A gear of radius R is placed between two parallel gear racks. The slats move at a speed of v_1 and v_2 towards each other. What is the gear speed

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.4">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.4.13.$ A gear of radius $R$ is placed between two parallel gear racks. The slats move at a speed of $v_1$ and $v_2$ towards each other. What is the gear speed

    <h3>Solution</h3>
    <p>
        <p>Let's move to the center of the disk. In this frame of reference, the speed of the upper and lower points of the disk is the same in magnitude and opposite in direction. Therefore, </p>

$$(v_{1} - v) = - (v_{2} - v)$$

From where

$$v = \frac{v_{1} + v_{2}}{2}$$

We will find the rotation frequency as

$$\nu = \frac{v}{R}$$

Substitute $v$

$$\fbox{$\nu = \frac{v_1 + v_2}{2R}$}$$

    <h4>Answer</h4>
    <p>
        $$n = (v_1 + v_2)/(2R)$$
    </p>


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