Question

The out side diameter of the playing area of an optical Blu-ray disc is 10.5cm, and the inside diameter is 4.75cm. When viewing movies, the disc rotates so that a laser maintains a constant linear speed relative to the disc of 8m/s as it tracks over the playing area.1) what is the average angular acceleration of a blu-ray as it plays 6.5h set of movies?

Answer 1

0.00788 rad/s^2

Explanation:

The radius is equal to half the diameter, therefore:

r1 = d1/2 = 10.5/2 cm = 5.25 cm = 0.0525 m

r2 = d2/2 = 4.75/2 cm = 2.375 cm = 0.02375 m

s = 8 m/s

t = 6.5 h = 23400 sec

The first thing is to calculate the maximum angular speed and the minimum angular speed, like this

`\begin{gathered} \omega_(\max )=(v)/(r_2)=(8)/(0.02375)=336.84 \\ \omega_(\min )=(v)/(r_1)=(8)/(0.0525)=152.38 \\ \omega=\omega_(\max )-\omega_(\min )=336.84-152.38 \\ \omega=184.46\text{ rad/s} \end{gathered}`

Now, the average angular acceleration would be the angular speed divided by the elapsed time:

`\alpha=(\omega)/(t)=(184.46)/(23400)=0.00788rad/s^2`

The average angular acceleration is 0.00788 rad/s^2