A uniform thin rod of length 0.55 m and mass 5.0 kg can rotate in a horizontal p

Question

A uniform thin rod of length 0.55 m and mass 5.0 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is a rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the direction of the bullet velocity makes an angle of 60° with the rod (see the figure). If the bullet lodges in the rod and the angular velocity of the rod is 11.0 rad/s immediately after the collision, what is the magnitude of the bullet's velocity just before impact?

Explanation / Answer

Given data

length=0.55m,mass M=5kg,

mass of the bullet mb=3gms=0.003kg

angle=60deg

angular velocity=11rad/s

vb=?

total moment of inertia Itotal=(1/12)ML2+mb(L/2)2

conservation of angular momentum

mb*vb(L/2)sin(theta)-Itotal*omega=0

mb*vb(L/2)sin(theta)=((1/12)ML2+mb(L/2)2)omega

vb=((1/12)ML2+mb(L/2)2)omega/mb(L/2)sin(theta)

vb=((1/12)*5*(0.55)2+(0.003)(0.55/2)2))(11)/(0.003)(0.55/2)(sin(60))

Vb=179m/s

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