Question 254: Centre of Mass and Rotational Motion

Question

The time dependence of the position of a particle of mass m = 2 is given by $$\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$$
. Its angular
momentum, with respect to the origin, at time t = 2 is

Accepted Answer

$$\overrightarrow v  = 2\widehat i - 6 + \widehat j$$
At t = 2
$$\overrightarrow v  = 2\widehat i - 12\widehat j$$
$$\overrightarrow P  = m\overrightarrow v  = 4i - 24\widehat j$$
At t = 2
$$\overrightarrow r  = 4\widehat i - 12\widehat j$$
$$\overrightarrow L  = \overrightarrow r  	imes \overrightarrow P  = \left| {\matrix{
   {\widehat i} & {\widehat j} & {\widehat k}  \cr 
   4 & { - 12} & 0  \cr 
   4 & { - 24} & 0  \cr

} } ight|$$
$$ = \left\{ {4( - 2) + 4 	imes 12} ight\}\widehat k$$
$$ = \left( { - 96 + 48} ight)\widehat k$$
$$ = \left(  -  ight)48\widehat k$$

Answer

36 $$\widehat k$$

Answer

- 48 $$\widehat k$$

Answer

$$ - 34\left( {\widehat k - \widehat i} \right)$$

Answer

$$48\left( {\widehat i + \widehat j} \right)$$

Centre of Mass and Rotational Motion

The time dependence of the position of a particle of mass m = 2 is given by $\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$ . Its angular momentum, with respect to the origin, at time t = 2 is

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