Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 67

Figure 11-54 is an overhead view of a thin uniform rod of length 0.600 m and mass \( M \) rotating horizontally at 80.0 rad/s counterclockwise about an axis through its center. A particle of mass \( M/3.00 \) and traveling horizontally at speed 40.0 m/s hits the rod and sticks. The particle's path is perpendicular to the rod at the instant of the hit, at a distance \( d \) from the rod's center. (a) At what value of \( d \) are rod and particle stationary after the hit? (b) In which direction do rod and particle rotate if \( d \) is greater than this value?