Loop Dynamics

[VGB]

AM itself is not a force but it is the product centripetal and tangential forces. If the forces are not constant but the mass is evenly distributed, then I think the semicircular loop shape is not going to remain stable. I don't have any model to support this, and I don't know how it will change in response to those unbalanced forces that are calculated is something that could be explored as part of this topic.

Hi Walter

Unfortunately, video wasn’t available when I was at school. While I was still allowed to go to art classes, they tried to get me to make clay pots. It was remarkably easy to cover half the classroom in clay, even if I was 6 feet away from the spinning wheel when the pot started to wobble and come apart.

Regards

Vince

[gordonjudd]

AM itself is not a force but it is the product centripetal and tangential forces.

Walter,
And I thought it was equal to the cross product of a r vector and a linear momentum vector. Not a force in sight in that L=rxp calculation. Live and learn.
Gordy

[Walter]

Gordy,

You have a mathematical representation but what does that actually represent in nature? If you are thinking the word product is limited to the mathematical definition of product as multiplication then I am sorry for any confusion because I was thinking along the lines of “is produced by”. I thought that was obvious but apparently not.

The component of any net force that causes circular motion is called a centripetal force. When the net force is equal to the centripetal force, and its magnitude is constant, uniform circular motion results.

I haven’t calculated the magnitude of the centripetal force around the loop specifically but for a mass M with tangential speed v at radius R, the centripetal force is Fc = Mv2/R. (Mass and tangential speed should sound familiar from the L=rxp formula).

In this case we have a constant linear mass density around the loop and R is constant but tangential speed is constantly varying. The centripetal force is constantly changing as we go around the loop. As I said previously I haven’t done a model but I expect the structure of the semicircular loop is not stable because of the non constant forces.

[VGB]

Why would the distribution of AM around the loop cause it to morph? Momentum is not a force so I don't see how it could produce a change in the shape of the loop.

Apologies Gordy I missed your question, we had a 141 year old rugby derby going on, so it’s been a bit lively here. As I mentioned on the COAM thread, I see momentum change in Dr Perkins loop formulation but not in your model

IMG_2051.jpeg (50.63 KiB) Viewed 284 times

Vince

[gordonjudd]

for a mass M with tangential speed v at radius R, the centripetal force is Fc = M\(v^{2}\)/R.

Walter,
That formula would apply to finding the expected string tension for a point mass traveling in a circular path with a radius R and tangential velocity v.

For a distributed mass with some linear mass density \(\rho_{l}\) and a tangential velocity v traveling in a circular path the expected tension is equal to \(\rho_{l}v^{2}\) independent of the radius.

There are any number of sites that show how that tension is calculated.

However, that tension is an internal (double ended) force so I don't see how it could cause a change in the shape of the loop.
Gordy

[Walter]

Gordy,

A centripetal force is a force that makes a body follow a curved path. The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.

Tension is the force in a string. It is described as the pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements.

If you hold up a weight by a piece of string the tension of the string will keep it in place but the weight is not moving in a circular orbit so this is not called the centripetal force.

While the magnitude of the two may be the same centripetal force is a net force whereas tension is an action/reaction force.

I’m not sure where you are going with this particular line of discussion. If you like I can probably generate the magnitude of the centripetal force around the loop but I think it will be directly proportional to the am at any point on the loop.

[VGB]

It seems that Walter is correct:

https://www.khanacademy.org/science/phy ... 2%80%8D%20.

A centripetal force is a net force that acts on an object to keep it moving along a circular path.……..

However, we should discuss how the object came to be moving along the circular path in the first place. Newton’s 1ˢᵗ law tells us that an object will continue moving along a straight path unless acted on by an external force. The external force here is the centripetal force.

It is important to understand that the centripetal force is not a fundamental force, but just a label given to the net force which causes an object to move in a circular path. The tension force in the string of a swinging tethered ball and the gravitational force keeping a satellite in orbit are both examples of centripetal forces. Multiple individual forces can even be involved as long as they add up (by vector addition) to give a net force towards the center of the circular path.

[Merlin]

In the meantime I've been working on comparing the angular momentum when shooting line in the fixed and loop centric frames.

Hi Walter

I understand this is an academic exercise since you do not seem to have a casting model dealing with shooting. If you shoot some line then the fly leg speed decreases (you take energy out of it to pull on the rod leg). The rod leg speed increases progressively so the time for which you have 5 m/s is unknown just as the fly leg speed at that time is. The dynamics of the loop is not straightforward and I am not convinced that one can forecast some morphing from the calculation of AM at a fixed point in time.

In the previous exercise without shooting, you calculate the AM at start, not its evolution as a function of time. Curiously I do not find the same amount of AM (around 0.0082 for you), I have something just below that level (0.00785). The calculation is: loop mass * squared loop diameter * rotation speed: 0.0157 * 0.5 ^2 * 10 / 0.5 = 0.0157*0.5 = 0.00785. Is it a question of rounded numbers?

Frankly speaking, I still do not see the benefit in understanding of using two frames for comparison of AM values.

Merlin

[Graeme H]

If you shoot some line then the fly leg speed decreases (you take energy out of it to pull on the rod leg).

Is this a measured observation or a forecast from your model?

Cheers,
Graeme

[VGB]

Good to see you back up Daniel

The dynamics of the loop is not straightforward and I am not convinced that one can forecast some morphing from the calculation of AM at a fixed point in time.

Going back to one of your earlier posts, the intent is to identify the mechanisms not produce a simulation. If you treat the graph as the progression of piece of mass moving around the loop, it takes a finite time to go from 0 to 180 degrees.

Frankly speaking, I still do not see the benefit in understanding of using two frames for comparison of AM values.

In the absence of measured data, I would suggest that it is a valid validation method for the models. The reference frame selected by Dr Perkins seems to produce a different outcome to the moving frame and I think that is worth investigating. I asked Gordy previously where he was taking his reference from and didn’t get an answer, perhaps you could explain it?

Vince