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

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

Step-by-step explanation

We want to find the angular acceleration of the DVD.

To do this, apply the formula for angular acceleration:

`\alpha=(\Delta\omega)/(\Delta t)=(\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=(1800-560)/(135) \\ \alpha=(1240)/(135) \\ \alpha=9.19\text{ }rad\/m^2 \end{gathered}`

That is the answer.