When a compact, efficient, or high-speed drive is needed, gear trains provide an effective and appropriate solution T OR F
Added by Heather B.
Step 1
Gear trains are mechanical systems that use gears to transmit power and motion between different components. They can change the speed, torque, and direction of movement. Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 55 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Adi S.
Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has $n_{1}$ teeth and the second gear has $n_{2}$ teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If $\omega_{1}$ and $\omega_{2}$ are the angular velocities of the first and second gears, respectively, then $$\begin{aligned}v_{2} &=v_{1} \\r_{2} \omega_{2} &=r_{1} \omega_{1} \\\omega_{2} &=\frac{r_{1}}{r_{2}} \omega_{1} \\\omega_{2} &=\frac{n_{1}}{n_{2}} \omega_{1} \end{aligned}.$$ A gear train consists of three gears meshed together (Figure 9 ). The middle gear is known as an idler. Show that the angular velocity of the third gear does not depend on the number of teeth of the idler gear (Gear 2 ).
Radian Measure
Velocities
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD