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A weather vane initially at rest has a moment of inertia of 0.115 kg · m2 about its axis of rotation. A 44.5 g piece of clay is thrown at the vane and sticks to it at a point 10.5 cm from the axis. The initial velocity of the clay is 18.5 m/s, directed perpendicular to the vane. Find the angular velocity of the weather vane just after it is struck.


    The moment of inertia of weather vane with piece of clay is
    I = I(vane) +mR^2 = 0.115+44.5•10^-3•(0.105)^2=
    = 1.2•10^-2 kg • m2.
    The torque due to the clay hitting is M=F•R
    F•t=Δp=m•v, therefore F=m•v/t.
    Then M=F•R=m•v•R/t.
    From Newton’s 2 Law for rotation M=I• ε.
    m•v•R/t =I•ε.
    m•v•R/I= ε• t = ω
    ω = m•v•R/I ==44.5•10^-3•18.5•0.105/1.2•10^-2= 7.21 rad•s

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