Can a vector with zero magnitude have certain direction?

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Discussion Overview

The discussion revolves around the concept of zero-magnitude vectors, particularly in the context of acceleration in various motion scenarios, including linear and circular motion. Participants explore whether a vector with zero magnitude can have a defined direction and how this relates to different types of acceleration.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants argue that a zero-magnitude vector does not have a defined direction, while others suggest that one can define a convention for convenience.
  • There is a discussion about whether one can say the acceleration is zero and directed to the right, with some asserting that it is more accurate to state that the acceleration directed to the right is zero.
  • Participants explore the case of circular motion, questioning whether the linear acceleration is zero and if it can have a tangential direction.
  • Some participants clarify that while the magnitude of centripetal acceleration is constant, its direction is continuously changing, leading to a distinction between constant magnitude and non-constant vector direction.
  • There is confusion regarding the definitions of linear and angular acceleration, with some participants asserting that both centripetal and tangential accelerations are components of linear acceleration.
  • One participant expresses doubt about the correct answers to a question regarding circular motion, particularly concerning the nature of linear acceleration and its components.
  • Another participant emphasizes that the magnitude of acceleration is not the same as the rate of change of speed, challenging a common misconception.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether a zero-magnitude vector can have a defined direction. There are multiple competing views regarding the nature of acceleration in circular motion and the definitions of linear and angular acceleration.

Contextual Notes

Some statements rely on specific definitions of acceleration and velocity, which may not be universally agreed upon. The discussion includes unresolved questions about the implications of zero magnitude in various contexts.

songoku
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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
 
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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
 
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songoku said:
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".
 
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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?

A.T. said:
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"?
 
songoku said:
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.
songoku said:
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.
 
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songoku said:
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.
 
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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
 
songoku said:
I thought there are 2 correct answers: B and C but now it seems that the correct answer is only B.
Correct.
songoku said:
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.
songoku said:
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.
songoku said:
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.
 
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songoku said:
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.
 
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  • #10
songoku said:
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.
 
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  • #11
A.T. said:
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 ?
 
  • #12
conscience said:
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 ?
Correct. The magnitude of the acceleration is constant. The complete vector is not since its direction is changing.
 
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  • #13
Thank you very much for all the help
 

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