The figure below is an overhead view of a thin uniform rod of length L0.6 m and

Question

The figure below is an overhead view of a thin uniform rod of length L0.6 m and mass M=15 kg and traveling horizontally at 60.0 rad/s counterclockwise about and axis through its center. A particle of mass m=5 kg and traveling horiontally at speed 30 m/s hits the rod and sticks. The particle's pathh 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 stationry after the hit? (The moment of inertia of a uniform thin rod through the centr is I=(ML^2)/2)

The figure below is an overhead view of a thin uniform rod of length L0.6 m and mass M=15 kg and traveling horizontally at 60.0 rad/s counterclockwise about and axis through its center. A particle of mass m=5 kg and traveling horiontally at speed 30 m/s hits the rod and sticks. The particle's pathh 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 stationry after the hit? (The moment of inertia of a uniform thin rod through the centr is I=(ML^2)/2)

Explanation / Answer

I1 = (1/12)*M*L^2 + (M/3)*(L/2)^2 = 0.42*M*L^2 = 0.12M

W1 = 20.5 rad/s

L1 = I1*W1 = 2.4 M


W2 = V/(L/2) = (Vp-6)*2/L = 2.41*(Vp-6)

Vp = (V+6)

W2 = Vp/3L

L2 = (1/12)*M*L^2*W2 + (M/3)*Vp*(L/2) = 0.276M *Vp - 0.83M

L2 = L1

0.276M *Vp - 0.83M = 2.4 M

Vp = 11.703m/s

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