Solution to problem 6.2.6 from the collection of Kepe O.E.

The coordinate of the center of gravity of the area of ​​the circular sector OAB can be determined with a radius r = 0.6 m and an angle a = 30°. The answer is 0.382.

Solution to problem 6.2.6 from the collection of Kepe O.?.

We present to your attention the solution to problem 6.2.6 from the collection of Kepe O.?. is a digital product that will help you solve this problem easily and quickly.

The task is to determine the coordinate xc of the center of gravity of the area of ​​the circular sector of the OAB for given values ​​of the radius r and angle a.

Our solution contains a detailed description of the steps you need to follow to get the correct answer. We also provide a ready-made answer, which is 0.382.

By purchasing our solution, you save time and get a guaranteed correct result.

Solution to problem 6.2.6 from the collection of Kepe O.?. is a digital product that is designed to solve a specific problem. The task is to determine the coordinate xc of the center of gravity of the area of ​​the circular sector of the OAB for given values ​​of the radius r and angle a.

To solve this problem, it is necessary to perform a number of mathematical operations, which are described in detail in our solution. We also provide a ready-made answer, which is 0.382.

By purchasing our solution, you save your time and get a guaranteed correct result. You can use this solution both to solve the problem yourself and to test your own solutions.

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Solution to problem 6.2.6 from the collection of Kepe O.?. consists in determining the coordinate xc of the center of gravity of the area of ​​the circular sector of the OAB. To do this, you need to know the radius of the circle and the angle of the sector. In this problem, the radius is 0.6 m and the angle is 30°.

First you need to determine the coordinates of the center of the circle, which is the basis of the sector. The coordinates of the center of the circle coincide with the coordinates of the center of gravity of the figure. The coordinates of the center of the circle can be found using the formula x = a and y = b, where a and b are the coordinates of a point lying on the circle.

Since the sector angle is 30°, the center of the circle is at a distance r/2 from the top of the sector. Thus, the coordinates of the center of the circle can be defined as x = r/2cos(α/2) and y = r/2sin(α/2), where α is the angle in radians.

After determining the coordinates of the center of the circle, it is necessary to calculate the xc coordinate of the center of gravity of the sector area. To do this, it is necessary to divide the moment of inertia of the figure relative to the OX axis by its area. Taking into account the symmetry of the figure relative to the OY axis, it is possible to calculate the moment of inertia only relative to the OX axis.

So, the coordinate xc of the center of gravity is calculated by the formula xc = (2r*sin(α/2)/(3α) - y)*S, where S is the area of ​​the sector.

Substituting the known values, we get the answer: xc = 0.382.

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