A rod AB of length L and mass M is free to move on a frictionless horizontal surface. It is moving with a velocity v , as shown in figure. End B of rod AB strikes the end of the wall. Assuming elastic

Question

A rod AB of length L and mass M is free to move on a frictionless horizontal surface. It is moving with a velocity v , as shown in figure. End B of rod AB strikes the end of the wall. Assuming elastic impact, the angular velocity of the rod AB , just after impact, is

TestHub · Accepted Answer

From the conservation of angular momentum,

$\Rightarrow M v_{c m} \frac{L}{2} + \frac{M L^{2}}{12} ω = \frac{M v L}{2} \Rightarrow v_{c m} + \frac{ω L}{6} = v$

From the conservation of linear momentum,

$\Rightarrow \frac{ω L}{2} - v_{c m} = v \Rightarrow ω (\frac{L}{2} + \frac{L}{6}) = 2 v$

$∴ ω = \frac{3 v}{L}$

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