Solution to problem 9.3.7 from the collection of Kepe O.E.

9.3.7 Does the OA crank rotate according to the law? = 0.4t².

It is necessary to determine the angular acceleration of the moving gear at a radius R = 2t = 0.2 m.

Answer: 0.8.

This problem is related to the kinematics of rotational motion. Knowing the law of change in the angle of rotation of the crank OA, we can calculate its angular velocity and angular acceleration. To do this, it is necessary to differentiate the given law twice with respect to time in order to obtain the angular velocity and angular acceleration:

? = 0.4t²

ω = d?/dt = 0,8t

α = dω/dt = 0.8

Thus, the angular acceleration of the moving gear is 0.8 rad/s², with radius R = 0.2 m.

Solution to problem 9.3.7 from the collection of Kepe O.?.

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Problem 9.3.7 from the collection of Kepe O.?. consists in determining the angular acceleration of the moving gear when the crank OA rotates according to the law? = 0.4t2. The radius of the gear is R = 2t = 0.2 m.

To solve the problem, it is necessary to calculate the angular velocity of the crank OA using the derivative of the rotation law ? by time t. Thus, we get:

? = d?/dt = 0.8t rad/s

Then, using the relationship between angular acceleration ? and linear acceleration a at the end of the gear, you can find the angular acceleration of the moving gear:

? = a/R

Thus,

a = ?R = (0.8t) * 0.2 m = 0.16t m/s²

At t = 1 s we get:

a = 0.16 m/s²

The angular acceleration of the moving gear is equal to:

? = a/R = 0.16 m/s² / 0.2 m = 0.8 rad/s²

Answer: 0.8.

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