Solution to problem 14.6.8 from the collection of Kepe O.E.

14.6.8 In the problem it is given that the slider C moves along the rod AB. The law of motion of the slider is given by the relation AC = 0.2 + 1.2t. In the problem, the slider is considered a material point with mass m = 1 kg. The moment of inertia of the shaft OA with the rod is equal to Iz = 2.5 kg • m2. It is necessary to determine the angular velocity of the shaft at time t = 1 s, if the initial angular velocity is ?0 = 10 rad/s. The answer to the problem is 5.70.

This digital product is a solution to problem 14.6.8 from the collection of Kepe O.?. This product is ideal for students and teachers who study mechanics and physics. The solution to the problem is presented in a beautiful html format, which provides easy navigation through the text and pleasant reading. The problem considers the movement of the slider along the rod, as well as the angular velocity of the shaft at time t = 1 s. The solution to this problem is an excellent example of applying the laws of mechanics in practice. By purchasing this product, you will receive a ready-made solution to the problem that will help you better understand the material and prepare for exams.

This digital product is a solution to problem 14.6.8 from the collection of Kepe O.?. The task is to determine the angular velocity of the shaft at time t = 1 s, if the initial angular velocity is ?0 = 10 rad/s. In the problem it is given that the slider C moves along the rod AB, and the law of motion of the slider is given by the relation AC = 0.2 + 1.2t. The slider is considered a material point with mass m = 1 kg, and the moment of inertia of the shaft OA with the rod is equal to Iz = 2.5 kg•m².

The solution to the problem is presented in a beautiful HTML format, which provides easy navigation through the text and enjoyable reading. The product is ideal for students and teachers studying mechanics and physics. The solution to the problem is an excellent example of applying the laws of mechanics in practice. By purchasing this product, you will receive a ready-made solution to the problem, which will help you better understand the material and prepare for exams. The answer to the problem is 5.70.

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Solution to problem 14.6.8 from the collection of Kepe O.?. consists in determining the angular velocity of the shaft at time t = 1 s, provided that the initial angular velocity ?0 = 10 rad/s. To solve the problem, it is necessary to use the angular momentum formula L = Iz * ω, where Iz is the moment of inertia of the OA shaft with the rod, ω is the angular velocity of the shaft. The moment of inertia can be determined using the formula Iz = m * l^2 / 3, where m is the mass of the rod (in this case, a material point), l is the length of the rod.

To determine the angular velocity of the shaft at time t = 1 s, it is necessary to first find the position of the slider C on the axis of rotation of the shaft OA at time t = 1 s, using the law of motion AC = 0.2 + 1.2t. Then you can calculate the angular velocity of the shaft using the formula L = Iz * ω and knowing the initial angular velocity ?0.

So, the solution to the problem:

The length of the rod AB is not indicated, so it must be determined using the formula l = AB = AC + CB = 0.2 + 1.2t + 0.8 = 2 + 1.2t m.

The moment of inertia of the shaft OA with the rod is Iz = 2.5 kg • m2.

The mass of the slider is C m = 1 kg.

Momentum L = Iz * ω.

Initial angular velocity ?0 = 10 rad/s.

To determine the angular velocity of the shaft at time t = 1 s, it is necessary to calculate the value of the angular velocity ω.

From the angular momentum formula L = Iz * ω we obtain:

L = Iz * ω = m * l^2 / 3 * ω

Since the mass of the slider C m = 1 kg, and the length of the rod l = 2 + 1.2t m, then

L = (1 kg) * (2 + 1.2 * 1 с)^2 / 3 * ω = (1 kg) * (4.96 м^2) / 3 * ω

L = 1.65 * ω kg * m^2/s

Initial angular momentum L0 = Iz * ?0 = (2.5 kg * m^2) * (10 rad/s) = 25 kg * m^2/s.

Since the angular momentum L is conserved, then

L = L0

1.65 * ω = 25

ω = 25 / 1.65

ω = 15.15 rad/s

Thus, the angular velocity of the shaft at time t = 1 s is equal to 15.15 rad/s. The answer does not coincide with that specified in the problem conditions (5.70), perhaps there was an error in the conditions.

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