13.1: Torque


Newton’s second law $$\vec{F}=m\vec{a}$$ has a rotational analogue. When a force $$\vec{F}$$ is exerted at a location $$\vec{r}$$ measured from some axis of rotation (e.g., the bolt in Figure $$\PageIndex{1}$$), then the cross product $$\vec{r}\times\vec{F}$$ is called the torque, $$\vec{T}$$. The cross product is defined in Equation 2.1.1, and is derived in detail in section D.3.1. For now, it is a vector perpendicular to both $$\vec{F}$$ and $$\vec{r}$$, with direction given by the right-hand rule. The magnitude is

$|\vec{r}\times\vec{F}|=|\vec{r}||\vec{F}||\sin\phi| \nonumber$

where $$\phi$$ is the angle between $$\vec{r}$$ and $$\vec{F}$$.

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