Solution to problem 15.6.2 from the collection of Kepe O.E.

15.6.2

What is the initial angular velocity ⌀₀ is it necessary to tell a homogeneous rod of length l = 3 m so that it rotates around the horizontal axis O and makes half a revolution?

Answer: 4.43.

To solve this problem it is necessary to use the laws of conservation of energy and angular momentum. When the rod rotates, its kinetic energy is converted into positional potential energy. When the rod reaches its maximum height point, all its kinetic energy will be converted into potential energy.

From the law of conservation of angular momentum it follows that the moment of inertia of the rod, multiplied by the initial angular velocity, must be equal to the moment of inertia of the rod, multiplied by its final angular velocity. The final angular velocity of the rod can be found from the condition that it makes half a revolution. In this case, the final angular velocity will be equal to zero.

From the law of conservation of energy it follows that the kinetic energy of the rod at the initial moment of time must be equal to the potential energy of the rod at the moment of its maximum height. This allows us to express the initial angular velocity in terms of the length of the rod and the acceleration of gravity. The result of solving the problem is the value of the initial angular velocity equal to 4.43 rad/s.

Solution to problem 15.6.2 from the collection of Kepe O..

This digital product is a solution to problem 15.6.2 from a collection of problems in physics, authored by O. Kepe. The solution to the problem was completed by a professional physics teacher and presented in PDF format.

Problem 15.6.2 is to determine the initial angular velocity of a homogeneous rod 3 m long, which makes a half revolution around a horizontal axis. The problem is solved using the laws of conservation of energy and angular momentum. The result is an initial angular velocity of 4.43 rad/s.

By purchasing this digital product, you receive a ready-made solution to the problem in a convenient format that can be used to prepare for exams, independently study physics, or to use as an example when solving similar problems.

Do not miss the opportunity to purchase the solution to problem 15.6.2 from the collection of Kepe O.. and improve your knowledge in the field of physics!

The digital product is a solution to problem 15.6.2 from a collection of problems in physics, authored by O.?. Kepe. This problem is to determine the initial angular velocity of a homogeneous rod 3 m long, which makes a half revolution around a horizontal axis. The solution to the problem was completed by a professional physics teacher and presented in PDF format.

To solve the problem, the laws of conservation of energy and angular momentum were used. When the rod rotates, its kinetic energy is converted into positional potential energy. When the rod reaches its maximum height point, all its kinetic energy will be converted into potential energy. From the law of conservation of angular momentum it follows that the moment of inertia of the rod, multiplied by the initial angular velocity, must be equal to the moment of inertia of the rod, multiplied by its final angular velocity. The final angular velocity of the rod can be found from the condition that it makes half a revolution, and in this case the final angular velocity will be equal to zero. From the law of conservation of energy it follows that the kinetic energy of the rod at the initial moment of time must be equal to the potential energy of the rod at the moment of its maximum height. This makes it possible to express the initial angular velocity in terms of the length of the rod and the acceleration of gravity.

The result of solving the problem is the value of the initial angular velocity equal to 4.43 rad/s. By purchasing this digital product, you receive a ready-made solution to the problem in a convenient format, which can be used to prepare for exams, independently study physics, or to use as an example when solving similar problems.

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Problem 15.6.2 from the collection of Kepe O.?. refers to the section of thermodynamics and is formulated as follows: “In a sealed vessel there is 0.5 mol of an ideal monatomic gas at a temperature of 300 K. How much work must be done on the gas so that its temperature increases to 600 K at constant pressure?”

Solving this problem requires the application of the law of conservation of energy and the ideal gas equation of state. First, it is necessary to calculate the initial volume of gas under given conditions, then, using the equation of state of an ideal gas, determine the initial pressure of the gas. Next, using the formula for the work that needs to be done on the gas, you can find the answer to the problem.

Solution to problem 15.6.2 from the collection of Kepe O.?. may be useful for students and teachers studying thermodynamics and wishing to test their knowledge and skills in solving problems on this topic.

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