Solution to problem 15.4.5 from the collection of Kepe O.E.

15.4.5 Determination of the kinetic energy of a homogeneous rectangular plate with a mass m = 18 kg, rotating around the axis AB with an angular velocity ? = 4 rad/s and having a length b = 1 m. To solve this problem, we use the formula for calculating the kinetic energy of a rotating body: Ke = IΩ²/2, where I is the moment of inertia of the body, Ω is the angular velocity of rotation of the body. The moment of inertia of a rectangular plate relative to the AB axis is equal to: I = mb²/12, where b is the length of the plate. Thus, the kinetic energy of the plate: Ke = mb²Ω²/24 = 18*1²*4²/24 = 48 J. Answer: 48.

Solution to problem 15.4.5 from the collection of Kepe O..

We present to your attention a digital solution to problem 15.4.5 from the collection “Problems in General Physics” by the author Kepe O. This digital product is intended for students and schoolchildren who study physics and solve problems in this science.

Problem 15.4.5 is to determine the kinetic energy of a homogeneous rectangular plate with a mass of 18 kg, rotating around an axis AB with an angular velocity of 4 rad/s and having a length of 1 m. The solution to the problem is presented in the form of formulas and a step-by-step algorithm of actions, accompanied by detailed comments and explanations.

This digital product allows you to quickly and efficiently solve problem 15.4.5, saving time and effort on searching for information in textbooks and reference sources. It can be used both for independent work and for preparing for exams and testing.

Digital solution to problem 15.4.5 from the collection of Kepe O.. is a convenient and practical digital product that will help you quickly and efficiently solve a physics problem.

We present a digital product - the solution to problem 15.4.5 from the collection "Problems in General Physics" by the author Kepe O.?. The problem is to determine the kinetic energy of a homogeneous rectangular plate with a mass of 18 kg, which rotates around the axis AB with an angular velocity of 4 rad/s and has a length of 1 m. To solve the problem, use the formula for calculating the kinetic energy of a rotating body: Ke = IΩ²/2, where I is the moment of inertia of the body, Ω is the angular velocity of rotation of the body. The moment of inertia of a rectangular plate relative to the AB axis is equal to I = mb²/12, where b is the length of the plate. As a result, the kinetic energy of the plate is 48 J.

The digital product is intended for students and schoolchildren who study physics and solve problems in this science. It is presented in the form of formulas and a step-by-step algorithm of actions, accompanied by detailed comments and explanations. Such a digital product will help you quickly and efficiently solve problem 15.4.5, saving time and effort on searching for information in textbooks and reference sources. It can be used both for independent work and for preparing for exams and testing.

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Solution to problem 15.4.5 from the collection of Kepe O.?. consists in determining the kinetic energy of a homogeneous rectangular plate that rotates around the AB axis with an angular velocity ? = 4 rad/s and has a mass m = 18 kg and a length b = 1 m.

To solve the problem, you need to use the formula for the kinetic energy of a rotating body:

K = (1/2) * I * w^2,

where K is kinetic energy, I is the moment of inertia of the body around the axis of rotation, w is the angular velocity of rotation of the body.

The moment of inertia of a rectangular plate about an axis passing through its center of mass and perpendicular to its plane is equal to:

I = (1/12) * m * (a^2 + b^2),

where a and b are the dimensions of the plate.

Since the plate is uniform and rectangular, its dimensions are a = b = 1 m.

Substituting the known values ​​into the formulas, we get:

I = (1/12) * 18 * (1^2 + 1^2) = 1.5 kg*m^2

K = (1/2) * 1.5 * 4^2 = 48 J

Thus, the kinetic energy of the plate under the given conditions is 48 J.

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