Answer:
[tex]\theta=76\ rad[/tex]
Explanation:
Hoven that,
Initial angular velocity of the wheel = 24 rad/s
Final angular velocity = 14 m/s
Time, t = 4 s
We need to find how many radians does the wheel turn through during the 4 s interval. Let the displacement is [tex]\theta[/tex]. Using second equation of rotational kinematics to find it such that,
[tex]\theta=\omega_i t+\dfrac{1}{2}\alpha t^2[/tex]
Where
[tex]\alpha[/tex] is angular acceleration
[tex]\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{14-24}{4}\\\\\alpha =-2.5\ rad/s^2[/tex]
So,
[tex]\theta=24\times 4+\dfrac{1}{2}\times (-2.5)\times 4^2\\\\\theta=76\ rad[/tex]
So, it will turn 76 radian during the 4 s interval.
