Question

The angular speed of digital video discs (DVDs) varies with whether the inner or outer part of the disc is being read. (CDs function in the same way.) Over a 135-minute playing time, the angular speed varies from 560 rpm to 1800 rpm.Assuming it to be constant, what is the angular acceleration of such a DVD?

Answer 1

ANSWER

$\begin{equation*} 9.19\text{ }rad\/m^2 \end{equation*}$

EXPLANATION

We want to find the angular acceleration of the DVD.

To do this, apply the formula for angular acceleration:

$\alpha=\frac{\Delta\omega}{\Delta t}=\frac{\omega_2-\omega_1}{t_2-t_1}$

where Δω = change in angular velocity

Δt = time taken

Therefore, the angular acceleration is:

$\begin{gathered} \alpha=\frac{1800-560}{135} \\ \alpha=\frac{1240}{135} \\ \alpha=9.19\text{ }rad\/m^2 \end{gathered}$

That is the answer.