Which washer, rotating around its axis or not rotating, will go the longest way to stop on a rough horizontal surface? The initial velocity of the puck centers is the same.

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    <h3 id="back-link"><a href="/#2.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $2.1.41.$ Which washer, rotating around its axis or not rotating, will go the longest way to stop on a rough horizontal surface? The initial velocity of the puck centers is the same.

    <h3>Solution</h3>
    <p>
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1. A reciprocating puck has only the kinetic energy of reciprocating motion $$K_1=\frac{mv^2}{2}$$ the flat motion of the puck, which is a superposition of translational and rotational motion, is characterized by two components of kinetic energy: translational and rotational: $$K_2=\frac{mv^2}{2}+J_z\frac{\omega ^2}{2}$$

$$K_2=\frac{mv^2}{2}+\frac{mr^2}{2}\cdot\frac{\omega ^2}{2}$$

$$K_2=\frac{m}{2}(v^2+\frac{r^2 \omega ^2}{2})$$

$$K_2=\frac{3}{4}mv^2$$

$$K_2>K_1$$
2. The initial kinetic energy of the washers in both cases will be spent on work against the friction force.
$$A_{тр} = µmg\Delta x$$
3. According to the theorem on the change in kinetic energy:
$$\frac{K_2}{K_1}=\frac{\Delta x_2}{\Delta x_1}=1.5$$

    <h4>Answer</h4>
    <p>
        Rotating
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