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Dynamics of a solid body

Problem 1.235

A force \(\mathbf{F}=A \mathbf{i}+B \mathbf{j}\) is applied to a point whose radius vector relative to the origin of coordinates \(O\) is equal to \(\mathbf{r}=a \mathbf{i}+\) \(+b \mathbf{j},\) where \(a, b, A, B\) are constants, and \(\mathbf{i}, \mathbf{j}\) are the unit vectors of the \(x\) and \(y\) axes. Find the moment \(\mathbf{N}\) and the arm \(l\) of the force \(\mathbf{F}\) relative to the point \(O\).

Reveal Answer
 1.235. N=(aB−bA)k, where k is the unit vector of the z axis; l=∣aB−bA∣/A2+B2‾\begin{aligned} &\text { 1.235. } \mathbf{N}=(a B-b A) \mathbf{k}, \text { where } \mathbf{k} \text { is the unit vector of the } z\\ &\text { axis; } l=|a B-b A| / \sqrt{\overline{A^{2}+B^{2}}} \end{aligned}
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