- #1
toothpaste666
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Homework Statement
A thin rod of mass M and length L is suspended vertically from a frictionless pivot at its upper end. A mass m of putty traveling horizontally with a speed v strikes the rod at its CM and sticks there. How high does the bottom of the rod swing?
Homework Equations
The Attempt at a Solution
First I must look at the collision:
[itex] v = ωR = ω\frac{L}{2} [/itex]
[itex] ω = \frac{2v}{L} [/itex]
[itex] I_m = mR^2 = m(\frac{L}{2})^2 = \frac{mL^2}{4} [/itex]
[itex] I_M = \frac{1}{12}ML^2 [/itex]
using angular momentum:
[itex] I_m (\frac{2v}{L}) = (I_m + I_M)ω [/itex]
[itex] \frac{mL^2}{4} (\frac{2v}{L}) = (\frac{mL^2}{4} + \frac{1}{12}ML^2)ω [/itex]
[itex] \frac{mLv}{2} = (\frac{mL^2}{4} + \frac{1}{12}ML^2)ω [/itex]Have I set this up right so far? I am trying to find the angular velocity at the end of the collision, convert it to linear velocity, and plugging that into an energy equation