Torque and Rotational


Torque is the ability of a force to cause an object to have angular acceleration. In simpler terms, it is the rotation of an object when it is pushed or pulled.


$\vec{\tau} = \vec{r} \otimes \vec{F} = \vert{r}\vert\vert{F}\vert sin\theta$

Converting from the linear $\vec{F} = m\vec{a}$, we get Newton’s Second Law for rotational motion: $\tau_{net} = Ia$


Special Cases

If the force applied to an object is perpendicular to the displacement vector r, the distance to the center can be used, thus making the torque a maximum for the given force. The equation for the magnitude of a torque, arising from a perpendicular force:

$\vert{\tau}\vert = (distance to center)(\vec{F})$



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