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Angular Momentum and Angular Impulse

AP Physics 1· difficulty 3/5

A horizontal stick (length LL, mass MM, Iend=13ML2I_\text{end} = \tfrac{1}{3}M L^2) hinged at one end is at rest. A small ball of mass mm moving perpendicular to the stick at speed vv strikes the far end and sticks. The angular speed of the system just after is

  • A

    Mv/(mL)M v/(m L)

  • B

    mvL/(13ML2+mL2)m v L/(\tfrac{1}{3}M L^2 + m L^2)

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  • C

    mv/(ML)m v/(M L)

  • D

    mv/(ML2)m v/(M L^2)

Explanation

Conservation of angular momentum about the hinge: mvL=(Iend+mL2)ω⇒ω=mvL/(13ML2+mL2)m v L = (I_\text{end} + m L^2) \omega \Rightarrow \omega = m v L/(\tfrac{1}{3} M L^2 + m L^2).

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