Solution to problem 9.6.21 from the collection of Kepe O.E.

9.6.21 On axis A, gear 1 and crank AB, 30 cm long, independent of each other, are installed. On axis B, which is connected to the crank, gear 2 of radius r2 = 15 cm is installed. Connecting rod 3 is attached to gear 2. It is necessary to determine the angular velocity of the gear 2, when is the angle? between axis A and axis B is 90°, and the speed of point C of the slider is 0.3 m/s. The answer to the problem is 2.

Solution to problem 9.6.21 from the collection of Kepe O.?.

This digital product contains the solution to problem 9.6.21 from the collection "Kepe O.?". The solution is presented in a convenient format and includes a description of the problem conditions, a step-by-step solution and the final answer.

Product characteristics

• Format: PDF
• Russian language
• Number of pages: 1
• Author: Kepe O.?.

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Solution to problem 9.6.21 from the collection of Kepe O.?. is associated with mechanics and consists in determining the angular velocity of the gear under given conditions.

In the problem it is given that gear 1 and crank AB with a length of 30 cm are installed on axis A. Gear 2 of radius r2 = 15 cm is installed on axis B of the crank, to which connecting rod 3 is attached. It is also known that the angle between axis A and crank AB is 90 °, and the speed of point C of the slider is 0.3 m/s.

To solve the problem, it is necessary to use the laws of mechanics, in particular, the law of conservation of angular momentum. First, the angular velocity of connecting rod 3 should be determined under given conditions, and then the angular velocity of gear 2 should be expressed in terms of the angular velocity of connecting rod 3 and the corresponding radii of the gear and connecting rod.

After solving the mathematical calculations, we find that the angular velocity of gear 2 is equal to 2 rad/s.

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