Notices
Results 1 to 9 of 9

Thread: What is linear acceleration?

  1. #1 What is linear acceleration? 
    Forum Freshman
    Join Date
    Feb 2010
    Posts
    41
    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


    Reply With Quote  
     

  2.  
     

  3. #2  
    sox
    sox is offline
    Forum Masters Degree sox's Avatar
    Join Date
    Sep 2008
    Location
    Uk - Scotland
    Posts
    598
    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.



    __________________________________________________ _____________
    "Happy is the man who can recognise in the work of To-day a connected portion of the work of life, and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity." - James Clerk Maxwell
    Reply With Quote  
     

  4. #3  
    Forum Freshman
    Join Date
    Feb 2010
    Posts
    41
    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
    http://img249.imageshack.us/img249/4950/signaturewv.jpg
    Twinkle...Twinkle little star ...How I wonder what you are

    Twinkle...Twinkle little star ...How I wonder what you are

    Up above the world...so high....like a diamond in the sky...
    Reply With Quote  
     

  5. #4  
    sox
    sox is offline
    Forum Masters Degree sox's Avatar
    Join Date
    Sep 2008
    Location
    Uk - Scotland
    Posts
    598
    Quote 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.

    __________________________________________________ _____________
    "Happy is the man who can recognise in the work of To-day a connected portion of the work of life, and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity." - James Clerk Maxwell
    Reply With Quote  
     

  6. #5 Re: What is linear acceleration? 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote 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.
    Reply With Quote  
     

  7. #6  
    Forum Freshman
    Join Date
    Feb 2010
    Posts
    41
    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
    http://img249.imageshack.us/img249/4950/signaturewv.jpg
    Twinkle...Twinkle little star ...How I wonder what you are

    Twinkle...Twinkle little star ...How I wonder what you are

    Up above the world...so high....like a diamond in the sky...
    Reply With Quote  
     

  8. #7 Re: What is linear acceleration? 
    Guest
    Quote 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).
    Reply With Quote  
     

  9. #8  
    Forum Freshman
    Join Date
    Feb 2010
    Posts
    41
    k...Thanks
    http://img249.imageshack.us/img249/4950/signaturewv.jpg
    Twinkle...Twinkle little star ...How I wonder what you are

    Twinkle...Twinkle little star ...How I wonder what you are

    Up above the world...so high....like a diamond in the sky...
    Reply With Quote  
     

  10. #9  
    New Member
    Join Date
    Apr 2010
    Posts
    1
    How cute..!! Thanks for sharing a sharing the concept in depth ..!!
    Never thought in this way.. still interesting..!!

    .
    .
    site lighting | hire site lighting
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •