Solution to problem 11.5.5 from the collection of Kepe O.E.

11.5.5 A coil rotating around the OO1 axis has an angular velocity ω = 2 rad/s. Point M moves along the coil according to the law M0M = 0.04t2. If the radius is r = 0.02 m, then it is necessary to determine the absolute acceleration of point M. The answer to the problem is 0.113.

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Problem 11.5.5 from the collection of Kepe O.?. describes the movement of point M, which moves along a coil rotating around the OO1 axis with an angular velocity ω = 2 rad/s. The law of motion of point M is given as M0M = 0.04t2, where t is the time of motion of point M. The radius of the coil is r = 0.02 m. It is necessary to determine the absolute acceleration of point M.

To solve the problem, it is necessary to calculate the speed and acceleration of point M relative to the center of the coil O, and then sum them with the corresponding values ​​associated with the rotation of the coil around the OO1 axis.

First, let's find the speed of point M relative to the center of the coil O. To do this, it is necessary to differentiate the given law of motion in time:

v = d(M0М)/dt = 0.08t

Then we find the acceleration of point M relative to the center of the coil O:

a = dv/dt = 0.08 м/c^2

Now let's find the acceleration of point M associated with the rotation of the coil around the OO1 axis. To do this, we use the formula for accelerating the center of rotation:

a_0 = rω^2 = 0.022^2 = 0.08 m/c^2

Finally, the absolute acceleration of point M is determined as the sum of the accelerations found earlier:

a_abs = √(a^2 + a_0^2) = √(0.08^2 + 0.08^2) = 0.113 м/c^2

Answer: 0.113 m/s^2.

Problem 11.5.5 from the collection of Kepe O.?. relates to the field of mathematics and is associated with solving systems of linear equations using the Cramer method. The problem contains a system of three equations with three unknowns that needs to be solved. To do this, you need to find the determinants of the matrix of the system and the matrix obtained from the system by replacing the columns. Then you should calculate the values ​​of the unknowns using Cramer's formulas. Solving the problem requires knowledge of matrix algebra and the ability to apply Cramer's method to solve systems of linear equations. Solving the problem can be useful in studying mathematics, physics, economics and other sciences in which problems arise with systems of linear equations.

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