2.

Expressing v2, we get:

v2 = (2/3) * (m1/m2) * v1.

The angular velocity of pipe 2 will be equal to the ratio of the linear velocity to its radius:

ω2 = v2 / R = (2/3) * (m1/m2) * v1 / R.

Using the law of conservation of angular momentum and data from the problem conditions, we obtain:

L1 = L2 => r1 * m1 * ω1 = r2 * m2 * ω2 => (2/3)R * m1 * 6 = R * m2 * ω2,

where

ω2 = (2/3) * (m1/m2) * 6 = 1.5 rad/s.

Thus, the angular velocity of the lifted pipe 2 is 1.5 rad/s.

Solution to problem 9.2.7 from the collection of Kepe O.?.

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This product is a solution to problem 9.2.7 from the collection of problems in physics by the author Kepe O.?. The problem requires finding the angular velocity of the lifted pipe 2 if the angular velocity of the winch drum 1 and the radius ratio r/R are known. The solution to the problem is based on the law of conservation of angular momentum and includes a detailed description of all stages of the solution, as well as the answer to the problem.

The product is designed in a convenient html format, which allows you to quickly and conveniently study the solution on any device with Internet access. In addition, the html format allows you to quickly navigate between different parts of the solution, which simplifies your work and saves time.

When purchasing this product, you receive a proven and high-quality solution to the problem, which will help you better understand and master the material in physics. In addition, you save your time and effort, since you can immediately move on to studying the solution, without wasting time solving a complex problem yourself.

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The product in this case is the solution to problem 9.2.7 from the collection of Kepe O.?. The task is to determine the angular speed of the lifted pipe 2, if the angular speed of the rotating drum of the winch 1 and the ratio of the radii of the drum and pipe are known. To solve the problem, it is necessary to use a formula to connect linear and angular velocities, and also take into account the ratio of radii. After appropriate calculations, the answer to the problem is the angular velocity of the lifted pipe equal to 1.5 rad/s.

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