Semantic question about equilibrium

[etotheipi]

If a body experiences acceleration in one direction and no acceleration in another (orthogonal) direction, is it accurate to state that the body is in static equilibrium in one direction only? Or is static reserved for strictly no acceleration in any direction? Apologies if this seems pedantic!

 

[Doc Al]

I'd go further and say that "static equilibrium" is reserved for things that aren't moving, much less accelerating. Nonetheless, you can certainly apply Newton's law in any direction: if the acceleration in a given direction is zero, the sum of the forces in that direction will be zero. (Kind of an "equilibrium" condition, but I wouldn't call it static.)

 

[etotheipi]

I'd go further and say that "static equilibrium" is reserved for things that aren't moving, much less accelerating. Nonetheless, you can certainly apply Newton's law in any direction: if the acceleration in a given direction is zero, the sum of the forces in that direction will be zero. (Kind of an "equilibrium" condition, but I wouldn't call it static.)

I agree with everything that you say, however if for instance a ball moves across a horizontal surface in some arbitrary motion, when we consider solely the vertical direction we can still write ##y = k##, ##y' = 0## and ##y''=0##, which appears to be precisely the conditions for static equilibrium in this one dimension.

 

[Doc Al]

What would be the advantage of using the term static equilibrium in that case? (Though I do see your point.)

 

[etotheipi]

What would be the advantage of using the term static equilibrium in that case? (Though I do see your point.)

Now that I think about it, probably none at all! To me it just seems like a succinct way of stating that there is neither velocity nor acceleration in a particular direction, which is slightly more constrained than just no acceleration.

In practice, the semantic distinction is probably not so important (i.e. common sense prevails), as you suggest!

 

[Mister T]

To me it just seems like a succinct way of stating that there is neither velocity nor acceleration in a particular direction, which is slightly more constrained than just no acceleration.

Are you thinking of only two spatial directions? If so, the term used for that is rectilinear motion.

Note that in general, any motion confined to a plane would have zero velocity and zero acceleration in the direction perpendicular to that plane.