Question 24: Centre of Mass and Rotational Motion

Question

The angular momentum of a body placed at origin of mass 1 kg and having position vector $$r = 3t\widehat i + 4\widehat j$$ is

Accepted Answer

Given, m = 1 kg, $$r = 3t\widehat i + 4\widehat j$$
Velocity of body, $$v = {{dr} \over {dt}}$$
$$ = {d \over {dt}}(3t\widehat i + 4\widehat j) \Rightarrow v = 3\widehat i$$
Angular momentum, $$L = m(r 	imes v)$$
$$ = 1 	imes [(3t\widehat i + 4\widehat j) 	imes 3\widehat i]$$
$$ = \left| {\matrix{
   {\widehat i} & {\widehat j} & {\widehat k}  \cr 
   {3t} & 4 & 0  \cr 
   3 & 0 & 0  \cr

} } ight|$$
$$ = [3t 	imes 0 - 4 	imes 3]\widehat k$$
$$ \Rightarrow L =  - 12\widehat i$$ J-s

Answer

time dependent

Answer

$$3\widehat k$$ J-s

Answer

$$ - 12\widehat k$$ J-s

Answer

0

Centre of Mass and Rotational Motion

The angular momentum of a body placed at origin of mass 1 kg and having position vector $r = 3t\widehat i + 4\widehat j$ is

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