Scalar term for acceleration

Question

Consider the following definitions:

Distance is the magnitude of the displacement
Speed is the magnitude of the velocity
X is the magnitude of the acceleration

Is there a term we use for X?

Possible duplicates: https://physics.stackexchange.com/q/477427/2451 , https://physics.stackexchange.com/q/517636/2451 and links therein. — Qmechanic, Jul 31 '22 at 08:11

score 0 · Accepted Answer · answered Jul 31 '22 at 07:38

There is no "term" for the magnitude of acceleration.

When refering to just the absolute value of acveleration, we use the phrase "Magnitude of acceleration" like you pointed out.

This is denoted by: $|\vec a|$

Do note though, that the magnitude of acceleration is not the rate of change of speed. Rather it is the absolute value of the rate of change of velocity.

The magnitude of acceleration simply tells you how fast velocity changes, but it doesn't tell you whether the change is an increase or decrease.

Hope this helps!

Neither is the speed the change of rate in distance. – user877329 Jul 31 '22 at 07:41 — user877329, Jul 31 '22 at 07:41

Cleonis · Answer 2 · 2022-07-31T07:55:06.567

0

Yeah, there is no word for that.

Of course that raises the question: why is there no word for that.

When there is a need for a word then over time the physics community converges on a particular word. There is no word: this is because there is no such need.

In theory of motion there is the equivalence class of inertial coordinate systems. Choice of zero point of position coordinate is arbitrary. Choice of zero point of velocity vector is arbitrary. Choice of orientation of an inertial coordinate system is arbitrary.

However, for all members of the equivalence class of inertial coordinate systems the zero point of acceleration is the same.

If the motion is in 2 or more spatial dimensions: for all members of the equivalence class of inertial coordinate systems the magnitude and direction of acceleration is the same.

In the case of displacement and velocity it is convenient to have a way of expressing displacement and velocity in a way that is independent of choice of zero point in space and/or zero point of orientation. Hence the convention of using the words 'distance' and 'speed' respectively. (Well, 'speed' is independent of choice of orientation only.)

In the case of the acceleration vector: for all members of the equivalence class of inertial coordinate systems the acceleration vector is the same anyway.

Therefore in physics the word acceleration always refers to the acceleration vector.

edited Jul 31 '22 at 07:55

answered Jul 31 '22 at 07:44

Cleonis

20,795

So whenever you got a scalar acceleration, you projected the acceleration on to some other vector, such as a surface normal. – user877329 Jul 31 '22 at 08:03
@user877329 Scalar acceleration is still the magnitude of the vector, not (the magnitude of) a projection. Conversely, the projection of a vector onto another vector is still a vector. Coordinate-acceleration is still vector valued, but analogous to speed by the reasoning above, the zero point being an arbitrary consequence of coordinate system. (For instance, describing the path of a ball rolling around on the bed of a truck putting on the brakes, the ball has a coordinate acceleration towards the front of the truck.) – g s Jul 31 '22 at 08:10
@gs I meant in a more general sense. Any scalar quantity with dimensions length/(time*time), in practice comes from the projection of the acceleration vector on to something dimensionless, such as the sufrace normal. – user877329 Jul 31 '22 at 08:25
@user877329 It's not clear why you mention the concept of 'projection on to'. For any vector A the magnitude of that vector is obtained by evaluating the vector inner product $\langle A, A \rangle $. The inner product of a vector A with a vector B is used too, but in different context. – Cleonis Jul 31 '22 at 13:22

Scalar term for acceleration

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