# What is a rigid body

Using the regular $\hat\imath,\hat\jmath$ basis, the known information just before impact is \[ \vec{r}_{PQ} = 2\,\hat\imath \qquad \vec{v}_P = -3\,\hat\imath \qquad \vec{a}_P = 0 \qquad \vec\omega = -2\,\hat{k} \qquad \vec\alpha = -3\,\hat{k}. \] The velocity and acceleration of $Q$ are given by \[\begin{aligned} \vec{v}_Q &= \vec{v}_P + \vec{\omega} \times \vec{r}_{PQ} \\ &= -3\,\hat\imath - 2\,\hat{k} \times 2\,\hat\imath \\ &= -3\,\hat\imath - 4\,\hat\jmath \\ \vec{a}_Q &= \vec{a}_P + \vec{\alpha} \times \vec{r}_{PQ} + \vec{\omega} \times (\vec{\omega} \times \vec{r}_{PQ}) \\ &= 0 - 3\,\hat{k} \times 2\,\hat\imath - 2\,\hat{k} \times (-2\,\hat{k} \times 2\,\hat\imath) \\ &= -6\,\hat\jmath - 2\,\hat{k} \times (-4\,\hat\jmath) \\ &= -8\,\hat\imath - 6\,\hat\jmath. \end{aligned}\]

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