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nchin
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A uniform thin rod of length 0.500 m and mass 4.0 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.0 g bullet traveling in the rotation plane is fired into one end of the rod. As viewed from above, the bullet's path makes angle θ = 60° with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after the collision, what is the bullet's speed just before impact?
Solution with diagram on page 4m problem #11.55:
http://www.ifm.liu.se/edu/coursescms/TFYA16/lessons/Le-8-extra.pdf
Moment inertia of system: I = Irod + mr^2
Solution:
conservation of ang momentum:
rmvsinθ = (1/12 ML^2 + mr^2)ω
So conservation of ang momentum is
Linitial = Lfinal
but this problem uses: ang momentum of a particle = ang momentum of a rigid body?
What i don't understand:
Why is the Moment inertia of system I = Irod + mr^2? what i did was before looking up the solution was:
ML^(2)/12 ω = rmvsinθ + MR^(2)ω
because ang momentum inital was just the rod rotating by itself and then comes the bullet so ang momentum of a bullet plus ang momentum of the rod. rmvsinθ = (Irod + mr^2)ω doesn't make sense to me. Also can someone explain to me what a rigid body is? because i know rigid body is L = Iω. Are rigid bodies like a rod, ring, disk or shell?
Solution with diagram on page 4m problem #11.55:
http://www.ifm.liu.se/edu/coursescms/TFYA16/lessons/Le-8-extra.pdf
Moment inertia of system: I = Irod + mr^2
Solution:
conservation of ang momentum:
rmvsinθ = (1/12 ML^2 + mr^2)ω
So conservation of ang momentum is
Linitial = Lfinal
but this problem uses: ang momentum of a particle = ang momentum of a rigid body?
What i don't understand:
Why is the Moment inertia of system I = Irod + mr^2? what i did was before looking up the solution was:
ML^(2)/12 ω = rmvsinθ + MR^(2)ω
because ang momentum inital was just the rod rotating by itself and then comes the bullet so ang momentum of a bullet plus ang momentum of the rod. rmvsinθ = (Irod + mr^2)ω doesn't make sense to me. Also can someone explain to me what a rigid body is? because i know rigid body is L = Iω. Are rigid bodies like a rod, ring, disk or shell?
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