Answer:
The angular acceleration is 1.825 rad/s²
Explanation:
Given that,
Angular velocity = 12 rad/s
Number of revolution = 18
Time = 6 sec
The wheel rotates during the 6 s interval is
[tex]\theta=18\times2\pi[/tex]
[tex]\theta=36\pi\ rad[/tex]
We need to calculate the angular acceleration
Using formula of displacement
[tex]\theta=\dfrac{1}{2}\times(\omega_{i}+\omega_{f})\times t[/tex]
Put the value into the formula
[tex]36\pi=\dfrac{1}{2}\times(\omega_{i}+12)\times6[/tex]
[tex]\omega_{i}=\dfrac{\pi}{3}[/tex]
[tex]\omega_{i}=1.047\ rad/sec[/tex]
We need to calculate the angular acceleration
Using formula of angular acceleration
[tex]\alpha=\dfrac{\omega_{f}-\omega_{i}}{t}[/tex]
Put the value into the formula
[tex]\alpha=\dfrac{12-1.047}{6}[/tex]
[tex]\alpha=1.825\ rad/s^2[/tex]
Hence, The angular acceleration is 1.825 rad/s²
