Question

A $3.0kg$ toy car moves along an $x$ axis with a velocity given by $\overrightarrow{V}=-2.0t^3\overrightarrow{i}m/s$, with $t$ in seconds. For $t>0$, what are the torque $\overrightarrow{r}$ on the car,both calculated about the origin?

Answer 1

This problem involves the vector cross product of vector lying in the $xy$ plane. For such vectors,if we write $\overrightarrow r=x' \widehat i+y' \widehat j$,thenwefind$\overrightarrow r \times \overrightarrow v=(x' v_y -y' v_x)\widehat k$.
The net force is in the $-\hat{i}$ direction (as one finds from differentiating the velocity expression, yielding the acceleration), so similar to what we found in part (a), we obtain $r=\overrightarrow{r}\times \overrightarrow{F}=0$.