The figure below shows an overhead view of a thin uniform rod of length 0.80 m a

Question

The figure below shows an overhead view of a thin uniform rod of length 0.80 m and mass M rotating horizontally at 50.0 rad/sec counterclockwise about an axis through its center. A particle of mass M/3 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. At what value of d are rod and particle stationary after the hit? a. 0.15 m. b. 0.35 m. c. 0.10 m. d. 0.25 m. e. 0.20 m.

Explanation / Answer

The angular momentum of the particle is L=dp=d(M/3)v

Angular momentum of the rod L=Iw

I = moment of inertia about the center = M*L²/12

w=50rad/sec

ML2w/ 12 =d (M/3)v   

d=*3*L²/(12*V) = *L²/(4*V)

=(50*0.80*0.80/4*40)=0.20m

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