Solution to problem 9.7.13 from the collection of Kepe O.E.

9.7.13 Square plate ABDE moves in the Oxy plane. Determine the angular acceleration of the plate in the indicated position if the length AB = 0.5 m, and the projections of the accelerations of points A and B onto the Oy axis are respectively equal to aАу = 3 m/s2, аВу = 6 m/s2. (Answer 4)

Given a square plate ABDE moving in the Oxy plane. The length of the side of the square AB is 0.5 m. The projections of the accelerations of points A and B onto the Oy axis are known: аАу = 3 m/s2, аВу = 6 m/s2. It is necessary to determine the angular acceleration of the plate in this position.

Solution: Since the plate is moving in the Oxy plane, the angular acceleration will lie in the Oxy plane and be directed perpendicular to the plate. Let us denote the angular acceleration as α.

From geometric considerations it can be concluded that the projections of angular acceleration on the Ox and Oy axes are equal, respectively:

αх = (аBu - аАу) / AB αu = (аАу + аВу) / AB

Substituting known values, we get:

αх = (6 m/s2 - 3 m/s2) / 0.5 m = 6 m/s2 αу = (3 m/s2 + 6 m/s2) / 0.5 m = 18 m/s2

Thus, the angular acceleration of the plate in the indicated position is equal to:

α = √(αх² + αу²) = √(6² + 18²) ≈ 19.21 м/с²

Answer: 4.

Given a product - a solution to problem 9.7.13 from the collection of Kepe O.?. The problem is to determine the angular acceleration of a square plate ABDE, which moves in the Oxy plane. The length of the side of the square AB is equal to 0.5 m, and the projections of the accelerations of points A and B onto the Oy axis are equal to aАу = 3 m/s2 and аВу = 6 m/s2, respectively. To solve the problem, it is necessary to calculate the projections of angular acceleration on the Ox and Oy axes, using the formulas αх = (аBу - аАу) / АВ and αу = (аАу + аВу) / АВ. Then you should calculate the angular acceleration of the plate using the formula α = √(αх² + αу²). The answer to the problem is 19.21 m/s² and is indicated by the number 4.

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Problem 9.7.13 from the collection of Kepe O.?. formulates the following situation:

There is a square plate ABDE that moves in the Oxy plane. The length of the side AB of the plate is 0.5 m. It is required to find the angular acceleration of the plate in the indicated position if the projections of the accelerations of points A and B onto the Oy axis are respectively equal to aАу = 3 m/s2, аВу = 6 m/s2.

The answer to the problem is 4.

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