Question #42050

This question tests the student's ability to correctly apply the Work-Energy Theorem in the presence of a reaction time gap and a time-dependent force.

A common trap is blindly integrating the angular acceleration from $t=0$ (ignoring the boundary condition $\omega=0$ at $t=1$), which yields an incorrect angular velocity of $13.5 \text{ rad/s}$ and a kinetic energy of $729 \text{ J}$.

Another mistake is calculating work as the time integral of torque ($\int \Gamma dt$) rather than the angular displacement integral ($\int \Gamma d\theta$), leading to $104 \text{ J}$.

The problem enforces the understanding that work is strictly zero when displacement is zero, despite a large applied force, and that kinematic integration must respect the physical release time.