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

Figure 11.37 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?