Solution to problem 15.6.5 from the collection of Kepe O.E.

Task 15.6.5:

For a rotor with a moment of inertia relative to the axis of rotation equal to 3 kg • m2, a constant moment of disturbing forces M = 9 N • m is applied. It is necessary to determine the angular acceleration of the rotor. (Answer: 3)

Solution to problem 15.6.5 from the collection of Kepe O..

We present to your attention the solution to problem 15.6.5 from the collection of Kepe O.. This digital product is an ideal choice for those who seek to deepen their knowledge in the field of mechanics. The solution to the problem is presented in a beautiful HTML format, making it easy to read and use on any device. The problem considers a rotor with a moment of inertia relative to the axis of rotation equal to 3 kg • m2, an applied constant moment of disturbing forces M = 9 N • m, and it is necessary to determine the angular acceleration of the rotor. The solution to the problem is accompanied by detailed explanations and calculations, which will help you better understand the physical principles underlying the solution of the problem.

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Solution to problem 15.6.5 from the collection of Kepe O.?. is a digital product that contains a detailed solution to a mechanics problem. The problem considers a rotor with a moment of inertia relative to the axis of rotation equal to 3 kg • m2, to which a constant moment of disturbing forces M = 9 N • m is applied. It is necessary to determine the angular acceleration of the rotor. The solution to the problem is presented in a beautiful HTML design, which makes it easy to read and use on any device. A detailed explanation and calculations are provided along with the solution to help you better understand the physics behind the solution. By purchasing this solution to the problem, you can deepen your knowledge in the field of mechanics. The answer to problem 15.6.5 is 3.

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Solution to problem 15.6.5 from the collection of Kepe O.?. consists in determining the angular acceleration of the rotor under given conditions. To do this, it is necessary to use the law of rotational motion, which states that the moment of force acting on a body is equal to the product of the moment of inertia of the body and its angular acceleration.

In this problem, the moment of inertia of the rotor (3 kg • m2) and the applied moment of force (9 N • m) are known. It is necessary to determine the angular acceleration of the rotor.

To solve the problem you need to use the formula:

М = Iα,

where M is the moment of force, I is the moment of inertia of the body, α is the angular acceleration of the body.

Substituting known values, we get:

9 N • m = 3 kg • m2 • α.

From here we find the angular acceleration of the rotor:

α = 3 rad/s2.

Thus, the angular acceleration of the rotor under given conditions is 3 rad/s2.

Solution to problem 15.6.5 from the collection of Kepe O.?. is as follows:

Given a sequence {an}, n = 1, 2, 3, ..., satisfying the conditions:

• a1 = 1;
• an+1 = (2n+1) / (n+2) * an - 2n / (n+2) * a(n-1) for all n ≥ 1.

We need to find an explicit form of the formula for an.

To solve this problem, it is necessary to use the method of mathematical induction and a recurrence relation defining the sequence {an}. At the same time, in the solution process, it is necessary to be able to perform algebraic transformations and solve equations.

The solution to the problem is to obtain a formula for an using the method of mathematical induction and the application of algebraic transformations. The final answer looks like:

and = (n+1) * 2^(n-1) / (n+2)!

where n ≥ 1.

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