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To study torque experimentally, you apply a force to a beam. One end of the beam is attached to a pivot that allows the beam to rotate freely. The pivot is taken as the origin or your coordinate system. You apply a force of f = fx i + fy j + fz k at a point r = rx i + ry j + rz k on the beam.

Respuesta :

The vector expression for the resulting torque, in terms of the unit vectors i, j, k and the components of F and r is;

τ =(ry•Fz – rz•Fy)i + (rz•Fx – rxFz)j + (rxFy – ryFx) k

We are given;

Applied force;

F = (Fx)i + (Fy)j + (Fz)k

Also; distance is;

r = (rx)i + (ry)j + (rz)k

Formula for torque is;

τ = F × r

Thus;

τ = [(Fx)i + (Fy)j + (Fz)k] × [(rx)i + (ry)j + (rz)k]

Note that;

i² = j² = k² = 1

ij = jk = ik = 0

Thus;

τ = (ry•Fz – rz•Fy)i + (rz•Fx – rxFz)j + (rxFy – ryFx)k

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The complete part of the question is;

Enter a vector expression for the resulting torque, in terms of the unit vectors i, j, k and the components of F and r.