ANSWER:
0.00788 rad/s^2
STEP-BY-STEP 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
[tex]\begin{gathered} \omega_{\max }=\frac{v}{r_2}=\frac{8}{0.02375}=336.84 \\ \omega_{\min }=\frac{v}{r_1}=\frac{8}{0.0525}=152.38 \\ \omega=\omega_{\max }-\omega_{\min }=336.84-152.38 \\ \omega=184.46\text{ rad/s} \end{gathered}[/tex]Now, the average angular acceleration would be the angular speed divided by the elapsed time:
[tex]\alpha=\frac{\omega}{t}=\frac{184.46}{23400}=0.00788rad/s^2[/tex]The average angular acceleration is 0.00788 rad/s^2
