Answer:
Angular acceleration, [tex]\alpha =20.32\ rad/s^2[/tex]
Explanation:
It is given that,
Displacement of the rotating wheel, [tex]\theta=37\ rev=232.47\ radian[/tex]
Time taken, t = 2.9 s
Initial speed of the wheel, [tex]\omega_i=0[/tex]
Final speed of the wheel, [tex]\omega_f=97.2\ rad/s[/tex]
Let [tex]\alpha[/tex] is the angular acceleration of the wheel. Using the third equation of kinematics to find it as :
[tex]\alpha=\dfrac{\omega_f^2-\omega_i^2}{2\theta}[/tex]
[tex]\alpha=\dfrac{(97.2)^2}{2\times 232.47}[/tex]
[tex]\alpha =20.32\ rad/s^2[/tex]
So, the angular acceleration of the wheel is [tex]20.32\ rad/s^2[/tex]. Hence, this is the required solution.
