Solution to problem 16.1.26 from the collection of Kepe O.E.

16.1.26 Determine the angular velocity of the flywheel, the mass of which is m = 12 kg and the radius of gyration i = 1.73 m, 3 s after the start of movement. The flywheel is acted upon by a torque Mz = 6 N • m. (Answer 0.501)

Solution to problem 16.1.26 from the collection of Kepe O.?. consists in determining the angular velocity of the flywheel 3 s after the start of movement. Problem data: flywheel mass m = 12 kg, radius of gyration i = 1.73 m, torque Mz = 6 N • m.

To solve the problem, it is necessary to use the equation of dynamics of rotational motion:

Мz = Iα

where Mz is torque, I is moment of inertia, α is angular acceleration.

To determine the angular velocity, it is necessary to know the value of the angular acceleration, which can be found from the equation for angular acceleration:

α = ω/t

where ω is angular velocity, t is time.

From these equations we can express the angular velocity of the flywheel 3 s after the start of movement:

Мz = Iα

α = Мz/I

ω = at

Substituting the data, we get:

α = Mz/I = 6 N • m / 1.73 m = 3.47 rad/s^2

ω = αt = 3.47 rad/s^2 * 3 s = 10.41 rad/s

Thus, the angular velocity of the flywheel 3 s after the start of movement is 10.41 rad/s (answer 0.501).

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Problem 16.1.26 from the collection of Kepe O.?. refers to the section "Integrals with a parameter". To solve it, you need to find the integral of a function containing a parameter over a given interval. Solving the problem will require knowledge of integration methods, as well as the ability to work with parameters in expressions. You may need to use trigonometric functions and substitutions of variables. The solution to problem 16.1.26 can be useful for students and teachers of mathematical specialties at universities, as well as for everyone who is interested in mathematics.

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