need help The following text explains a single-stage gear train. Gear trains are utilized in various products, including clocks and automotive transmissions, to modify the angular velocity of a component. The size of each gear is determined by the number of its teeth rather than its radius. Assume the first gear has \( n_1 \) teeth, and the second gear has \( n_2 \) teeth.**Diagram Explanation:**The diagram shows two interlocking gears. Gear 1, labeled with \( n_1, \omega_1 \), rotates counterclockwise, and Gear 2, labeled with \( n_2, \omega_2 \), rotates clockwise.**Key Concepts:**Since the tooth spacing is identical for both gears, the ratio of their radii corresponds to the ratio of the number of teeth. When meshed, both gears share the same linear velocity. Given that \( \omega_1 \) and \( \omega_2 \) represent the angular velocities of the first and second gears, respectively, the following relationships hold:\[v_2 = v_1\]\[r_2\omega_2 = r_1\omega_1\]\[\omega_2 = \frac{r_1}{r_2} \omega_1\]\[\omega_2 = \frac{n_1}{n_2} \omega_1\]**Example Problem:**The first gear in a single-stage gear train has 45 teeth and an angular velocity of 3 revolutions per second. The second gear has 6 teeth. To find the angular velocity of the second gear, use the given formula:\[\omega_2 = \frac{45}{6} \times 3\]Calculate this to find the angular velocity of the second gear. (Round your answer to two decimal places.)

Given information: The number of teeth in the first gear train (n1) = 45 The angular velocity of…

The first gear in a single-stage gear train has 45 teeth and an angular velocity of 3 revolutions per second. The second gear has 6 teeth. Find the angular velocity of the second gear. (Round your answer to two decimal places.)

The first gear in a single-stage gear train has 45 teeth and an angular velocity of 3 revolutions per second. The second gear has 6 teeth. Find the angular velocity of the second gear. (Round your answer to two decimal places.)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

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The following text explains a single-stage gear train. Gear trains are utilized in various products, including clocks and automotive transmissions, to modify the angular velocity of a component. The size of each gear is determined by the number of its teeth rather than its radius. Assume the first gear has \( n_1 \) teeth, and the second gear has \( n_2 \) teeth.

**Diagram Explanation:**
The diagram shows two interlocking gears. Gear 1, labeled with \( n_1, \omega_1 \), rotates counterclockwise, and Gear 2, labeled with \( n_2, \omega_2 \), rotates clockwise.

**Key Concepts:**
Since the tooth spacing is identical for both gears, the ratio of their radii corresponds to the ratio of the number of teeth. When meshed, both gears share the same linear velocity. Given that \( \omega_1 \) and \( \omega_2 \) represent the angular velocities of the first and second gears, respectively, the following relationships hold:

\[
v_2 = v_1
\]

\[
r_2\omega_2 = r_1\omega_1
\]

\[
\omega_2 = \frac{r_1}{r_2} \omega_1
\]

\[
\omega_2 = \frac{n_1}{n_2} \omega_1
\]

**Example Problem:**
The first gear in a single-stage gear train has 45 teeth and an angular velocity of 3 revolutions per second. The second gear has 6 teeth. To find the angular velocity of the second gear, use the given formula:

\[
\omega_2 = \frac{45}{6} \times 3
\]

Calculate this to find the angular velocity of the second gear. (Round your answer to two decimal places.)

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