the problem is the following:(adsbygoogle = window.adsbygoogle || []).push({});

we have a vertical wooden bar pivoted from the top end, length [tex] 2 l [/tex], mass [tex] M [/tex]

a bullet with mass [tex] m [/tex] hits it in the middle at velocity [tex] v [/tex] and gets stuck

i am asked to find the angular velocity [tex] \omega [/tex] 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, [tex] I_{\Sigma}=\frac{1}{3} M (2l)^2 + m l^2 = \frac{4}{3} M l^2 + m l^2[/tex]

Conservation of angular momentum gives me [tex]m v l = \omega I_{\Sigma} [/tex], from which [tex] \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} [/tex]

Whereas conservation of energy says [tex] \frac{m v^2}{2} = \frac{\omega^2 I_{\Sigma}}{2} [/tex], which gives [tex] \omega = \sqrt{\frac{m}{I_{\Sigma}}} v = \sqrt{\frac{m}{\frac{4}{3}M + m}}\cdot \frac{v}{l} [/tex]

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 [tex] m [/tex], [tex] v [/tex] and [tex] \omega[/tex] look superscripted but [tex] M [/tex] and [tex] 2 l [/tex] don't ?

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# Homework Help: Angular momentum vs energy

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