Thread: What is linear acceleration?

Hi,
What is the linear acceleration of a body moving in a circular path?
its written in my book that its zero since the magnitude of velocity is constant

BUT the direction is changed so it can't be zero so this didn't persuade me.

Also I DUNNO the difference between the linear acceleration and the centripetal acceleration in a circular motion.

Thanks

Acceleration is the rate of change of velocity, not speed.

Velocity is speed with direction.

Thus, even if we maintain our speed, if we change direction (as we do if we move in a circular path) technically we are accelerating.

This is an example of angular acceleration. As the acceleration is due to a chnage of direction.

Linear acceleration is when we keep our direction constant but change our speed.

Hence your book is correct.

Linear acceleration is when we keep our direction constant but change our speed.

Do you mean that linear acceleration is the acceleration of the body when it moves tangentially to its circular path?

suppose we moved a body in a circle and when we let it go , it moves in a st line tangent to this circle , and since the speed is constant (according to inertia) then the body has no linear acceleration?

Do i get it in the right way??

Thanks

Originally Posted by Misr

Linear acceleration is when we keep our direction constant but change our speed.

Do you mean that linear acceleration is the acceleration of the body when it moves tangentially to its circular path?

Yup you've pretty much got the idea.

This picture might help.


Let's first make a few assumptions.

1) Let's assume that this polygon is your circle.
2) Each side of the polygon shows the direction our body is moving in at a particular instant in time.
3) The body is moving at a constant speed around the circle.
4) The body is moving anti-clockwise.

If our body has a constant speed (not velocity), whilst travelling around the circle, this means that the speed is the same for every line on the polygon.

We see that after each instant the path changes direction. But the speed stays the same.

Now remember velocity is both speed and direction. So as we move round our polygon we are changing directions; so technically we are experiencing an acceleration. Specifically, angular acceleration.

We have said that our speed on each line of the polygon is the same. Thus we are not experiencing any acceleration with respect to speed. That is we have no linear acceleration.

Originally Posted by Misr

Hi,
What is the linear acceleration of a body moving in a circular path?
its written in my book that its zero since the magnitude of velocity is constant

BUT the direction is changed so it can't be zero so this didn't persuade me.

Also I DUNNO the difference between the linear acceleration and the centripetal acceleration in a circular motion.

Thanks

It sounds as though your book needs some editing.

1. It is possible to go in a circle and change both speed and direction. In that case the magnitude of the velocity is not constant.

2. In uniform circular motion, which a more restrictive condition than simply "moving in a circular path"" it is true that the magnitude of velocity (speed) does not change.

3. The term "linear acceleration" is not standard. It appears to me that the author of your text book means by "linear acceleration" the time derivative of speed. I would have construed linear acceleration to mean acceleration of a body moving along a trajectory that is a straight line. Those are two very different things.

4. Normally centrepital acceleration is that component of the acceleration vector that is perpendicular to the velocity vector. In the case of uniform circular motion the acceleration is centrepetal and is directed towards the center of the circle.

Your skepticism is well-founded. It is clear that you understand acceleration and are being confused by some rather odd terminology in your book. My personal impression is that you understand this better than the joker that wrote the book.

1. It is possible to go in a circle and change both speed and direction. In that case the magnitude of the velocity is not constant.

2. In uniform circular motion, which a more restrictive condition than simply "moving in a circular path"" it is true that the magnitude of velocity (speed) does not change.

My book is talkin bout uniform circular motion , so nothin wrong with it .

4. Normally centrepital acceleration is that component of the acceleration vector that is perpendicular to the velocity vector. In the case of uniform circular motion the acceleration is centrepetal and is directed towards the center of the circle.

mmm , acceleration has two components , one is centripetal , the other is tangent (tangential or linear acceleration

Yup you've pretty much got the idea.

This picture might help.


Let's first make a few assumptions.

1) Let's assume that this polygon is your circle.
2) Each side of the polygon shows the direction our body is moving in at a particular instant in time.
3) The body is moving at a constant speed around the circle.
4) The body is moving anti-clockwise.

If our body has a constant speed (not velocity), whilst travelling around the circle, this means that the speed is the same for every line on the polygon.

We see that after each instant the path changes direction. But the speed stays the same.

Now remember velocity is both speed and direction. So as we move round our polygon we are changing directions; so technically we are experiencing an acceleration. Specifically, angular acceleration.

We have said that our speed on each line of the polygon is the same. Thus we are not experiencing any acceleration with respect to speed. That is we have no linear acceleration.

Yeah got it now...
Thanks for all of you

Originally Posted by Misr

Hi,
What is the linear acceleration of a body moving in a circular path?
its written in my book that its zero since the magnitude of velocity is constant

BUT the direction is changed so it can't be zero so this didn't persuade me.

Also I DUNNO the difference between the linear acceleration and the centripetal acceleration in a circular motion.

Thanks

The acceleration vector of an object in centripedal motion is always towards the centroid of the circular path, while the velocity vector is always tangent to the circular path (calculus is especially useful when it comes to such computations). Centripedal acceleration can be computed by the following formula:



This aids us when computing force:




As you can see by looking at the above formula for acceleration, one cannot move in a circular path with no acceleration (as this would imply a velocity of zero, and therefore no distance traveled, implying that one is not only not moving in a circular path, but not moving at all).

k...Thanks

How cute..!! Thanks for sharing a sharing the concept in depth ..!!
Never thought in this way.. still interesting..!!

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