# Direction of Acceleration

#### omgwtf

Yep, another question :)

Can someone please explain what the direction of acceleration actually is?

I know acceleration can be either negative or positive, but from what I've seen it's not related to the direction at all, because, for example, an object can be accelerating positively and have a 'downward' direction and likewise for an object with a negative direction.

I'm not sure how acceleration can even have a direction (eg, north, south, northeast, etc) considering it's just a method of measuring how much velocity an object gains/loses over time, if I'm not mistaken.

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#### FZ+

I'm not sure how acceleration can even have a direction (eg, north, south, northeast, etc) considering it's just a method of measuring how much velocity an object gains/loses over time, if I'm not mistaken.
Velocity is a vector (ie. it has direction as well as magnitude) so it follows naturally that acceleration, which is the rate of change in velocity should be a vector as well.

Consider this example. You throw a ball in a horizontal direction. As the ball flies, it's path of flight or velocity becomes steadily curved downwards. It is not meaningful to just say that the ball accelerates. It could be accelerating up into space. You must say that the ball is accelerating towards the centre of mass of the earth. Hence, you add a direction to the acceleration experienced by the ball to fully express it's motion.

Is that clear?

#### omgwtf

Oh, so it's the effect gravity has on an object? But doesn't gravity always push downwards, and therefore the direction of acceleration would always be downward on an object?

#### STAii

Well, not only gravitation causes acceleration, any resultant force on any object (that has any mass) will cause an acceleration, FZ+ was only giving and example.
In gravitation specifically, (if the two objects are spherical, or almost sperical, and each object is 'outside' the surface of the other object) the acceleration of any of the two objects is directed towards the center of mass of the other object. You see, the direction 'down' is not really liked in physics, since (if you were looking from moon for example) the way a person sees 'down' in US is not the same direction a person sees 'down' in Australia (it might be almost the other way), but in both cases people (anywhere in the world) understand 'down' as 'towards the center of earth', so in physics we prefer to say that the acceleration due to gravitational field of earth points towards the center of mass of earth, or what normal people call 'down'.

#### omgwtf

Well, not only gravitation causes acceleration, any resultant force on any object (that has any mass) will cause an acceleration, FZ+ was only giving and example.

So the direction of acceleration is always the direction that the object moved (not sure of a better term) from, unless it is interfered with from an outside force (eg, gravity in an the example of throwing a ball away from the center of the Earth) after which the direction of acceleration becomes the direction in which the force is 'moving' the object?

In gravitation specifically, (if the two objects are spherical, or almost sperical, and each object is 'outside' the surface of the other object) the acceleration of any of the two objects is directed towards the center of mass of the other object.

Er, but say if I dropped a small metal pyramid from a building it would still accelerate towards the center of the Earth, correct?

You see, the direction 'down' is not really liked in physics, since (if you were looking from moon for example) the way a person sees 'down' in US is not the same direction a person sees 'down' in Australia (it might be almost the other way), but in both cases people (anywhere in the world) understand 'down' as 'towards the center of earth', so in physics we prefer to say that the acceleration due to gravitational field of earth points towards the center of mass of earth, or what normal people call 'down'

Ah, that makes alot of sense, thanks for clearing that up. Btw, what would 'forward' and 'backward' be in physics? (Edit: Also, what would directions such as southeast and northwest be called in physics terminology?)

Thanks.

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#### FZ+

No no no!

The direction of acceleration is the direction in which the velocity changes.

Maybe what is confusing us is the use of the coordinate system. Suppose we define an arbitary system of cartesian coordinates Up Down, And Forward and Back (2D for simplicity's sake and simplify so that gravity is a force in the downwards direction at all times). We throw the ball horizontally, so that it's velocity is x m/s in the full horizontal direction. As the ball flies, it undergoes gravity in the downwards direction, so that it's velocity is not just x but also y downwards. Hence we say the ball has accelerated downwards in the y direction.

The basis of Newton's 1st and 2nd laws are that force is responsible for acceleration. If you push an object (in this model free from other forces), then it has an acceleration in the direction you pushed.

The idea is that to make these ideas meaningful, you must define a system of coordinates. It can be polar (based on angles and magnitudes) or cartesian (Based on magnitude at 90 degrees to each other). In the north south etc, we use the geographical north pole as the north, and the other directions at 90 degrees to it along the face of the earth. Generally this works as a cartesian system. Foward generally refers to "in the direction of current motion relative to the earth" and backwards refers to the opposite.

#### STAii

Originally posted by omgwtf
Er, but say if I dropped a small metal pyramid from a building it would still accelerate towards the center of the Earth, correct?
Yeah sure, i made a bigger statement just to avoid any mistakes.
You see, if the earth was donut-shaped, then the gravitional force will not always point towards the center of mass of the donut (the earth).
But since earth is almost a sphere, you can say that any object (whatever its shape is) that lies outside the surface of earth will have be attracted towards the center of earth.

I think FZ+ answered your other questions and made everything clear (and i also think i need a good course to learn how to use english to express my ideas! Sorry if i caused any cofusion).

#### omgwtf

The direction of acceleration is the direction in which the velocity changes.

You mean the direction of the velocity?

Maybe what is confusing us is the use of the coordinate system. Suppose we define an arbitary system of cartesian coordinates Up Down, And Forward and Back (2D for simplicity's sake and simplify so that gravity is a force in the downwards direction at all times). We throw the ball horizontally, so that it's velocity is x m/s in the full horizontal direction. As the ball flies, it undergoes gravity in the downwards direction, so that it's velocity is not just x but also y downwards. Hence we say the ball has accelerated downwards in the y direction.

So the direction of acceleration only covers the last change in the direction of velocity? For example, if an object's velocity changed directions 3 times (once north, the other east, and the last west), the direction of acceleration would be west?

The basis of Newton's 1st and 2nd laws are that force is responsible for acceleration. If you push an object (in this model free from other forces), then it has an acceleration in the direction you pushed.

Ah, that's what I meant in my last post in regards to the direction of acceleration without any interfering forces.

Now, if a force does interfere (such as gravity) with an object while it is accelerating, the object's direction of acceleration would become the direction in which the force is 'pushing' it, correct?

#### FZ+

You mean the direction of the velocity?
No, the CHANGE in velocity.
Let's try a different approach...
Have you any formal education in vector mathematics? Or calculus? Just to know where we are with this...