First slide

Law of conservation of angular momentum

Question

Consider a rod of mass M and length L pivoted at its centre is free to rotate in a vertical plane. The rod is at rest in the vertical position. A bullet of mass M moving horizontally at a speed v strikes and embedded in one end of the rod. The angular velocity of the rod just after the collision will be

Moderate

A

$\frac{v}{L}$
B

$\frac{2 v}{L}$
C

$\frac{3 v}{2 L}$
D

$\frac{6 v}{L}$

Solution

Apply conservation of angular momentum about the pivot point
$0 + M V L / 2 = I ω$ HERE I= $M \frac{L^{2}}{12} + M {[\frac{L}{2}]}^{2}$
$\Rightarrow ω = \frac{3 v}{2 L}$

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