How To Find Line Of Action Of Resultant Force

The line of action is shown as the vertical dotted line. It extends in both directions relative to the forcefulness vector, but is most useful where it defines the moment arm.

In physics, the line of action (likewise called line of awarding) of a force F is a geometric representation of how the force is applied. It is the line through the signal at which the forcefulness is applied in the same direction as the vector F → .^[1] ^[2]

The concept is essential, for instance, for agreement the cyberspace effect of multiple forces applied to a torso. For example, if 2 forces of equal magnitude deed upon a rigid trunk along the aforementioned line of action just in opposite directions, they cancel and have no cyberspace effect. Just if, instead, their lines of activity are not identical, but merely parallel, and so their outcome is to create a moment on the body, which tends to rotate it.

Adding of torque [edit]

For the simple geometry associated with the figure, there are 3 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{aligned}||{\vec {\tau }}||&=||{\vec {r}}\times {\vec {F}}||\\&=rF_{\perp }\\&=r_{\perp }F\\&=||rF\sin \theta ||\,,\end{aligned}}

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 ${\vec {F}}$

References [edit]

^ *Kane, Thomas R.; Levinson, David A. (1985), Dynamics: Theory and Awarding, McGraw-Hill Series in Mechanical Engineering, McGraw-Hill, Inc., ISBN0-07-037846-0
^ Mungan, Carl E. "Dispatch of a pulled spool." The Physics Teacher 39.8 (2001): 481-485. https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/TPT.pdf