Solution to problem 14.5.17 from the collection of Kepe O.E.

14.5.17 Consider a mechanical system consisting of a cylinder 1 and a load 2, rotating around an axis of rotation with an angular velocity ? = 20 rad/s. The cylinder has a moment of inertia about this axis I = 2 kg • m2, and the radius of the cylinder is r = 0.5 m. Load 2 has a mass m2 = 1 kg. Let's find the kinetic moment of the mechanical system relative to the axis of rotation.

The kinetic moment of a mechanical system can be calculated by the formula L = L1 + L2, where L1 is the kinetic moment of cylinder 1, and L2 is the kinetic moment of load 2.

The kinetic moment of cylinder 1 can be calculated using the formula L1 = I1 * ?, where I1 is the moment of inertia of cylinder 1 relative to the axis of rotation, and ? - angular speed of rotation.

Substituting the values, we get:

L1 = I1 * ? = 2 kg • m2 * 20 rad/s = 40 kg • m2/s

The kinetic moment of load 2 can be calculated by the formula L2 = m2 * r2 * ?, where m2 is the mass of load 2, and r2 is the distance from load 2 to the axis of rotation.

Substituting the values, we get:

L2 = m2 * r2 * ? = 1 kg * (0.5 m)2 * 20 rad/s = 5 kg • m2/s

Then the kinetic moment of the mechanical system will be equal to:

L = L1 + L2 = 40 kg • m2/s + 5 kg • m2/s = 45 kg • m2/s

Thus, the kinetic moment of the mechanical system relative to the axis of rotation is equal to 45 kg • m2/s.

Solution to problem 14.5.17 from the collection of Kepe O.?.

We present to your attention the solution to one of the problems from the collection of Kepe O.?. - "Physical tasks."

The digital product is a complete and detailed solution to Problem 14.5.17, which concerns the rotation of a mechanical system consisting of a cylinder and a weight around an axis of rotation.

To solve this problem, the basic laws of mechanics and formulas necessary to calculate the kinetic moment of a mechanical system relative to the axis of rotation are used.

Our solution is presented in a convenient and understandable format that will help you easily understand the principle of solving the problem and get the desired result.

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We present to your attention the solution to problem 14.5.17 from the collection of Kepe O.?. - "Physical tasks."

Given a mechanical system consisting of a cylinder 1 and a load 2, rotating around an axis of rotation with an angular velocity ? = 20 rad/s. The cylinder has a moment of inertia about this axis I = 2 kg • m2, and the radius of the cylinder is r = 0.5 m. Load 2 has a mass m2 = 1 kg.

It is necessary to find the kinetic moment of the mechanical system relative to the axis of rotation. The kinetic moment of a mechanical system can be calculated by the formula L = L1 + L2, where L1 is the kinetic moment of cylinder 1, and L2 is the kinetic moment of load 2.

The kinetic moment of cylinder 1 can be calculated using the formula L1 = I1 * ?, where I1 is the moment of inertia of cylinder 1 relative to the axis of rotation, and ? - angular speed of rotation. Substituting the values, we get:

L1 = I1 * ? = 2 kg • m2 * 20 rad/s = 40 kg • m2/s

The kinetic moment of load 2 can be calculated by the formula L2 = m2 * r2 * ?, where m2 is the mass of load 2, and r2 is the distance from load 2 to the axis of rotation. Substituting the values, we get:

L2 = m2 * r2 * ? = 1 kg * (0.5 m)2 * 20 rad/s = 5 kg • m2/s

Then the kinetic moment of the mechanical system will be equal to:

L = L1 + L2 = 40 kg • m2/s + 5 kg • m2/s = 45 kg • m2/s

Answer: 45 kg • m2/s.

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