Robittybob1

Your diagrams don't show Earth and Moon orbit around the Sun and the E-M barycenter very accurately. The barycenter line would be the curve of the circle and Earth and Moon swapping sides across this line.

That is true but I was just making the point you can't say "the objects don't move". Even if they only move a little bit, they still move and if there wasn't enough friction between them and the table they would continue and fall onto the floor (Newton's First Law). I edited my previous post late (I forgot to press the "save Changes" button before I went out to do some chores) so I'll repeat it here: And as I asked before but this time I will say it differently too: "And do you accept that the rate of sliding increases as the object slides gaining energy from the friction acting on it in the tangential direction?" changes to: "And do you accept that the rate of sliding in the radial direction increases as the object slides gaining energy from the friction acting on it (positive work) in the tangential direction?"

I disagree with you when you say "neither the table or object moves only the cloth". The objects on the table cloth do move, you can see them moving, but the movement is not enough to make them fall off the table. As Swansont said "The surface does positive work tangentially because it's moving." So The surface (tablecloth) does positive work (on the plates etc) because its moving. And as I asked before but this time I will say it differently too: "And do you accept that the rate of sliding increases as the object slides gaining energy from the friction acting on it in the tangential direction?" changes to: "And do you accept that the rate of sliding in the radial direction increases as the object slides gaining energy from the friction acting on it (positive work) in the tangential direction?"

I can't see any way to take measurements of the situation, so could it be done just from logic? Like we say the object is always on the same surface with the same coefficient of friction and it also always at the same radius at the same time. The speeds are split into the tangential and radial direction and we can be sure the tangential speed never exceeds the tangential speed of the surface (one limit) and the radial speed starts from zero at the time the centripetal force required is exceeded. Then we'd say there is no more angular acceleration of the turntable once it begins to slip. The dynamic friction being less than the static friction allows the radial motion to continue but the centripetal force will always be in the radial direction no matter how much the object slips behind the starting radial line. Each increment in the radial direction puts the object onto a surface that is going proportionally faster tangentially. We could calculate what centripetal force it would take to hold it at any new position, 1. when it wasn't slipping and 2. at its new velocity gained from the work done on it by the turntable (OK I see that now, that is if the object wasn't on the turntable but being held by a string at that instant at that new velocity). The object on the surface gains angular momentum due to the tangential friction forces being applied to it. In that table the coefficient of friction of glass on teflon was 0.1 and the static and dynamical friction were the same values, so we could use a glass object on a smooth plastic surface with a coefficient of friction of 0.1. I could set up an Excel spreadsheet that gives me the values if I moved the object in 1 mm increments, that might give me an initial idea of the relationship between the two speeds. Does anyone know how do the problem with calculus?

What amazes me is that there seems to be two types of friction acting on the object at the same time. In the radial direction there is still some centripetal friction slowing it down (doing negative work) and the tangential friction which is speeding up the object (doing positive work on it) Does it slow down more than it speeds up? Or the other way, round does it speed up more than it slows down? How would we do the maths of that? I would say the coefficient of friction would be the same in either direction for a starter.

And do you accept that the rate of sliding increases as the object slides gaining energy from the friction acting on it in the tangential direction? It is tricky, for most would think friction slows things down but not if the surface it is on is moving faster than it is.

With a = 4 * Pi^2 * r / T^2 (a being the centripetal acceleration to keep the acceleration constant (for if it rises things like strings break objects overcome friction or even the rotating mass may even begin to disintegrate) we would have to vary r and T in such a way that the ratio of r/T^2 stayed constant, e.g. if the radius increases there has to be an inverse square drop in the period. The usual way of exceeding the friction or the tensile strength of the string is to increase the rotational speed or other words decrease the period. In the case of the ruptured string there will be no more forces and the object till leave at a tangent to the circle it last was travelling. Whereas with the sliding object there will still be frictional forces acting on it till it has reached the edge of what it was on. So here the friction is doing positive work on the object, and it will accelerate in its tangential speed (decrease the period) and make the tendency to slide even worse.

I'm just a bit amazed that radial acceleration equals velocity squared divided by the radius. Has that got a similar equation for linear motion? Same here has [latex]a_{centripetal} = \frac{v_{tang}^2}{r}[/latex] does this have a linear analog? Well we aren't going to get a radius in linear so my memory just goes blank on this question. Work calls so I can't check it out right now.

First Law: https://www.grc.nasa.gov/www/k-12/airplane/newton1g.html can we therefore make Force = ma = mv^2/r? if v = 2Pi*r/T (the circumference / period ma = mv^2/r divide both sides by m a = v^2/r a = (2*Pi*r/T)^2 / r a = 4 * Pi^2 * r^2 * T^-2 / r one r cancels out. a = 4 * Pi^2 * r * T^-2 a = 4 * Pi^2 * r / T^2 a = W^2 * r Omega (angular velocity) squared times radius. Is that correct? The centripetal acceleration is the angular velocity squared times radius.

OK but in one of our discussions there was a mass orbiting a central point, when the speed of rotation increases at some point the centripetal force will be exceeded (i.e the string breaks, or the object slips) was that because of the object's increased inertia or increased momentum (or impulse) or something else? When objects collide they have momentum, energy and there are forces and impulses. Am I right thinking it all comes down to forces (and mass) and everything results from them?

That was what I am trying to get my head around. A month ago I put a question into Google, something like "does inertia increase with velocity?" and there were answers at odds with each other. That is why I am tending to the view that since inertial mass and gravitational mass equals each other and since gravitational mass is not affected by non relativistic speeds, I'm tending to view inertia is more like mass that doesn't change. So those who say "moving object has more inertia than a stationary one" are wrong and are really talking about momentum. Do you say "a moving object has more inertia than a stationary one"?

Mass has inertia whether moving or not, so it seems more like mass than momentum. I don't know. I saw a demonstration of how to place a hammer head on a handle and one method was to use the inertia of the head. I suppose someone else would put it down to the kinetic energy or even the momentum the head had.

I am making some very unlikely conditions especial of having zero dynamic friction, yet sufficient friction to keep the mass rotating at 0.5 r with a velocity of 0.5 v (v being the linear velocity at the outer edge). Inertia will then keep the mass going in the direction and speed it was at the time the static friction was exceeded. If my line diagram is right it will hit the circumference at about (but less than) 60 degrees rather than the 45 degrees I estimated before. But this would be so unlikely as when I try and sense the difference between static and dynamic friction is not as great as that. I'll see if there are any records of these measurements on the net. If I get the smartphone and something up loaded I could draw the diagram and you could check to see if my reasoning is right. Static and Kinetic Coefficient of Friction Reference Table http://blog.mechguru.com/machine-design/typical-coefficient-of-friction-values-for-common-materials/

How do you relate inertia to this impulse? Are we really talking about change in momentum when we generally talk of inertia? Is there is a formula linking inertia to force or mass?

The equipment I used had a total radius of about 1 meter, so lets assume in one of my many runs I placed the object at 0.5 m to begin with. That being what I would call quite close to the center for it took quite a fast spin rate to get it sliding. From the maths while it is not sliding the linear speed of any part of the platform is proportional to its radius, so the speed of the surface when the object started to slip at the 0.5 m mark is half the speed at the outer edge. If the object was to leave at a true tangent by the time it got to the outer edge it would have had to double its linear speed. It must be achieving part of this requirement as if begins to slip backward a little, implying that there is a frictional force accelerating the object in the tangential direction WRT to any point the object is at on the platform. But any increase in linear speed only makes the rate of slipping increase. I found you could make it start off slowly if I gradually brought the rotational rate up. To stop a slow slip it might be possible to slow the turntable. That may have happened but it wasn't done deliberately. You can hear the jar sliding over the surface so that would be indicated by a sound followed by no sound. The sound is the same regardless of the direction of slip. (I just tested that rubbing my had in different directions across my computer table, but the frequency changes, so sound could be used to measure the speed of slipping. So if I do the video I'll see if we can record the sound as well. Now what I was getting to was that if it started slipping at 0.5 meter the maximum transverse component (assuming the acceleration from the dynamic friction to be zero) would it have a linear speed equal to 0.5 Vt (Vt being the tangential velocity of the outer rim at 1 meter? Somehow I have to account for the time it took to slip as well, That is where the video would assist for timing is rather awkward having to look after the object and spinning the turntable and then timing it as well. I'd need an able bodied assistant. It is really complicated to think of all the motions involved. PS: Thinking about it, this velocity vector would meet the outer circumference at 45 degrees, so would you accept that the object would appear to leave at a 45 degree angle to the tangent in this hypothetical situation? In the physical situation there will some dynamical friction so the velocity of the object will be increasing as it slides across the surface so the angle it leaves at will be less than 45 degrees to the tangent, but as it is slipping it will not be at the true tangent. Well that is the logic and now to see if I can record this on a smart phone.

I'll see if I can borrow a smart phone. As long as you don't ask me to film it from the rotating frame. In the weekend I hoped on the merry go round and got spun around. I hate that. Maybe I could mount the smart phone and film it in the rotating frame, for it all happens within a quadrant. Thanks for the correction, "the static friction is greater than the dynamic friction, so once it starts moving there is no easy way to stop it". That was what I had intended to say.

In the tablecloth the force on the objects is the frictional force between the table cloth and the objects on the table. Is this a case of unbalanced forces?

It was more or less what I predicted. It was a very low coefficient of friction. Whether this had a bearing on the result will need further investigation. It certainly made me think about how friction works and what happens if the surface providing the normal force is accelerated in an ever changing direction from underneath an object. http://www.scienceforums.net/topic/88420-centrifugal-forces-appear-to-act-opposite-to-gravity-how-is-this-possible/page-22#entry868431 I had the radial line on the platform as a reference. If it had moved away from the line in the same direction as the spin I would have said "forward". I haven't said anything about forces but it was evident as well that the jar didn't go off at a tangent to the perimeter but at an angle which was a combination of the rate it increased radius and the angular speed it had gained from being carried by the surface. I would have posted in the other thread but I was not able to post into it (some sort of permission restriction had been imposed, so I was left without an option but to start another discussing the results that I had observed). It has taught me plenty. As far as the reason the mass starts sliding in the first place, it is the very bit that is radial at the start of the motion that is in question. At all times the jar has inertia. Does inertia increase with velocity? There is some reason the frictional forces were not enough to hold it in circular motion. I am looking into how inertia works in conjunction with friction. I don't have sufficient knowledge to explain it yet. The static friction is less than dynamic friction, so once it starts moving there is no easy way to stop it. Can we say "inertia overcomes the frictional force"? Would that mean inertia increases as the rotational velocity rises? I'll have to find out if this is the case. Do you know how inertia works?

It was a matter of understanding what the symbols meant. Thanks.

When the surface an object is sitting on is accelerated from under it the object also slides and accelerates, so is inertia capable of contributing to a type of force, without an external force acting on the inertial mass? There is the classic pulling the tablecloth from under the place settings.

I placed glass jar on a playground merry go round which had a very shiny plastic surface. There was minimal friction. If it was placed near the edge it didn't take much angular speed to make it slide off and the initial sliding motion was radial but the further out it went the more it slid backwards to the direction of spin. If I started it off close in it needed a much higher angular velocity to get it started and the degree of swing to a transverse direction was much more accentuated. I understand this to be due to the very low friction meaning it was unable to accelerate to the linear velocity of the surface at the ever increasing radius. When it fell off it was always going slower than the tangential speed of the outer edge. The speed at which it approaches the outer edge increases as it slides. Once it starts sliding you don't need to increase the rotational velocity any further.

So when you push from two directions perpendicular to each other but only one force is great enough to overcome friction on its own (assuming the mass has equal friction in all directions), do those two forces combine vectorially based on the amount of the initial strength of two individual forces? So two forces acting at right angles add together to make a stronger force. Is that right?

They won't rotate (odd number of cogs). - so nil centripetal forces.

I realise I don't fully understand friction. All things regarding friction discussion welcome here please. Take a mass on a sloped table the friction holds it there. Apply a force from the side and increase the force till it moves. What direction will it move? Will it always move in the direction of the net force? Not just the direction of the force overcoming the friction. Are the forces of friction always present or do they build up to resist a push?

There will be plenty examples of centrifugal forces in that movie. Cheers. Minus 2 for a bit of humour I like the spirit around here! I was trying to understand this friction thing. Once friction is overcome what direction does something move?