Answer
Given,
time = 8 s
θ = 17.5 rad
initial angular velocity = 0 rad/s
Using rotational motion equation
[tex]\theta=\omega_{0} t+0.5 \alpha t^{2}[/tex]
[tex]17.5=0+0.5 \alpha(8)^{2}[/tex]
[tex]\alpha = 0.546 \ rad/s^2[/tex]
a. angular acceleration [tex]\alpha=0.546 \ rad/s^2[/tex]
b. Average angular velocity = total angle/total time taken
=[tex]\dfrac{17.5}{8}[/tex]= 2.187 rad/s
c. we have,
[tex]\omega=\omega_{0}+a t[/tex]
[tex]=0+0.546 \times 8[/tex]
Angular velocity at end of 8 seconds [tex]=\omega=4.368[/tex] rad/s
d. we have, additional angle in next 8 seconds:
[tex]\theta=\omega_{0} t+0.5 \alpha {t}^{2}[/tex]
[tex]=4.368 \times 8+0.5 \times 0.546 \times 8^{2}[/tex]
[tex]=52.416[/tex] rads
