A force is applied at the point relative to a pivot

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Mechanics & Dynamical Systems · Rotation, rigid bodies and accelerated frames

Mathematical Methods for Physics, Ch Matrices, determinants and systems of linear equations

Problem

A force F=(5.0,0,10.0) N\mathbf{F} = (5.0, 0, 10.0)\,\mathrm{N} is applied at the point r=(0.10,0.20,0.05) m\mathbf{r} = (0.10, 0.20, 0.05)\,\mathrm{m} relative to a pivot, in a right-handed Cartesian frame. ((a)) Compute the torque τ=r×F\boldsymbol{\tau} = \mathbf{r}\times\mathbf{F} about the pivot, using the determinant rule. ((b)) Check the result by confirming r⋅τ=0\mathbf{r}\cdot\boldsymbol{\tau} = 0 and F⋅τ=0\mathbf{F}\cdot\boldsymbol{\tau} = 0. ((c)) Looking down from +z+z, the parts of r\mathbf{r} and F\mathbf{F} in the xyxy plane are (0.10,0.20) m(0.10, 0.20)\,\mathrm{m} and (5.0,0) N(5.0, 0)\,\mathrm{N}. Use the right-hand rule on these two to predict the sign of τz\tau_z, and compare with your answer to (a).

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