What does torque depend upon? I know torque depends on force and moment arm, but does it depend on choice of origin? Because I think choice of origin determines its moment arm.
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2$\begingroup$ Have you read en.wikipedia.org/wiki/… $\endgroup$– BMSCommented Oct 14, 2014 at 6:48
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2 Answers
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Torque is defined as $\vec \tau = \vec r \times \vec F$, where $\vec r$ is the displacement vector from the origin to the point at which the force is applied. This means that torque depends very much on the choice of origin. Then again, the choice of origin also affects the inertia tensor.
So long as you get all of the physics correct, you can choose any origin you want. The ultimate answer will be the same regardless of choice of origin. That said, some choices vastly complicate the equations of motion while other choices vastly simplify the equations of motion. The "best" choice of origin is the one that results in the simplest equations of motion. This varies from problem to problem. There is no hard and fast rule that says always choose origin X (whatever "X" may be).
answered Oct 14, 2014 at 9:50
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$\begingroup$ Means choice of origin is arbitrary ? $\endgroup$ Commented Oct 14, 2014 at 12:30
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1$\begingroup$ @user60180 - Completely arbitrary. That said, some arbitrary choices are "better" (easier to describe) than are others. $\endgroup$ Commented Oct 14, 2014 at 12:32
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Torque is often given as the simple equation: $$ \tau = {rFsin\theta} $$
It is the net perpendicular force which is found by finding the $sin\theta$ of the force applied where $\theta$ is the angle at which it is applied.
Since torque is dependent on angular momentum and is also defined as $\tau = \frac{\partial L}{\partial t}$
The choice of origin matters when determining the displacement vector ($L=r\times p$) where $r= displacement\space vector$ and $p = linear\space momentum$.
