Answer:
2.78 s
Explanation:
We are given that
Torque,[tex]\tau=23 Nm[/tex]
Initial angular velocity,[tex]\omega_0=22.6 rad/s[/tex]
Final angular velocity,[tex]\omega=-22.6 rad/s[/tex]
Mass,m=2 kg
R=0.53 m
r=0.27 m
Moment of inertia of system=[tex]I=2m(R^2+r^2)[/tex]
[tex]I=2\times 2((0.53)^2+(0.27)^2}=1.4152 kgm^2[/tex]
Angular acceleration,[tex]\alpha=-\frac{\tau}{I}=-\frac{23}{1.4152}=-16.25rad/s^2[/tex]
[tex]\alpha=\frac{\omega-\omega_0}{t}[/tex]
[tex]t=\frac{\omega-\omega_0}{\alpha}[/tex]
[tex]t=\frac{-22.6-22.6}{-16.25}=2.78 s[/tex]
