Solution to problem 9.2.12 from the collection of Kepe O.E.

9.2.12 Does the OA crank rotate according to the law? = 0.5t. It is necessary to determine the angular speed of wheel 1 of the planetary mechanism if the length of link OA is 0.2 meters and the radii of all wheels are the same. Answer: 0.

To solve this problem, it is necessary to determine the angular velocity of wheel 1 of the planetary mechanism. To do this, you can use a formula that connects the speed of a point on a circle with the angular speed of rotation: v = Rω, where v is the speed of a point on a circle, R is the radius of the circle, ω is the angular speed of rotation.

In our case, all wheels have the same radius, so we can immediately proceed to calculating the angular velocity. Angular velocity is defined as the derivative of the rotation angle with respect to time: ω = dφ/dt.

The crank rotation law is given as φ = 0.5t, so you can find the angular velocity as a derivative of this function: ω = d(0.5t)/dt = 0.5 rad/s.

Since wheel 1 is connected to link OA, its angular velocity will be equal to the angular speed of link OA. The OA link, in turn, connects all the wheels of the planetary mechanism. Since the radii of all wheels are the same, the angular velocity of all wheels will also be the same and equal to ω = 0.5 rad/s.

Thus, the answer to the problem is 0, because the angular velocity of wheel 1 of the planetary mechanism is zero.

Solution to problem 9.2.12 from the collection "Problems in Theoretical Mechanics" by O. Kepe.

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A digital product is offered - a solution to problem 9.2.12 from the collection "Problems in Theoretical Mechanics" by Kepe O.?.

To solve this problem, it is necessary to determine the angular velocity of wheel 1 of the planetary mechanism, which is connected to the OA link. The radii of all wheels are the same, so you can immediately proceed to calculating the angular velocity.

Angular velocity is defined as the derivative of the rotation angle with respect to time: ω = dφ/dt. The crank rotation law is given as φ = 0.5t, so you can find the angular velocity as a derivative of this function: ω = d(0.5t)/dt = 0.5 rad/s.

Since wheel 1 is connected to link OA, its angular velocity will be equal to the angular speed of link OA. The OA link, in turn, connects all the wheels of the planetary mechanism. Since the radii of all wheels are the same, the angular velocity of all wheels will also be the same and equal to ω = 0.5 rad/s.

Thus, the answer to the problem is 0, because the angular velocity of wheel 1 of the planetary mechanism is zero.

By purchasing this digital product, you get access to a complete and detailed solution to the problem in a beautiful html format, with explanations and formulas, which will help you better understand and assimilate the material on theoretical mechanics. This is a useful and high-quality solution to a theoretical mechanics problem that will help you prepare for exams or improve your knowledge in this field.

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This product is a solution to problem 9.2.12 from the collection of Kepe O.?. The task is to determine the angular velocity of wheel 1 of the planetary mechanism during rotation of the crank OA, which rotates according to the law? = 0.5t. The length of the link OA is 0.2 m, and the radii of all wheels are the same. The answer to the problem is 0.

Thus, this product is intended for those who are interested in solving problems in mechanics and want to receive a ready-made solution to this specific problem from the collection of Kepe O.?.

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