Solution to problem 21.1.3 from the collection of Kepe O.E.

Problem 21.1.3 is to determine the natural frequency of small vibrations of a ring gear 1 with a mass of 40 kg, which can rotate relative to the center 2, compressing the springs. In the equilibrium position, the springs are not deformed. The radius of inertia of the crown is 0.24 m, the stiffness coefficient of one spring is 5 • 105 N/m, and the radius of the crown is r = 0.2 m.

To solve the problem it is necessary to use the equation of small oscillations:

ω^2 = k / I,

where ω is the natural frequency, k is the spring stiffness coefficient, I is the moment of inertia.

Let's calculate the moment of inertia of the ring gear relative to the center:

I = (m * r^2) / 2,

where m is the mass of the crown, r is the radius of the crown.

Substituting the known values, we get:

I = (40 kg * 0.2 m)^2 / 2 = 0.32 kg * m^2.

Now we can calculate the natural frequency of small oscillations:

ω = √(k / I) = √(5 • 10^5 N/m / 0.32 kg * m^2) ≈ 29.7 rad/s.

Thus, the natural frequency of small vibrations of the ring gear is 29.7 rad/s.

Solution to problem 21.1.3 from the collection of Kepe O.?.

We present to your attention the solution to problem 21.1.3 from the collection of Kepe O.?. - a digital product that will help you successfully complete a physics task. This product is intended for schoolchildren, students and anyone interested in physics.

Product description:

• Title: Solution of problem 21.1.3 from the collection of Kepe O.?.
• Product type: digital product
• Format: PDF
• Russian language
• Number of pages: 1
• Description: Solution to problem 21.1.3 from the collection of Kepe O.?. consists in determining the natural frequency of small vibrations of the ring gear, which can rotate relative to the center, compressing the springs. To solve this problem, the equation of small vibrations and formulas for calculating the moment of inertia and natural frequency are used. The solution is presented in a clear and concise form, which will make it easy to understand and remember the material.

Product advantages:

• An easy to understand solution to the problem
• Suitable for schoolchildren, students and anyone interested in physics
• File in PDF format, which can be downloaded immediately after payment
• Beautiful design in HTML format

How to use the product:

Download the file with the solution to problem 21.1.3 from the collection of Kepe O.?. after payment. Open the file in a PDF viewer. Study the solution to the problem and use it for your learning purposes.

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This item is digital and available in PDF format only. After payment you will receive a link to download the file. No physical copies of the item will be sent by mail.

Solution to problem 21.1.3 from the collection of Kepe O.?. is a digital product that contains a solution to a given physical problem. The task is to determine the natural frequency of small vibrations of a ring gear weighing 40 kg, which can rotate relative to center 2, compressing the springs. In this case, the springs are not deformed in the equilibrium position. The radius of inertia of the crown is 0.24 m, the stiffness coefficient of one spring is 5 • 105 N/m, and the radius of the crown is r = 0.2 m.

To solve the problem, the equation of small vibrations is used: ω^2 = k / I, where ω is the natural frequency, k is the spring stiffness coefficient, I is the moment of inertia. The moment of inertia of the ring gear relative to the center is calculated by the formula: I = (m * r^2) / 2, where m is the mass of the ring, r is the radius of the ring.

Substituting the known values, we get: I = (40 kg * 0.2 m)^2 / 2 = 0.32 kg * m^2. Now we can calculate the natural frequency of small vibrations: ω = √(k / I) = √(5 • 10^5 N/m / 0.32 kg * m^2) ≈ 29.7 rad/s.

The solution to the problem is presented in the form of a PDF file, which contains a concise and understandable description of the solution. The file can be downloaded immediately after payment. The product also has a beautiful design in HTML format. The solution is suitable for use for educational purposes by schoolchildren, students and anyone interested in physics.

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Problem 21.1.3 from the collection of Kepe O.?. consists in determining the natural frequency of small vibrations of a gear ring weighing 40 kg, which can rotate relative to the center when the springs are compressed. In the equilibrium position, the springs are not deformed. The radius of inertia of the crown (0.24 m), the stiffness coefficient of one spring (5 • 105 N/m) and the radius of the crown (0.2 m) are given. The answer to the problem is 29.7.

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