# torque Definition and Topics - 480 Discussions

In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically

τ

{\displaystyle {\boldsymbol {\tau }}}
or τ, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
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 magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured 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

{\displaystyle \mathbf {r} }
is the position vector (a vector from the point about which the torque is being measured to the point where the force is applied),

F

{\displaystyle \mathbf {F} }
is the force vector,

×

{\displaystyle \times }
denotes the cross product, which produces a vector that is perpendicular to both r and F following the right-hand rule,

θ

{\displaystyle \theta }
is the angle between the force vector and the lever arm vector.The SI unit for torque is the newton-metre (N⋅m). For more on the units of torque, see § Units.

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Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin. I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)
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3. ### Tangential velocity of rotating rod

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4. ### Torque calculations: Rotating vertical shaft

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Question : Solution attempt : for
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18. L

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26. ### Torque on a circular current loop

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27. ### What force will be felt by ##B## when a rod is rotated?

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29. ### Integral for the calculation of torque

Hello, I found an integral to calculate the torque from the applied torsional shear stress, and I didn't find an explanation of how this integral is deviated. Where does it come from? Could someone explain? T = ∫τ⋅r⋅dA = ∫τ⋅2πr⋅dr, where T is the torque and τ the shear stress. Thanks a lot!
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