Re: [Phys-L] fundamental notion of force --> using an arrow to represent something more than a vector

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

I have been one of those who have associated the point of application of a force and the line of action of a force, with the force, and thought of the force as a bound vector or a sliding vector (free to slide along the line of action), but you have shown me the light, Philip.  Thanks!  The key is to separate the force, represented by a plain old vector, from the location of the interaction.  We use a position vector to specify the location of the interaction; it represents how far and which way you have to go from some specified point in space to get to the location of the interaction (or the effective location of the interaction for the case of a distributed load such as that of the gravitational interaction).  I appreciate John raising this point; it certainly made me think about it.

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of Philip
> Keller
> Sent: Saturday, October 24, 2015 10:03 AM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] fundamental notion of force --> using an arrow to
> represent something more than a vector
>
> I think I am missing the point.
>
> A force is a vector.  But a rope is not.  And a "lever-arm" is a vector.
> But a beam is not.
>
> When a rope pulls on a beam, we define the force vector with magnitude
> and direction.  But the force vector is not a physical entity.  It is a
> mathematical abstraction.  And it does not have location.  When we are
> working with those abstractions, we find it convenient to move them
> around, such as when adding them tip-to-tail.  We can move the force but
> we are not moving the rope. We are moving them in an abstract vector
> space, not the real world. [Just this week, I have been teaching first year
> students how to take the forces on a free-body diagram and and add them
> tip-to-tail.]
>
> Similarly, lever-arm is a vector.  We can define it as the displacement vector
> from the chosen pivot axis to the point of application of the _rope_ (not "the
> force", the rope).  Moving the real-world rope will change the lever arm
> vector.  Moving the abstract (vector-space) force will not.
>
> Then, we can define torque = r x F = |r| times |F| times sine of angle
> between them.  Go ahead and move F or r wherever you want...torque
> won't change.
>
>
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