- #1
roam
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Homework Statement
I need some help with the following problem:
http://desmond.imageshack.us/Himg62/scaled.php?server=62&filename=problem1p.jpg&res=landing
The Attempt at a Solution
(i) I used the conservation of angular momentum (since there is no external torque):
[itex]L_{before} = mv(\frac{L}{2})[/itex]
[itex]L_{after} = m \left( \frac{v}{2} \right) \left( \frac{L}{2} \right) + \frac{mL^2}{3} \omega_o[/itex]
Lbefore = Lafter
[itex]mv(\frac{L}{2}) = m \left( \frac{v}{2} \right) \left( \frac{L}{2} \right) + \frac{mL^2}{3} \omega_o[/itex]
Solving for ωo:
[itex]\omega_o = \frac{3mv}{4ML}[/itex]
Is this correct?
(ii) I'm very confused by this part. How do I know what v must be in order for the rod to swing at 90°?
I know that the distance the rod has moved is equal to: s=L(90°). And here is the equation for torque:
[itex]\tau = mgL \sin \ 90 = m \frac{d \omega}{dt} = m \frac{d \frac{3mv}{4ML}}{dt}[/itex]
However the RHS becomes 0 when I differentiate it with respect to time. So how can I solve this? How else can I express v in terms of m, M, L, and g?
Any help is really appreciated.
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