Question

Force $\overrightarrow{F}=-10\widehat{ȷ}\mathrm{N}$is exerted on a particle at $\overrightarrow{r}=(5\widehat{ı}+5\widehat{ȷ})\mathrm{m}$. What is the torque on the particle about the origin?

Short answer

The particle's torque around the origin is$-(50\mathrm{N}\cdot \mathrm{m})\widehat{k}$.

Step-by-step solution

Formula for torque

Another technique to combine two vectors is to use the vector or cross product, which produces a vector that is perpendicular to both of the originals.

Torque is the cross product of the radius vector (from the axis of rotation to the site of force application) and the force vector in vector form.

$T=r\times F$

$T$is torque.

$F$ is force.

Calculation of Torque

The torque on the particle of origin

$r\times F=\left|\begin{array}{ccc}i& j& k\\ 5\mathrm{m}& 5\mathrm{m}& 0\mathrm{m}\\ 0\mathrm{N}& -10\mathrm{N}& 0\mathrm{N}\end{array}\right|$

$=i\left(0\right)-j\left(0\right)+k\left(\right(5\mathrm{m}\left)\right(-10\mathrm{N})-0\mathrm{N}\cdot \mathrm{m})$

$=-k(50N-m)$