6. Torque

Measure of rotational force applied to an object that causes it to rotate around an axis

$$\vec{\tau} = \vec{r} \times \vec{F} \quad (Nm)$$

Consider a force ($\vec{F}$) acting on a particle (mass $m$, distance from axis $r$) that causes it to accelerate around an axis

$$\vec{F} = ma_t$$

since

$$a_t = \alpha r$$

then

$$\vec{F} = m r \alpha$$

multiply both sides by $r$

$$\vec{F}r = m r^2 \alpha$$

then

$$\vec{\tau} = I \alpha$$