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.

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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