The figure is an overhead view of a thin uniform rod of length 0.510 m and mass

Question

The figure is an overhead view of a thin uniform rod of length 0.510 m and mass M rotating horizontally at 89.0 rad/s counterclockwise about an axis through its center. A particle of mass M/3.20 and traveling horizontally at speed 35.0 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) FOR rod and particle system, applying angular momentum conservation during the collsiion,

(M L^2 / 12) (wi) + (M/3.20) (vi) (d) = 0

(M L^2 / 12)(89) = (M / 3.20) (35)(d)

d = 0.678L^2

d = 0.678 x 0.510^2 = 0.18 m

(B) if d is greater then angular momentum of particle is greater.

angular momentum of particle is in clockwise direction hence

rod and particle will move in clockwise direction.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.