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Engineering and Tech / Engineering Mechanics Dynamics (1) 1 14 / Chapter 18 / Problem 18-33

Engineering Mechanics Dynamics (1) 1 | 14th Edition | ISBN: 9780133915389 | Authors: Russell C. Hibbeler

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The two 2-kg gears A and B are attached to the ends of a 3-kg slender bar. The gears

Chapter 18, Problem 18-33

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QUESTION:

The two 2-kg gears A and B are attached to the ends of a 3-kg slender bar. The gears roll within the fixed ring gear C, which lies in the horizontal plane. If a \(10-N \cdot m\) torque is applied to the center of the bar as shown, determine the number of revolutions the bar must rotate starting from rest in order for it to have an angular velocity of \(\omega_{AB} = 20 \ rad/s\). For the calculation, assume the gears can be approximated by thin disks. What is the result if the gears lie in the vertical plane?

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QUESTION:

The two 2-kg gears A and B are attached to the ends of a 3-kg slender bar. The gears roll within the fixed ring gear C, which lies in the horizontal plane. If a \(10-N \cdot m\) torque is applied to the center of the bar as shown, determine the number of revolutions the bar must rotate starting from rest in order for it to have an angular velocity of \(\omega_{AB} = 20 \ rad/s\). For the calculation, assume the gears can be approximated by thin disks. What is the result if the gears lie in the vertical plane?

ANSWER:

Step 1 of 5

Since the bar A B starts from rest, the initial kinetic energy is zero. The final kinetic energy is

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