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Uniform circular motion and velocity vector

  1. Sep 14, 2005 #1
    hi

    Object in uniform circular motion is moving around the perimeter of the circle with a constant speed and while the speed of the object is constant, its velocity is changing . The direction is always directed tangent to the circle

    To my question . Velocity vector at particular point A is tangent to the circle

    Doesn't velocity vector at particular point show the current direction and speed an object has ?

    Or does velocity vector at particular point show the direction in which the velocity vector had to point in order for the object to reach that particular point A on a circle ( in which case velocity vector at point A in reality already has different direction ) , or does it show where the velocity vector has to point in order for object to move to next (nearest) point on circle ?

    thank you
     
  2. jcsd
  3. Sep 14, 2005 #2

    Doc Al

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    This is correct.
     
  4. Sep 14, 2005 #3
    But then how does an object move from point A to the next point since current velocity isn't pointing towards the next point but instead is tangent to a circle ?
     
  5. Sep 14, 2005 #4

    Doc Al

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    The velocity tells the speed and direction that the object has at a particular instant. But the velocity is changing. Circular motion involves an acceleration towards the center: The object is constantly being pulled toward the center of the circle, its direction constantly changing so that it remains tangent to the circle.

    If, for some reason, the accelerating force is removed, then the object will keep moving in the direction it was going (tangent to the circle at that point) at the instant the force was removed.
     
  6. Sep 15, 2005 #5
    But why is velocity vector each moment tangent to the circle ? Where's the proof of that ?

    and also,doesn't the resulting velocity depend on all forces acting upon object ? And since one of the forces is also centripetal force then resulting velocity vector shouldn't be tangent to circle since at that very moment there is also centripetal force acting up on the object ? Gosh , am I confused
     
    Last edited: Sep 15, 2005
  7. Sep 15, 2005 #6

    Doc Al

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    You can prove it for yourself. Draw a circle. Mark two points very close to each other, representing two positions of the object. The line between those points represents the displacement from one moment to the next. To find the velocity at a point, take the limit as the two positions approach each other. In that limit, the velocity vector is tangent to the circle. (This may help: http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l1a.html; or this: http://www.staff.amu.edu.pl/~romangoc/M2-2-uniform-circular-motion.html)

    The motion definitely is a product of the forces acting on the object. If there were no centripetal force, the object would continue moving in a straight line. (This may help: http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l1c.html)
     
  8. Sep 15, 2005 #7

    HallsofIvy

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    The "uniform circular motion" only holds when centripetal force is the only force acting on the object. The reason the circular motion is "uniform" (constant speed) is precisely because the velocity is tangent to the circle. The tangent is perpendicular to the radius which is the line of force.
    Any component of force in the same direction as velocity would change the speed. A component of force perpendicular to the velocity only changes the direction. In uniform circular motion the force is along a radius, the velocity is perpendicular to that radius (tangent to the circle) so only the direction of the velocity changes.
     
  9. Sep 15, 2005 #8
    Well this is confusing . I thought in order for an object to move or at least start moving in certain direction ,or in a case of circle having velocity tangent to a circle , some force has to applied in that direction . But you are saying the only force is only along radius ?!


    What do you mean by "take the limit" ?


    I'm truly sorry for taking you the extra time
     
  10. Sep 15, 2005 #9

    Doc Al

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    Just a nitpick: If the motion is circular the velocity will be tangent to the circle, even if the speed varies.

    As you said, uniform circular motion implies that the net force is completely centripetal (no tangential component).
     
  11. Sep 15, 2005 #10

    Doc Al

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    A (net) force is not needed to maintain straightline motion! That's Newton's 1st law.

    Forces are needed to change motion. To change the speed or the direction of motion requires a force. For uniform circular motion, the force is centripetal; that force is always sideways to the velocity: it changes the direction of motion but not the speed.
     
  12. Sep 15, 2005 #11
    So how does an object gain velocity in the first place , if only force is centripetal which only changes direction ?
     
  13. Sep 15, 2005 #12

    Doc Al

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    If the object starts from rest another force (noncentripetal) is required to get it moving! But once it's moving, a centripetal force will keep it turning in a circle.

    You can think of the instantaneous velocity as the limit of the average velocity. No matter what the trajectory of a particle, its instantaneous velocity is always tangential to its path. (This discussion may help: http://www.ux1.eiu.edu/~cfadd/1150/03Vct2D/disp.html)
     
  14. Sep 15, 2005 #13
    Unfortunatelly I'm not yet familiar with limits
    Does this mean that in order to understand why velocity is tangent to the circle you have to know about limits ?

    In any case,thank you very much for your help and time
     
  15. Sep 17, 2005 #14
    I don't want to beat a dead horse but something's been bugging me about this and here it is

    When you throw an object in straight line the gravity is also perpendicular to horizontal component of velocity and yet vertical ( gravity ) component of velocityit changes the magnitude of velocity . Why is centripetal force different ?
     
  16. Sep 17, 2005 #15
    how do you calculate velocity?? You have to consider both X and Y components. When thrown in a straight line, the object's horizontal velocity doesnt change. However, since gravity is pulling it down, the VERTICAL velocity component will change.

    Centripetal force is a force that points to the center of the circle of motion. IT ONLY changes the direction of the particle in motion arond the circle. This is only valid is the force is a constant, mind you. If you apply a constant force on something in a straight line without any friction on the surface you will contnually speed it up. If the force you applied is also involved in changing the direction (i.e. imparting acceleration to both x and y components) the velocity will not necessarily change, as is the case for centripetal force.
     
  17. Sep 17, 2005 #16
    And that is the confusing part . Why is centripetal force only changing the direction but unlike gravity force doesn't add its own velocity component ?
     
  18. Sep 17, 2005 #17

    Doc Al

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    Because centripetal force is always sideways to the direction of motion.

    If you could arrange for the gravitational force to be sideways to the motion, that too would only change the direction of motion and not the speed. Hint: Think of the moon orbiting the earth.
     
  19. Sep 18, 2005 #18
    God , you're gonna think of me as even more of mentally challenged then before

    So you are saying that since centripetal force only pulls on object for such a brief period of time , that it only has time to change velocity's direction and then it already its changes position and the story again repeats itself ?

    But , when you think about it , gravity force should also then change velocity vector's position at that first moment it starts pulling on object's velocity position , and then changing it even further by adding y component to velocity vector
     
  20. Sep 18, 2005 #19

    Doc Al

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    Better to think of the direction of the centripetal force as constantly changing to match the changing direction of the object. If you twirl a ball on a string, as the ball moves around the circle the string automatically follows, always staying perpendicular to the ball's velocity.

    Which is exactly what it does, in ordinary circumstances, like when you toss a ball in the air. If you toss a ball horizontally, the first instant the force is perpendicular to the velocity, so its direction changes. But then it's no longer moving horizontally any more, so gravity is no longer perpendicular to the motion: the ball starts speeding up as it falls. (Gravity keeps pulling straight down.) If the ball were moving fast enough (very fast), so fast that the earth curved away at the same rate as the ball fell, then the earth's pull would remain perpendicular: the ball would circle the earth, in orbit, exactly as the moon circles the earth. (Or course, due to air resistance--and mountains--throwing a ball that fast is not practical!)
     
  21. Sep 18, 2005 #20
    But when you see drawings ( on internet or in books ) of forces pulling on objects tossed horizontally , it is portrayed as if the horizontal velocity vector never changes direction , meaning is always horizontal , and only net force keeps changing . Yet you are saying that at that first moment velocity vector changes direction .

    So if you toss a ball with 16 km per hour horizontally , then at that first moment when gravity starts pulling on ball and changes only velocity's direction ( and doesn't yet change its magnitude ), then velocity vector is still 16 km per hour but is pointing somewhere else ?
    Then what is the magnitude of a horizontal component at that instant ?

    uh , I'm sorry to keep pulling you back into this discussion . I will do my best to not bother you anymore
     
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