Solution to problem 14.4.22 from the collection of Kepe O.E.

It is necessary to calculate the moment of inertia of a thin homogeneous disk with mass m = 0.8 kg and radius r = 0.1 m relative to the Ox1 axis, if the angles α = 30°, β = 60°, γ = 90°.

The moment of inertia of a thin homogeneous disk can be calculated using the formula:

I_x1 = (m·r²)/4

Where:

• m - disk mass;
• r - disk radius;

For a given disk, angles α = 30°, β = 60°, γ = 90°, which means that the O axes_x1, O_x2 and O_x3 coincide with the x, y and z axes respectively.

Thus, the moment of inertia of the disk relative to the Ox1 axis is equal to:

I_x1 = (m·r²)/4 = (0,8·0,1²)/4 = 2,5 · 10^-3

So the answer is 2.5 10^-3.

Solution to problem 14.4.22 from the collection of Kepe O..

This solution is a high-quality and reliable solution to problem 14.4.22 from the collection of Kepe O.. The solution was made by an experienced specialist in the field of physics and mathematics and meets all requirements and quality standards.

Problem 14.4.22 requires calculating the moment of inertia of a thin homogeneous disk relative to the Ox1 axis at given angles α = 30°, β = 60°, γ = 90° and mass m = 0.8 kg and radius r = 0.1 m.

Our solution contains a detailed description of the process of calculating the moment of inertia of the disk, as well as all the necessary formulas and calculations. In addition, we have presented our solution in a beautiful and understandable html format so that you can easily and quickly familiarize yourself with the solution to the problem and use it for your own purposes.

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The proposed solution to problem 14.4.22 from the collection of Kepe O.?. is of high quality and reliable. To calculate the moment of inertia of a thin homogeneous disk with a mass of 0.8 kg and a radius of 0.1 m relative to the Ox1 axis at given angles α = 30°, β = 60°, γ = 90°, we use the formula Ix1 = (m r2)/4 , where m is the mass of the disk, r is its radius.

For a given disk, the angles α = 30°, β = 60°, γ = 90°, which means that the Ox1, Ox2 and Ox3 axes coincide with the x, y and z axes, respectively. Therefore, the moment of inertia of the disk relative to the Ox1 axis is equal to Ix1 = (m·r2)/4 = (0.8·0.12)/4 = 2.5 · 10-3.

Our solution contains a detailed description of the process of calculating the moment of inertia of the disk, as well as all the necessary formulas and calculations. We have presented our solution in a beautiful and understandable format so that you can quickly and easily familiarize yourself with it and use it for your purposes.

By purchasing our solution, you can be confident in its quality and reliability, and also receive a convenient and understandable product in a beautiful format.

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Solution to problem 14.4.22 from the collection of Kepe O.?. consists in determining the moment of inertia of a thin homogeneous disk with mass m = 0.8 kg and radius r = 0.1 m relative to the Ox1 axis, if angles α = 30°, β = 60°, γ = 90°.

To solve the problem, it is necessary to use the formula for the moment of inertia of a thin disk relative to an axis passing through its center of mass:

I = (m * r^2) / 2

Here m is the mass of the disk, r is its radius.

However, in this problem it is required to find the moment of inertia about an axis different from the axis passing through the center of mass. To do this, you need to use the formula for converting the moment of inertia about one axis to the moment of inertia about another axis:

I1 = I2 + m * d^2

Here I1 is the moment of inertia relative to the new axis, I2 is the moment of inertia relative to the old axis (in this case, the axis passing through the center of mass), m is the mass of the disk, d is the distance between the axes.

To solve the problem, it is necessary to determine the distance between the axes. To do this, you can use the cosine theorem:

d^2 = r^2 + R^2 - 2 * r * R * cos(γ)

Here R is the distance from the center of the disk to the new axis, γ is the angle between the line connecting the center of the disk and the new axis, and the line connecting the center of the disk and the old axis.

After substituting known quantities into the formulas and performing the necessary calculations, we get the answer:

I = (m * r^2) / 2 + m * (r^2 + R^2 - 2 * r * R * cos(γ))

I = 2.5 * 10^-3 kg * m^2

Thus, the moment of inertia of a thin homogeneous disk with a mass of 0.8 kg and a radius of 0.1 m relative to the Ox1 axis, if the angles α = 30°, β = 60°, γ = 90°, is equal to 2.5 * 10^-3 kg * m^2.

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