Solution to problem 14.1.10 from the collection of Kepe O.E.

Let us consider a homogeneous equilateral triangle OAB with mass m = 5 kg, which rotates uniformly around a fixed axis. We need to determine its angular velocity? with the main vector of external forces equal to 300 N and length l equal to 0.4 m.

To solve the problem, we use the formula for the moment of force: M = F * l, where F is the magnitude of the force, l is the length of the vector.

Since the triangle is equilateral, its center of mass is at the intersection of the medians, and the angle between the medians is 60 degrees. Therefore, each median divides the triangle into two equal parts, and we can only consider one half of the triangle.

Let's divide the main vector into two components in the direction of the median and perpendicular to them. Since the medians equally divide the triangle into equal parts, the components of the main vector will also be equal.

Thus, we can consider only one component of the main vector. Its value is equal to F/2 = 150 N.

The length of the median is l/2 = 0.2 m.

The moment of force is equal to M = F * l/2 = 150 * 0.2 = 30 N * m.

According to the law of conservation of angular momentum, the moment of inertia of a body multiplied by its angular velocity must remain constant. Since the moment of inertia of an equilateral triangle is equal to 1/6 * m * a^2, where a is the length of the side of the triangle, then:

M * t = 1/6 * m * a^2 * ?, where t is the rotation time.

From the properties of an equilateral triangle it follows that a = 2/3 * l. Substituting all known values, we get:

30 * t = 1/6 * 5 * (2/3 * 0,4)^2 * ?.

Solving the equation, we obtain the angular velocity: ? = 16.1 rad/s.

Solution to problem 14.1.10 from the collection of Kepe O.?.

This digital product is a solution to problem 14.1.10 from the collection of Kepe O.?. in physics. The solution is made by a professional teacher and presented in a beautifully designed HTML page.

The problem considers the rotation of a homogeneous equilateral triangle around a fixed axis. The solution uses formulas for the moment of force and the law of conservation of angular momentum.

By purchasing this digital product, you receive a ready-made solution to the problem, which can be used to independently prepare for exams or to test your knowledge in physics. In addition, you can use a designed HTML page to conveniently and beautifully view the solution to the problem.

Purchase the solution to problem 14.1.10 from the collection of Kepe O.?. right now and improve your knowledge in physics!

This digital product is a solution to problem 14.1.10 from the collection of problems in physics O.?. Kepe. The problem is to determine the angular velocity of a homogeneous equilateral triangle with a mass of 5 kg when rotating around a fixed axis with a main vector of external forces equal to 300 N and a rotation beam length equal to 0.4 m.

To solve the problem, formulas for the moment of force and the law of conservation of angular momentum were used. The solution is made by a professional teacher and presented in a beautifully designed HTML page.

By purchasing this digital product, you receive a ready-made solution to the problem, which can be used to independently prepare for exams or to test your knowledge in physics. In addition, you can use a designed HTML page to conveniently and beautifully view the solution to the problem.

Purchase the solution to problem 14.1.10 from the collection of Kepe O.?. right now and improve your knowledge in physics! Answer to the problem: 16.1 rad/s.

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Problem 14.1.10 from the collection of Kepe O.?. consists in determining the angular velocity of a homogeneous equilateral triangle OAB with a mass of 5 kg, which rotates uniformly around a fixed axis. The following data are given: the main vector of external forces acting on the triangle is 300 N, and the length l is 0.4 m.

It is necessary to determine the angular velocity of this triangle. The answer to the problem is 16.1.

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