Uniform circular motion and velocity vector

[beginner16]

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

 

[Doc Al]

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

This is correct.

 

[beginner16]

This is correct.

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 ?

 

[Doc Al]

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.

 

[beginner16]

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

 

[Doc Al]

But why is velocity vector each moment tangent to the circle ? Where's the proof of that ?

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)

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 ?

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 )

 

[HallsofIvy]

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 ?

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.

 

[beginner16]

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.

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 ?!

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.

What do you mean by "take the limit" ?


I'm truly sorry for taking you the extra time

 

[Doc Al]

The reason the circular motion is "uniform" (constant speed) is precisely because the velocity is tangent to the circle.

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).

 

[Doc Al]

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 ?!

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.

 

[beginner16]

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.

So how does an object gain velocity in the first place , if only force is centripetal which only changes direction ?

 

[Doc Al]

So how does an object gain velocity in the first place , if only force is centripetal which only changes direction ?

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.

What do you mean by "take the limit" ?

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)

 

[beginner16]

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

 

[beginner16]

I don't want to beat a dead horse but something's been bugging me about this and here it is

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.

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 ?

 

[stunner5000pt]

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 doesn't 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.

 

[beginner16]

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.

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 ?

 

[Doc Al]

Why is centripetal force only changing the direction but unlike gravity force doesn't add its own velocity component ?

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.

 

[beginner16]

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.

God , you're going to 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

 

[Doc Al]

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 ?

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.

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

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!)

 

[beginner16]

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 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

 

[HallsofIvy]

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 .

No, you don't see anything of the kind. It true that "horzontal velocity vector" never changes direction- because it is always horizontal! Do you mean something else? I'm interpreting "Horizontal velocity vector" as the horizontal component of velocity. It is also true, and more important, that the horizontal velocity vector never changes magnitude- precisely because the force (vertical) perpendicular to the horzontal velocity. Net force does not change- it remains exactly the same. The vertical component of velocity does change, which is why the object does not just move horizontally but moves downward in a parabola.

Yet you are saying that at that first moment velocity vector changes direction .

Yes, the velocity vector is constantly changing- the horizontal component does not change but the vertical component does and the velocity vector is the sum of those.

 

[beginner16]

you are taking things out of context hallsofivy . I asked this because Doc Al said in his last post that in first instant gravity force changes direction of objects velocity ( that is prior to changing magnitude of velocity )

 

[Dorothy Weglend]

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 ?

It isn't different, this is exactly what everyone here has been telling you. Gravity is the centripetal force which pulls the ball towards the center of the earth. With normal throwing speed, it will curve toward the Earth in a parablolic path. With just the right speed (which is very large), the horizontal velocity of the ball will exactly balance the curvature of the earth, and it will orbit the earth. With more velocity, it will escape the centripetal attraction of gravity, and fly in a straight line out into space.

This was one of Newton's great discoveries, and there is a nice picture of this from one of his books on this webpage:

http://galileoandeinstein.physics.virginia.edu/lectures/Newton.html

Dot

 

[Doc Al]

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 .

I think I may have added to your confusion without meaning to. The horizontal component of the velocity doesn't change, since the only force acting on the object acts vertically. What I should have said is that only for an instant does the velocity remain horizontal. As the gravitational force adds vertical speed, the direction of motion changes. (My point was that only in cases where the direction of the force remains perpendicular to the motion will the direction change without the speed changing. That is not the case here.)

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 ?

The horizontal component of the velocity remains constant. The vertical component component is given by $g t$ and is downward.

 

[Doc Al]

you are taking things out of context hallsofivy . I asked this because Doc Al said in his last post that in first instant gravity force changes direction of objects velocity ( that is prior to changing magnitude of velocity )

I tried to state things more carefully in my last post; please read it.

It's true that at the initial instant, the acceleration is perpendicular to the velocity. But we are interested in what happens after this "instant".

 

[beginner16]

only for an instant does the velocity remain horizontal.

I know

As the gravitational force adds vertical speed, the direction of motion changes.

I know

(My point was that only in cases where the direction of the force remains perpendicular to the motion will the direction change without the speed changing. That is not the case here.)

I know it does but still don't understand why

The horizontal component of the velocity remains constant. The vertical component component is given by $g t$ and is downward.

I know


I guess I'm too dumb to find an answer among all the posts you've taken the time to write

thank you for having the patience

PS-arguments about object orbiting around a planet are too advanced for me since that topic is still 15 more pages into the book