Solution to problem 19.2.9 from the collection of Kepe O.E.

19.2.9 It is necessary to calculate the angular acceleration of the drum for given values ​​of its moment of inertia relative to the axis of rotation I3 = 0.1 kg • m, the moment of a pair of forces acting on the drum, M = 0.6 N • m, body masses m1 = m2 = 10 kg and radii R = 0.2 m and r = 0.1 m. (Answer 1)

To solve the problem we use the equation of moments:

ΣM = Iα,

where ΣM is the sum of all moments, I is the moment of inertia of the drum relative to the axis of rotation, α is the angular acceleration.

Let's consider the moments acting on the drum:

1. The moment of a pair of forces M acting on the drum.
2. The moment created by the masses of bodies m1 and m2 located at a distance R from the axis of rotation.

Thus, the sum of the moments:

ΣM = М - (m1 + m2)gR,

where g is the acceleration of gravity.

We substitute the values ​​and solve the equation for angular acceleration:

Iα = М - (m1 + m2)gR,

α = (М - (m1 + m2)gR) / I.

We substitute the values ​​and get the answer:

α = (0.6 N • m - 2 • 10 kg • 9.81 m/s² • 0.2 m) / 0.1 kg • m² = 6 rad/s².

We present to you the solution to problem 19.2.9 from the collection of Kepe O.?. in electronic format.

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The offered product is an electronic file with a detailed solution to problem 19.2.9 from the collection of Kepe O.?. in physics. The problem requires calculating the angular acceleration of a drum for given values ​​of its moment of inertia, the moment of a pair of forces acting on the drum, body masses and radii.

The solution to the problem is based on the use of the moment equation: ΣM = Iα, where ΣM is the sum of all moments, I is the moment of inertia of the drum relative to the axis of rotation, α is the angular acceleration.

Having analyzed in detail the moments acting on the drum, the author of the solution writes down an equation for the sum of the moments and substitutes the given values. The equation is then solved for angular acceleration.

The result is an answer to the problem: the angular acceleration of the drum is 6 rad/s².

By purchasing this product, you receive a high-quality solution to problem 19.2.9 from the collection of Kepe O.?. in a convenient electronic format. The solution is made at a professional level and contains all the necessary calculations and formulas to obtain the correct answer. The file is designed in a convenient and beautiful HTML format, which allows you to quickly and easily familiarize yourself with the material and use it for educational purposes.

By purchasing this product, you will expand your horizons and improve your skills in the field of physics.

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The product in this case is the solution to problem 19.2.9 from the collection of Kepe O.?. The task is to determine the angular acceleration of the drum, provided that the moment of inertia of the drum relative to the axis of rotation (I3 = 0.1 kg • m), the moment of a pair of forces acting on the drum (M = 0.6 N • m), and the mass of bodies are known (m1 = m2 = 10 kg) and radii (R = 0.2 m, r = 0.1 m). The answer to the problem is 1.

To solve the problem, it is necessary to use the laws of mechanics and formulas related to the rotational motion of bodies. The solution to the problem will contain step-by-step calculations and explanations of how the answers to each of the steps were obtained.

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