Line of action

{{Short description|Geometric representation of a force on an object}}

{{for|the board game|Lines of Action}}{{Merge to|Torque|discuss=Talk:Torque#Proposed merge of Line of action into Torque|date=February 2025}}

File:Torque lever arm w point of application and line of action.svg

In physics, the line of action (also called line of application) of a force ({{vec|F}}) is a geometric representation of how the force is applied. It is the straight line through the point at which the force is applied, and is in the same direction as the vector {{vec|F}}.*{{citation

| last1 = Kane | first1 = Thomas R. | last2 = Levinson | first2 = David A.

| title = Dynamics: Theory and Application

| series = McGraw-Hill Series in Mechanical Engineering

| year = 1985

| publisher = McGraw-Hill, Inc.

| isbn = 0-07-037846-0}}{{Cite web |last=Mungan |first=Carl E. |title=Acceleration of a pulled spool. The Physics Teacher 39.8 (2001): 481-485. |url=https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/TPT.pdf |website=www.usna.edu}} The lever arm is the perpendicular distance from the axis of rotation to the line of action.{{Cite web |title=PHYSICS 151 – Notes for Online Lecture #20 |url=https://www.physics.unl.edu/~klee/phys151/lectures/notes/lec20-notes.pdf |website=www.physics.unl.edu}}

The concept is essential, for instance, for understanding the net effect of multiple forces applied to a body. For example, if two forces of equal magnitude act upon a rigid body along the same line of action but in opposite directions, they cancel and have no net effect. But if, instead, their lines of action are not identical, but merely parallel, then their effect is to create a moment on the body, which tends to rotate it.{{Citation needed|date=February 2025}}

Calculation of torque

For the simple geometry associated with the figure, there are three equivalent equations for the magnitude of the torque associated with a force $\vec F$ directed at displacement $\vec r$ from the axis whenever the force is perpendicular to the axis:

: $\begin{align}
||\vec\tau|| & = ||\vec r\times\vec F|| \\
& = rF_\perp \\
& = r_\perp F \\
& = ||r F \sin\theta|| \,,
\end{align}$

where $\vec r\times\vec F$ is the cross-product, $F_\perp$ is the component of $\vec F$ perpendicular to $\hat r$ , $r_\perp$ is the moment arm, and $\theta$ is the angle between $\vec r$ and $\vec F$ .{{Citation needed|date=February 2025}}

References

Category:Force