# Can a vector with zero magnitude have certain direction?

songoku
Let say a car move with constant speed to the right. Can I say the acceleration is zero and is directed to the right?

Or we can not assign certain direction to a zero-magnitude vector because I can also say that the car has zero backward acceleration (directed to left)?

Thanks

2022 Award
It has no defined direction, as you reason in your last paragraph.

Don't let that stop you defining a convention if it's convenient to do so, but be clear that you're defining a "house rule" when you're doing it

• songoku
Can I say the acceleration is zero and is directed to the right?
No, but you can say: "The acceleration directed to the right is zero".

• songoku
songoku
Ok so for another case: an object moves in circular with constant speed.
The linear acceleration will be zero. The direction of this linear acceleration will be tangential or we can not assign the direction to this zero linear acceleration of circular motion?

No, but you can say: "The acceleration directed to the right is zero".
I can also say: "the acceleration directed to any direction is zero"?

2022 Award
Ok so for another case: an object moves in circular with constant speed.
The linear acceleration will be zero. The direction of this linear acceleration will be tangential or we can not assign the direction to this zero linear acceleration of circular motion?
There's only one thing: the acceleration. You can resolve that into radial and tangential components, certainly, and you may find that there is no component in the tangential direction. That's fine - all you are saying is that the acceleration is perpendicular to the tangential direction. See above regarding whether this zero component points in the clockwise or anticlockwise direction.
I can also say: "the acceleration directed to any direction is zero"?
Yes. Or just "the acceleration is zero", which is the way I'd phrase it.

• songoku
Ok so for another case: an object moves in circular with constant speed.
The linear acceleration will be zero. The direction of this linear acceleration will be tangential ...
No. The angular acceleration is zero. The linear acceleration is non-zero and centripetal. The tangential component of linear acceleration is zero.

• songoku
songoku
I find this problem when reviewing about circular motion: Which statement is correct regarding a car moving in circular with constant angular speed?
a. Its linear velocity is constant
b. Its linear velocity is changing
c. Its linear acceleration is zero
d. Its linear acceleration is constant
e. Its angular acceleration is changing

I thought there are 2 correct answers: B and C but now it seems that the correct answer is only B.

At first, I have my doubt about answer C because I think the magnitude is zero but there is still direction (tangential) so maybe it is wrong to state that "linear acceleration is zero" (maybe the question means that both the magnitude and direction is zero).

And I also think that in circular motion, there are 2 accelerations: centripetal and linear (tangential). But the correct concept will be: the centripetal and tangential accelerations are both linear acceleration in circular motion?

I also want to ask about centripetal acceleration. By definition, acceleration is rate of change of velocity. When the tangential acceleration is zero, the object will move with constant linear velocity because the rate of change of linear velocity is zero. But what about centripetal acceleration? Does centripetal acceleration cause the change of velocity when an object moves in circular based on the same definition of acceleration?

Thanks

2022 Award
I thought there are 2 correct answers: B and C but now it seems that the correct answer is only B.
Correct.
At first, I have my doubt about answer C because I think the magnitude is zero
The magnitude is not zero - an object moving at speed v in a circle of radius r has acceleration ##v^2/r## - the centripetal acceleration.
But the correct concept will be: the centripetal and tangential accelerations are both linear acceleration in circular motion?
I'd say that there is just acceleration. This can always be broken down into a component towards the centre of the circle and a component tangential to the circle. If you want to view them as separate things, though, they are both linear accelerations, yes.
When the tangential acceleration is zero, the object will move with constant linear velocity
No. It moves with constant linear speed, but speed is the magnitude of the velocity vector. The vector is changing all the time, as this is circular motion and the direction is never constant.

• songoku
But the correct concept will be: the centripetal and tangential accelerations are both linear acceleration in circular motion?
Yes, linear acceleration and angular acceleration are two different quantities. Centripetal acceleration and tangential acceleration are components of linear acceleration.

• songoku
Homework Helper
I think the magnitude is zero but there is still direction (tangential)
If I understand your confusion, you may be reasoning that...

Speed is the magnitude of velocity.
Acceleration is the rate of change of velocity.
Therefore the magnitude of acceleration is the rate of change of speed.

That's wrong. The magnitude of a rate of change is not, in general, equal to the rate of change of the magnitude. "Rate of change" and "magnitude" do not commute.

• songoku and Ibix
conscience
Yes, linear acceleration and angular acceleration are two different quantities. Centripetal acceleration and tangential acceleration are components of linear acceleration.

In the question stated in post#4 , acceleration has same magnitude v2/r and is always directed towards the center . So why do we say that linear acceleration is not constant ?

Is it because even though the acceleration is always pointing towards the center , that direction itself is continuously changing ?

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