Solution to problem 16.1.31 from the collection of Kepe O.E.

Solution to problem 16.1.31 from the collection of Kepe O..

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The solution is presented in the form of a convenient HTML page, which describes the process of solving the problem step by step. The solution uses basic laws of physics, such as the law of change of momentum for rotational motion.

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Digital product "Solution to problem 16.1.31 from the collection of Kepe O.?." provides a detailed solution to a physics problem that may arise when studying physics. The solution to this problem involves the use of basic laws of physics, such as the law of change of momentum for rotational motion.

For the convenience of users, the solution to the problem is presented in the form of a convenient HTML page, which describes the solution process step by step. The solution is equipped with a beautiful html design, formulas, images and explanations, which allows you to better understand the process of solving the problem and consolidate the learned material.

Solution to problem 16.1.31 from the collection of Kepe O.?. consists in determining the time during which the angular velocity of the ball will double under the influence of the torque Mz. To solve the problem, it is necessary to use data on the moment of inertia and the initial angular velocity of the ball.

By purchasing this digital product, you receive a complete and detailed solution to problem 16.1.31 from the collection of Kepe O.?. in Physics, which will be useful and practically applicable in your studies and daily life, and can also be used as reference material when preparing for exams and tests in Physics. The answer to the problem is 15.

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Problem 16.1.31 from the collection of Kepe O.?. consists in determining the time during which the angular velocity of a homogeneous ball with a moment of inertia Iz = 4 kg • m2 doubles under the influence of a torque Mz = 1.2 N • m.

From the conditions of the problem we know the initial value of the angular velocity of the ball ?0 = 4.5 rad/s and the moment of inertia Iz = 4 kg • m2. It is necessary to determine the time during which the angular velocity will double under the action of a moment Mz = 1.2 N • m.

To solve the problem, you can use the equation of dynamics of rotational motion:

Mz = Iz * α

where Mz is torque, α is angular acceleration, Iz is moment of inertia.

It is also known that angular acceleration is related to angular velocity and time as follows:

α = Δω / Δt

where Δω is the change in angular velocity, Δt is the time during which the change occurs.

Thus, to determine time, you need to find the change in angular velocity using the initial and final values ​​of angular velocity, and then express time in terms of angular acceleration and torque.

From the conditions of the problem it follows that we need to find the time during which the angular velocity will double, that is, it will be equal to 2 * ?0 = 9 rad/s.

Using the equation of rotational motion dynamics, we can express angular acceleration:

α = Mz / Iz = 1.2 N • m / 4 kg • m2 = 0.3 rad/s2

Then we express time in terms of angular acceleration and change in angular velocity:

Do = 2 * ?0 - ?0 = ?0

Δt = Δω / α = 4.5 rad/s / 0.3 rad/s2 = 15 s

Answer: 15 s.

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