The figure is an overhead view of a thin uniform rod of length 0.500 m and mass
ID: 1499407 • Letter: T
Question
The figure is an overhead view of a thin uniform rod of length 0.500 m and mass M rotating horizontally at 76.0 rad/s counterclockwise about an axis through its center. A particle of mass M/2.60 and traveling horizontally at speed 42.0 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?
Explanation / Answer
a) Angular momentum is conserved.
L1 = L2
=> Irodrod - (M/2.60)vd = 0
=> ML2rod/12 = Mvd/2.60
=> d = 2.60L2rod/12v = 2.60 * 0.52 * 76 / (12 * 42) =0.098 m
b) If d > 0.098 m, net initial angular momentum will be in clockwise direction, so the rod and particle system will rotate clockwise.