torque in cartesian coordinates - Physics - System Of Particles And Rotational Motion

Question

torque in cartesian coordinates

Hansraj Rai · Accepted Answer

Dear Student!

Position vector in Cartesian coordinates,

$\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}$

Force in Cartesian coordinates,

$\vec{F} = F_{x} \hat{i} + F_{y} \hat{j} + F_{z} \hat{k}$

Expression for torque in Cartesian coordinates,

$\vec{τ} = \vec{r} \times \vec{F} = (x \hat{i} + y \hat{j} + z \hat{k}) \times (F_{x} \hat{i} + F_{y} \hat{j} + F_{z} \hat{k})$

On solving and equating the components along x, y and z direction,

$τ_{x} = y F_{z} - z F_{y} τ_{y} = z F_{x} - x F_{z} τ_{z} = x F_{y} - y F_{x}$