Dynamics of a spiral movement

[irdeg]

Homework Statement

As you'll know, the driving force for a circular movement is a centripetal force. But wat is the dynamics for a spiral movement, i.e. an increasing circular movement? And how can I produce it, let's say for a little spherical object, in real life?

The Attempt at a Solution

I guess there will also be a force parallel to the velocity. I don't know how to create a force that is allways parallel to the velocity.​

 

[gneill]

Hi irdeg,

Welcome to Physics Forums!

Maybe try thinking about what would happen if the "centripetal" force happened to not actually point towards the center, but instead was directed at some constant angle to the radius vector.

 

[haruspex]

a spiral movement,

Which type of spiral? Geometric, arithmetic...?

 

[irdeg]

Hi irdeg,

Welcome to Physics Forums!

Maybe try thinking about what would happen if the "centripetal" force happened to not actually point towards the center, but instead was directed at some constant angle to the radius vector.

View attachment 232086

So, there will be a component parallel to the velocity and the radius of the circle would grow over time. How could I, practically create something like that?

 

[irdeg]

Which type of spiral? Geometric, arithmetic...?

I would prefer arithmetic.

 

[Orodruin]

Regardless of how an object is moving, its acceleration (and hence the force acting on it) will be perpendicular to the velocity unless the speed is increasing or decreasing. This follows directly from differentiating $v^2 = \vec v^2$ with respect to time.

Now, this means that in an accelerated circular motion (i.e., increasing speed) there is also a force component parallel to the velocity, but this is true regardless of the shape of the motion.

 

[gneill]

So, there will be a component parallel to the velocity and the radius of the circle would grow over time. How could I, practically create something like that?

That's a very vague question. What are the boundaries on your definition of "practical"?

 

[Charles Link]

A centripetal force that increases linearly with time will produce a spiral motion. See https://www.physicsforums.com/insights/frenet-equations-2-d-result-cornu-spiral/ $\\$ I read somewhere where they have used this principle in some carnival rides, where they used the spiral path to produce such a force. The speed doesn't change with such a spiral.

 

[gneill]

A centripetal force that increases linearly with time will produce a spiral motion. See https://www.physicsforums.com/insights/frenet-equations-2-d-result-cornu-spiral/

So a "practical" demonstration might be to have a charged particle moving perpendicularly to an increasing or decreasing magnetic field, hence continuously changing the centripetal force.

 

[haruspex]

So a "practical" demonstration might be to have a charged particle moving perpendicularly to an increasing or decreasing magnetic field, hence continuously changing the centripetal force.

Yes, and you would not need it to vary over time. It could be a field which is strongest at some central axis then falling off at greater radii. Depending on the injection parameters the particle could spiral in or out.

 

[Charles Link]

So a "practical" demonstration might be to have a charged particle moving perpendicularly to an increasing or decreasing magnetic field, hence continuously changing the centripetal force.

The one problem I see with that is the time varying magnetic field necessarily generates an EMF with a component parallel to the path so that the electron will necessarily speed up, and the simple result that follows from the equations that say the particle will have constant speed will not apply. In addition the particle radiates which will cause the particle to slow down. $\\$ Because the accelerating (because of the circular path) charged particle radiates, it is found charged particles in a uniform magnetic field do follow a spiral path. I believe I have seen cloud chamber experiments at Fermilab that showed this result.