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# Moment and torque

A torque $(\vecphy{\tau})$ or moment $(\vecphy{M})$ is the tendency of a force to twist or rotate an object about an axis. The concept of moment can be confused with the momentum $(p=mv).$

The magnitude of $\tau$ is given by the product of the force $F$ and the perpendicular distance $r$ between the point at which the force is applied and the axis of turning: $$\tau=M=rF$$

The SI unit of torque is the Newton metre $(N m)$. It is dimensionally equivalent to the unit of work (i.e. $1\text{ J}=1\text{ N m}$) but describes a different quantity.

When you hold a pen lying on the table at its middle and push it at its tip, the pen will turn around its middle.

$F_1$ on the left acts alone and will change the overall direction of the object as well as creating rotational acceleration. The couple of $F_2$ and $F_3$ creates a moment but no net force.