- #1
uq_civediv
- 26
- 0
the problem is the following:
we have a vertical wooden bar pivoted from the top end, length 2 l, mass M
a bullet with mass m hits it in the middle at velocity v and gets stuck
i am asked to find the angular velocity \omega of the system bar+bullet immediately after the hit
i do know this calls for applying the conservation of energy or angular momentum, for some reason however i get different results
Both if them involve the moment of inertia of the combined system, I_{\Sigma}=\frac{1}{3} M (2l)^2 + m l^2 = \frac{4}{3} M l^2 + m l^2
Conservation of angular momentum gives me m v l = \omega I_{\Sigma}, from which \omega = \frac{m v l}{I_{\Sigma}} = \frac{m v l}{\frac{4}{3}M l^2+m l^2} = \frac{m}{\frac{4}{3}M+m} \cdot \frac{v}{l}
Whereas conservation of energy says \frac{m v^2}{2} = \frac{\omega^2 I_{\Sigma}}{2}, which gives \omega = \sqrt{\frac{m}{I_{\Sigma}}} v = \sqrt{\frac{m}{\frac{4}{3}M + m}}\cdot \frac{v}{l}
So the big question is where did I mess up this time. I know it's something really basic because I can't see it. Usually i ask a deskmate or someone to have a look if they spot something really simple but since nobody's around I had to come here.
P.S. while you're at it, why do my m, v and \omega look superscripted but M and 2 l don't ?
we have a vertical wooden bar pivoted from the top end, length 2 l, mass M
a bullet with mass m hits it in the middle at velocity v and gets stuck
i am asked to find the angular velocity \omega of the system bar+bullet immediately after the hit
i do know this calls for applying the conservation of energy or angular momentum, for some reason however i get different results
Both if them involve the moment of inertia of the combined system, I_{\Sigma}=\frac{1}{3} M (2l)^2 + m l^2 = \frac{4}{3} M l^2 + m l^2
Conservation of angular momentum gives me m v l = \omega I_{\Sigma}, from which \omega = \frac{m v l}{I_{\Sigma}} = \frac{m v l}{\frac{4}{3}M l^2+m l^2} = \frac{m}{\frac{4}{3}M+m} \cdot \frac{v}{l}
Whereas conservation of energy says \frac{m v^2}{2} = \frac{\omega^2 I_{\Sigma}}{2}, which gives \omega = \sqrt{\frac{m}{I_{\Sigma}}} v = \sqrt{\frac{m}{\frac{4}{3}M + m}}\cdot \frac{v}{l}
So the big question is where did I mess up this time. I know it's something really basic because I can't see it. Usually i ask a deskmate or someone to have a look if they spot something really simple but since nobody's around I had to come here.
P.S. while you're at it, why do my m, v and \omega look superscripted but M and 2 l don't ?
