Help with Physics signs and directions

• love2learn1
In summary: It just simplifies the math.In summary, the author writes that "up" is the positive direction and that "down" is the negative direction. This notation is used to simplify the math when referring to the acceleration due to gravity.
love2learn1
The acceleration due to gravity is -9.8m.s^2 , so what does the up mean, and what does the negative mean? I thought that the negative sign always means down and you don't need to put the direction in brackets.

The author wrote to tell you that "up" is the positive direction.
This means that -9.8m.s-2 could mean the object is going down and gaining speed or it is going up and losing speed (or momentarily stationary).

The sign convention is arbitrary - you don't have to call "up" positive and in many situations it makes the math easier to make down positive.
You don't have to make the x-axis horizontal either, or the y-axis vertical.

But you do have to say somewhere what convention you are using, and you have to be consistent within the problem.

But if it says - and [up] doesn't that mean that up is the negative direction

love2learn1 said:
The acceleration due to gravity is -9.8m.s^2

That seems an odd bit of notation. Where did you see it?

Since you know that the acceleration due to gravity is always down, if it's given as negative that means you are taking up as positive.

Doc Al said:
That seems an odd bit of notation. Where did you see it?

Since you know that the acceleration due to gravity is always down, if it's given as negative that means you are taking up as positive.

The notation does seem odd. He's using where a unit vector would be used. Unit vectors have multiple conventions, but I've never seen

x hat, y hat, z hat
i, j, k,
e1, e2, e3

They use similar notations in high school physics. In US and Canada.
[E], [N], [W], .

love2learn1 said:
But if it says - and [up] doesn't that mean that up is the negative direction
What the author wrote makes sense to me. That is how I would say it, if I were explaining it with words. "In SI units, g equals minus nine point eight in the 'up' direction". And then if I define 'down' to be the negative of 'up', then it is equivalent to saying: "In SI units, g equals nine point eight in the 'down' direction"

Yep, it looks like they are using to represent a unit vector in the up direction, like flatmaster pointed out. Makes sense to me, though I don't recall seeing that.

So does this mean that up was not chosen as the positive direction? I'm really confused on the sign conventions in physics. Why do you need the ?

It means that "up" is the positive direction. Therefore "down" is the negative direction, and since the number given has a - sign, it indicates a downward acceleration.

If they had written it as "9.8 m/s^2 [D]" it would have meant the same thing.

I've never seen this particular notation either, but it's been more than forty years since I was in high school. The textbooks I've used and taught from at college level would say something like

$$\vec a = -9.8 \hat y \text{ m/s^2}$$

where ##\hat y## is a unit vector that points upwards. Some books use ##\hat x##, ##\hat y## and ##\hat z## for the unit vectors, others use ##\hat i##, ##\hat j## and ##\hat k##. Or they use boldface instead of the caret ("hat").

I'm really confused on the sign conventions in physics.
Beginning students often get confused when a negative sign is used with a positive direction.
The sign convention is the same in physics as it is in mathematics.
It indicates a deficit of something.

-10m is a deficit of 10m in the upwards direction ... which is the same as saying "10m downwards".

You could just say, "well why not just say so then?"
The reason is because it makes the math easier when you refer to only one positive direction.
If you went 10m and then 20m [D] you'd end up 10m [D] ... which you did intuitively.
In math you'd have to convert one of the or [D] first so you can say (taking [D] as positive)
(-10m[D]) + 20m[D] = (20-10)m[D] = 10m[D]
In math, 10m[D] is "ten meters multiplied by the direction [downwards]".

But if it says - and [up] doesn't that mean that up is the negative direction
...
So does this mean that up was not chosen as the positive direction?
Unless it says something else in the book (or wherever you saw the notation) then .. no. Treat the indicator in brackets as the positive direction.
In the case of - that would indicate that "upwards" is the positive direction.

A negative value of a positive direction is the same as the positive value on the negative direction.

Using math notation we can say "down is the opposite of up" like this:

[D] = - so:

-9.9 = -1x9.8x =9.8x(-1)x = 9.8(-) = 9.8[D]

Why do you need the ?

Because the direction of the positive axis is entirely arbitrary - if a direction is not specified, then the reader could get confused about what was intended. Maybe it seems obvious to you know, which direction things like gravity should be? Why bother saying it? Isn't it just being pedantic?

But if the problem is, say, a box sliding down a slope, then it makes the math easier to put the +x axis pointing down along the slope. This means the -y axis does not point in the direction of gravity.

If the author did not tell the reader that the +x axis was taken to be "down along the slope" then the reader may not realize that and get confused.

Somewhere where the reader can see it there has to be some indicator.
You could write: the initial velocity is -23m/s [down along the slope] with acceleration +9.8/2m/s/s [down along the slope] or just say +x dir = [down along the slope] (I'd use the last one personally.)

Whatever you use - it has to be clear to the reader, which is why I suspect the author of the notation you are referring to has actually explained it someplace and maybe you just missed it? Whatever - it is a failure to communicate. Learn from it.

Last edited:
It's all a matter of context. Anyone starting on any calculation of this sort is free to use either convention they want - as long as they stick to it throughout.
If we do calculations about falling bodies (down mineshafts and off cliffs) we often choose 'downward motion' to be positive and, hence the acceleration due to gravity will be a positive value. We state (or strongly imply) that this is what we mean and then we stick with that convention and get the right answer (how far down, etc.).
If we do calculations on a ballistics problem, we would (instinctively) be pointing the gun in a direction we would call Positive (UP = positve this time) and then our initial velocity would be positive and the acceleration would be negative.

1. What are the common signs and symbols used in physics?

In physics, there are several common signs and symbols used to represent different quantities and concepts. Some of the most frequently used signs and symbols include the Greek letter alpha (α) for acceleration, the letter g for gravitational acceleration, and the letter F for force.

2. How do I read and interpret vector directions in physics?

In physics, vector directions are represented by arrows. The direction of the arrow indicates the direction of the vector, while the length of the arrow represents the magnitude. To read and interpret vector directions, you must pay attention to both the direction and magnitude of the vector.

3. What is the difference between velocity and speed?

Velocity and speed are often used interchangeably, but they are actually different concepts. Speed is a measure of how fast an object is moving, while velocity is a measure of an object's speed and direction of motion. In other words, velocity is a vector quantity, while speed is a scalar quantity.

4. How can I determine the direction of acceleration in a given scenario?

The direction of acceleration depends on the change in velocity. If an object is speeding up, its acceleration will be in the same direction as its velocity. If an object is slowing down, its acceleration will be in the opposite direction of its velocity. In circular motion, the acceleration is always directed towards the center of the circle.

5. What is the right-hand rule in physics?

The right-hand rule is a mnemonic used to determine the direction of a vector resulting from a cross product. To use the right-hand rule, point your right thumb in the direction of the first vector, and your fingers in the direction of the second vector. The direction your palm is facing will be the direction of the resulting vector.

• Other Physics Topics
Replies
4
Views
3K
• Other Physics Topics
Replies
2
Views
850
• Aerospace Engineering
Replies
14
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
378
• Other Physics Topics
Replies
39
Views
2K
• Introductory Physics Homework Help
Replies
44
Views
3K
• Introductory Physics Homework Help
Replies
7
Views
563
• Introductory Physics Homework Help
Replies
2
Views
403
• Other Physics Topics
Replies
3
Views
1K
• Other Physics Topics
Replies
15
Views
2K