The figure is an overhead view of a thin uniform rod of length 0.520 m and mass
ID: 1502156 • Letter: T
Question
The figure is an overhead view of a thin uniform rod of length 0.520 m and mass M rotating horizontally at 98.0 rad/s counterclockwise about an axis through its center. A particle of mass M/3.00 and traveling horizontally at speed 38.0 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 of the rod is L1= I*w = (1/12)*M*L^2*w
angular momentum of the particle is L2 = m*v*d = (M/3)*38*d
(1/12)*M*L^2*w= (M/3)*v*d
d = w*L^2/(4*v) = 98*0.52^2/(4*38) = 0.174 m
b) in the original direction of the rod