The time dependence of the position of a particle of mass m = 2kg is given by . Its angular momentum, with respect to the origin, at time t = 2 is :

Engineering

Physics

Angular Momentum and Conservation of Angular Momentum

Question

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

$36 \hat{k}$

$- 48 \hat{k}$

$- 34 (\hat{k} - \hat{i})$

$48 (\hat{i} + \hat{j})$

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At t = 2

$\vec{v} = 2 \hat{i} - 12 \hat{j}$

$\vec{P} = m \vec{v} = 4 \hat{i} - 24 \hat{j}$

At t = 2

$\vec{r} = 4 \hat{i} - 24 \hat{j}$

$\vec{L} = \vec{r} \times \vec{P} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 4 & - 12 & 0 \\ 4 & - 24 & 0 \end{matrix} |$

$= {4 (- 24) + 4 \times 12} \hat{k}$

$= (- 96 + 48) \hat{k}$

$= (-) 48 \hat{k}$