Question 735: Centre of Mass and Rotational Motion

Question

A wooden log of mass M and length L is 
hinged by a frictionless nail at O; a bullet 
of mass m strikes with velocity $v$ and sticks 
to it. Find angular velocity of the system 
immediately after the collision about O.
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1mh7ehng7/8a9b484d-f856-4dba-a26c-9adf237784f0/3c439070-b23f-11f0-b513-6785eb3a49c0/file-jaoe38c1mh7ehng8.png?format=png)

Accepted Answer

A bullet of mass $m$ strikes the wooden log of 
mass M and length L and sticks to it.
Angular momentum of the system, about 
point O, remains conserved. Initial angular 
momentum = Final angular momentum.
$	herefore$ $mv 	imes L = {I_0}\omega $ ..... (i)
${I_0} = {I_{\log }} + {I_b}$
${I_0} = {{M{L^2}} \over 3} + m{L^2}$
${I_0} = {L^2}\left( {{M \over 3} + m} ight) = {L^2}\left( {{{M + 3m} \over 3}} ight)$
$	herefore$ $mvL = {L^2}\left( {{{M + 3m} \over 3}} ight)\omega $
$\omega  = {{3mv} \over {L(M + 3m)}}$

Answer

$\left[\frac{4 m v}{(\mathbf{M}+3 m) \mathrm{L}}\right]$

Answer

$\left[\frac{3 m v}{(\mathbf{M}+3 m) \mathrm{L}}\right]$

Answer

$\left[\frac{5m v}{(\mathbf{M}+3 m) \mathrm{L}}\right]$

Answer

$\left[\frac{3 m v}{(3\mathbf{M}+m) \mathrm{L}}\right]$

Centre of Mass and Rotational Motion

A wooden log of mass M and length L is hinged by a frictionless nail at O; a bullet of mass m strikes with velocity v and sticks to it. Find angular velocity of the system immediately after the collision about O.

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