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RJLiberator
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Homework Statement
A bird m_b=0.470kg, is flying horizontally at v_b=2.50 m/s, not paying much attention, when it suddenly flies into a stationary vertical rod, hitting it d=25cm below the top. The rod is uniform, L=0.740m long, has a mass of m_r =1.60kg and is hinged at its base. This time the bird goes splat on the rod, and is stuck to it at the point of impact. What is the angular velocity w_f of the bird+rod just after the collision?
What we have:
Mass of bird: 0.470 kg
Mass of rod = 1.60 kg
Initial Velocity of bird: 2.50 m/s
Length of rod = 0.740m
Distance of impact from top of rod = 0.25m
I_rod = 1/3M*d^2
Homework Equations
Conservation of Angular Momentum L_0=L_1
L = mvrsin(theta)
L= Iw
v=w*r
The Attempt at a Solution
First I calculated the Angular momentum of the bird prior to collision
L=mrv
L=0.470kg*(0.740m-0.25m)*2.50m/s
Sin here is 90 degrees and thus is simply 1.
L=0.57575
*NOTE: Did I use the right measurement for r?
Next, I found the post-collision angular momentum to be:
L_f=(m_b+m_r)*v_1*r + I_rod*w_f
L_f=(m_b+m_r)*d^2*w_f+(1/3)*m_r*d^2*w_f
Simple algebraic manipulation gets us:
w_f=0.57575/((0.470+1.6)(0.490^2)+(1/3)(1.60)(0.490^2))
for an answer of 0.921 rads/sec
My questions/concerns:
1) Is this the right method to approach this problem? Do I have any need to use conservation of mechanical energy to help solve this problem? All I am looking for is w_f.
2) Did I use the correct value for d throughout this problem? Namely (0.740-0.25).
3) Is it okay to be using the moment of inertia about the end of the rod for this problem? (1/3*M*d^2)
Thank you.