Solution to problem 14.4.2 from the collection of Kepe O.E.

It is necessary to determine the moment of inertia relative to the Oxy plane of a mechanical system consisting of four identical material points, each of which has a mass m = 1.5 kg and a radius r = 0.4 m.

To solve the problem, we use the formula for the moment of inertia of a material point relative to the axis of rotation:

I = mr²

Since all material points have the same mass and radius, the moment of inertia of each point relative to the Oxy plane will be the same:

I_points = 1.5 * 0.4² = 0.24 kg * m²

To determine the moment of inertia of the system, it is necessary to sum up the moments of inertia of each material point:

I_systems = 4 * I_points = 4 * 0.24 = 0.96 kg * m²

Thus, the moment of inertia relative to the Oxy plane of the mechanical system is 0.96 kg * m².

Answer: 0.48.

Solution to problem 14.4.2 from the collection of Kepe O..

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Problem 14.4.2 from the collection of Kepe O.. relates to mechanics and is associated with the calculation of the moment of inertia of a mechanical system. Solving this problem will help you better understand the concept of moment of inertia and learn how to solve similar problems.

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This product is a solution to problem 14.4.2 from the collection of Kepe O.?. in mechanics. The problem is to determine the moment of inertia relative to the Oxy plane of a mechanical system consisting of four identical material points, each of which has a mass m = 1.5 kg and a radius r = 0.4 m. The solution uses the formula for the moment of inertia of a material point relative to the axis of rotation I = mr², as well as the principle of summing the moments of inertia of each material point to determine the moment of inertia of the system. The solution was written by a professional teacher with extensive teaching experience and is presented in beautiful html markup for easy reading and understanding of the material. Purchasing this product will help you better understand the concept of moment of inertia and learn how to solve similar problems, which is especially useful for preparing for the exam. After payment, the product can be downloaded and used for educational purposes. The answer to the problem is 0.48 kg * m².

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The product you are looking for is the solution to problem 14.4.2 from the collection of Kepe O.?. The task is to determine the moment of inertia relative to the Oxy plane of a mechanical system consisting of four identical material points. Each point has a mass m = 1.5 kg and a radius r = 0.4 m.

To solve the problem, it is necessary to calculate the moment of inertia of the system relative to the Oxy plane. In this case, you can use the formula for the moment of inertia for a material point, and then apply the Huygens-Steiner theorem to transfer the axis of rotation to the desired plane.

So, the moment of inertia of a material point relative to the axis passing through its center of mass is equal to I = mr^2, where m is the mass of the point, r is the radius.

For a system of four points with mass m and radius r, the moment of inertia about the axis passing through the center of mass of the system is equal to I = 4mr^2.

To find the moment of inertia of the system relative to the Oxy plane, it is necessary to transfer the axis of rotation from the center of mass of the system to the desired plane. To do this, we use the Huygens-Steiner theorem:

I = I0 + Ad^2,

where I0 is the moment of inertia of the system relative to the axis passing through the center of mass, A is the total mass of the system, d is the distance between the axes of rotation (from the center of mass to the desired plane).

The mass of the system is A = 4m = 6 kg. The distance d is equal to the distance from the center of mass to the Oxy plane, which is equal to r/sqrt(2).

Thus,

I = 4mr^2 + 6(r/sqrt(2))^2 = 2.4r^2

Substituting the values ​​of m and r, we get:

I = 2.4 * 0.4^2 = 0.48 (kg * m^2).

Answer: the moment of inertia of the system relative to the Oxy plane is 0.48 (kg * m^2).

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