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# Suppose a piece of dust finds itself on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)

Solution

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$\textbf{Knowns}$

\normalsize We know that the rotational kinematic equations that describe the relationship among the rotational angle $\color{#c34632}\theta$, the initial angular velocity $\color{#c34632}\omega_o$, the angular acceleration $\color{#c34632}\alpha$ and time $\color{#c34632}t$ is given by:

$\begin{gather*} \theta = \omega_o\ t + \dfrac{1}{2}\alpha t^2\tag{1} \end{gather*}$

We also know that the relation between the linear distance $\color{#c34632}x$ and the rotational angle $\color{#c34632}\theta$ is given by:

$\begin{gather*} x = r\theta\tag{2} \end{gather*}$

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