Solution to problem 14.6.5 from the collection of Kepe O.E.

14.6.5 Rotating tank 1 has a moment of inertia about the vertical axis Oz equal to 1 kg•m2 and rotates with an angular velocity ω0 = 18 rad/s. After valve 2 has been opened, the tank is filled with bulk material. If the moment of inertia of a filled tank is 3 kg•m2, then it is necessary to determine its angular velocity. The answer is 6.

Solution to problem 14.6.5 from the collection of Kepe O.?.

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The solution to Problem 14.6.5 describes a rotating tank whose moment of inertia changes after it is filled with bulk material. Solving this problem will help you better understand the concept of moment of inertia and angular velocity.

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The offered product is a solution to problem 14.6.5 from the collection of Kepe O.?. The problem describes a rotating tank with a changing moment of inertia after filling it with bulk material. The solution includes a detailed description of all the steps required to solve the problem and the answer to the question posed. This product can be useful for students and teachers to prepare for exams, independently study a topic, or check the correctness of a problem solution. The solution is presented in the form of a beautifully designed HTML page that makes it easy to read and navigate on any device, including computers, tablets and mobile devices.

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For problem 14.6.5 from the collection of problems by Kepe O.?. the following condition is imposed:

At the initial moment of time, tank 1 with a moment of inertia of 1 kg•m2 rotates with an angular velocity ω0 = 18 rad/s. Valve 2 is open and bulk material begins to flow into the tank. After filling, the moment of inertia of the system increases to 3 kg•m2. It is required to find the angular velocity of a filled tank.

To solve the problem, we will use the law of conservation of angular momentum, which states that the angular momentum of a closed system remains constant in the absence of external moments. Therefore, we can write:

I1 * ω0 = I2 * ω2,

where I1 and I2 are the moments of inertia of the tank before and after filling, respectively, ω0 is the initial angular velocity, and ω2 is the desired angular velocity of the filled tank.

Solving the equation for ω2, we get:

ω2 = ( I1 / I2 ) * ω0 = ( 1 / 3 ) * 18 rad/s = 6 rad/s.

Answer: 6.

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