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Conservation of Angular Momentum

AP Physics 1· difficulty 4/5

m, v M, L

A bullet of mass mm moving horizontally with speed vv embeds in the bottom of a uniform rod (mass MM, length LL) hinged at its top. Just after embedding, what is the angular speed of the rod-bullet system?

  • A

    mvL(M/3+m)L2\dfrac{mvL}{(M/3 + m)L^2}

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  • B

    3mvML\dfrac{3mv}{ML}

  • C

    2mvML\dfrac{2mv}{ML}

  • D

    mv(M+m)L\dfrac{mv}{(M+m)L}

Explanation

Conserve angular momentum about hinge: mvL=(Irod+mL2)ωmvL = (I_{rod} + mL^2)\omega with Irod=13ML2I_{rod} = \tfrac{1}{3}ML^2. So ω=mvL/[(M/3+m)L2]\omega = mvL/[(M/3 + m)L^2].

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