torque

Torque, moment, or moment of force is rotational force. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector.
The symbol for torque is typically



τ


{\displaystyle \tau }
, the lowercase Greek letter tau. When it is called moment of force, it is commonly denoted by M.
The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the origin to the point of force application, and the angle between the force and lever arm vectors. In symbols:





τ

=

r

×

F





{\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \,\!}





τ
=
‖

r

‖

‖

F

‖
sin
⁡
θ




{\displaystyle \tau =\|\mathbf {r} \|\,\|\mathbf {F} \|\sin \theta \,\!}

where





τ



{\displaystyle {\boldsymbol {\tau }}}
is the torque vector and



τ


{\displaystyle \tau }
is the magnitude of the torque,
r is the position vector (a vector from the origin of the coordinate system defined to the point where the force is applied)
F is the force vector,
× denotes the cross product,which is defined as magnitudes of the respective vectors times sin θ.
θ is the angle between the force vector and the lever arm vector.
The SI unit for torque is N⋅m/rad. For more on the units of torque, see Units.

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