Solution to problem 15.4.1 from the collection of Kepe O.E.

15.4.1

Given: rotation speed of the fan impeller = 90 rpm, moment of inertia of the wheel relative to the axis of rotation = 2.2 kg • m2.

You need to find: the kinetic energy of the wheel.

Answer:

Let's convert the fan wheel speed from rpm to rad/s:

$\omega = \dfrac{2\pi n}{60}$, where $n$ is the rotation speed in rpm, $\omega$ is the rotation speed in rad/s.

Substituting the values, we get:

$\omega = \dfrac{2\pi \cdot 90}{60} \approx $9.42/с.

The kinetic energy of the wheel is calculated by the formula:

$E_k = \dfrac{J\omega^2}{2}$, where $J$ is the moment of inertia of the wheel relative to the axis of rotation.

Substituting the values, we get:

$E_k = \dfrac{2,2 \cdot 9,42^2}{2} \approx 97,7$.

Answer: The kinetic energy of the wheel is 97.7.

Solution to problem 15.4.1 from the collection of Kepe O..

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This product is a digital solution to problem 15.4.1 from the collection of problems in physics by Kepe O.?. The product includes a step-by-step description of the process of solving the problem with detailed calculations and an answer.

To solve the problem, it is necessary to convert the rotation speed of the fan wheel from revolutions per minute to radians per second, using the relation $ \omega = \dfrac{2\pi n}{60}$, where $n$ is the rotation speed in revolutions per minute, $ \omega$ - rotation frequency in radians per second. Then using the formula for kinetic energy $E_k = \dfrac{J\omega^2}{2}$, where $J$ is the moment of inertia of the wheel relative to the axis of rotation, you can calculate the kinetic energy of the wheel.

By purchasing this product, the buyer receives a ready-made solution to problem 15.4.1 from the collection of Kepe O.?. in a convenient and beautiful format, which allows you to save time on solving the problem yourself and conveniently use the acquired knowledge for further preparation.

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The product in this case is the solution to problem 15.4.1 from the collection of Kepe O.?. The problem is formulated as follows: it is required to determine the kinetic energy of the fan impeller if its rotation speed (90 rpm) and the moment of inertia relative to the axis of rotation (2.2 kg • m2) are known.

The solution to this problem can be obtained by applying the formula for calculating the kinetic energy of a rotating body:

Eк = (I * w^2) / 2,

where Ek is kinetic energy, I is moment of inertia, w is angular velocity.

Substituting the known values, we get:

Ek = (2.2 * (90 * 2 * π / 60)^2) / 2 ≈ 97.7 J.

Thus, the answer to the problem is 97.7.

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