Centripetal Vs. Centrifugal
Iconoclast
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To: Dave Jackson
Even if Leonardo had a 1000 HP engine driving his screw it most likely would not work as designed. The Archimedes water lift operated on the same principle when he invented it and it is still in use under various forms today to raise water from one low point to a higher point or, to provide liquid under pressure from one point to another. The reasons it works are two fold. One the operating fluid is denser and the other reason is that there is a close tolerance duct around the screw. If Leonardo had the 1000 HP engine and he had a duct around the screw it might have worked. Today, it's called a gas turbine.
Sikorsky used this principle to deliver oil to the outer bearing of the CH-37 tail rotor gear box and the Apache electronics air conditioning system also uses Archimedes screws in the compressor.
Even if Leonardo had a 1000 HP engine driving his screw it most likely would not work as designed. The Archimedes water lift operated on the same principle when he invented it and it is still in use under various forms today to raise water from one low point to a higher point or, to provide liquid under pressure from one point to another. The reasons it works are two fold. One the operating fluid is denser and the other reason is that there is a close tolerance duct around the screw. If Leonardo had the 1000 HP engine and he had a duct around the screw it might have worked. Today, it's called a gas turbine.
Sikorsky used this principle to deliver oil to the outer bearing of the CH-37 tail rotor gear box and the Apache electronics air conditioning system also uses Archimedes screws in the compressor.
Iconoclast
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To: Dave Jackson
Regarding Newton’s law that deals with action and reaction there is a lot of action but due to the lack of a ducting and adequate power to spin the screw there is minimal reaction. The law applies but the design was lacking. Helicopters don’t require a duct because of the amount of air that they can displace resulting in aerodynamic lift or, if you subscribe to the application of that same Newton’s law the reaction of the blade impacting the air results in a vertical component referred to as lift. Also for maximum effect with a duct the screw should be reversed so the pointy end is down thus allowing the air to be compressed but then again that is a gas turbine engine as I previously indicated or possibly an Atlas Copco axial compressor..
Regarding Newton’s law that deals with action and reaction there is a lot of action but due to the lack of a ducting and adequate power to spin the screw there is minimal reaction. The law applies but the design was lacking. Helicopters don’t require a duct because of the amount of air that they can displace resulting in aerodynamic lift or, if you subscribe to the application of that same Newton’s law the reaction of the blade impacting the air results in a vertical component referred to as lift. Also for maximum effect with a duct the screw should be reversed so the pointy end is down thus allowing the air to be compressed but then again that is a gas turbine engine as I previously indicated or possibly an Atlas Copco axial compressor..
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dave
of couse the screw would work. it works in water(propeller) and a helicopter blade is basicaly a screw. aeroplane blades are often called screws.
helmet
i understand how you understand the consept of newtons law. i dont obviosly dont and also wont set my self to beleive in one mans rules. but it is inconclusive to me to say somthing stationairy is in equelibrium and something spinning is not.
eg. the tractor spining around the stump could be said to be in equelibrium if it doesnt move the stump. centrefugal=centripital(vorticy's law of phisics)
of couse the screw would work. it works in water(propeller) and a helicopter blade is basicaly a screw. aeroplane blades are often called screws.
helmet
i understand how you understand the consept of newtons law. i dont obviosly dont and also wont set my self to beleive in one mans rules. but it is inconclusive to me to say somthing stationairy is in equelibrium and something spinning is not.
eg. the tractor spining around the stump could be said to be in equelibrium if it doesnt move the stump. centrefugal=centripital(vorticy's law of phisics)
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Leonardo's screw lacks antitorque. As the non-screwing part starts counter rotating, sufficient power won't be applied to the screw. The machine would then fall to the ground, the non-rotating part would stop it's counter rotation, and the machine could leap into the air again.
Screws work in other areas but only when there is something to counter the rotation.
___________________
Vorticey, much of what is being discussed depends on specific definitions. For this discussion, equilibrium means that all forces balance, or the net force is zero. To move the tractor in a circle there must be a net force to the center of the circle. Therefore it is not in equilibrium.
___________________
Dave, pick a reference point as one of the planets. That planet requires no centripetal acceleration in that reference frame.
That's the point of a lot of this. How you pick your reference frame depends on what physics you can observe, and how they work. However, picking a reference frame does not change where effort was or was not expended. This is why real and apparent forces must be defined.
[ 22 December 2001: Message edited by: heedm ]</p>
Screws work in other areas but only when there is something to counter the rotation.
___________________
Vorticey, much of what is being discussed depends on specific definitions. For this discussion, equilibrium means that all forces balance, or the net force is zero. To move the tractor in a circle there must be a net force to the center of the circle. Therefore it is not in equilibrium.
___________________
Dave, pick a reference point as one of the planets. That planet requires no centripetal acceleration in that reference frame.
That's the point of a lot of this. How you pick your reference frame depends on what physics you can observe, and how they work. However, picking a reference frame does not change where effort was or was not expended. This is why real and apparent forces must be defined.
[ 22 December 2001: Message edited by: heedm ]</p>
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Lu, vorticey & heedm
Oops! Sorry, the Leonard comment did not come across as desired.
Lu had questioned the need to use higher levels of science. By way of a questioning example, I was trying to show that Newton's laws do not make Leonardo wrong. Newton allows for a deeper understanding of rotorcraft, but Leonardo's explanation is absolutely correct, from a very simplistic perspective.
In fact, Leonardo's description of operation is too advanced for someone who has no conceptualization of the screw and thread. <img src="eek.gif" border="0">
_______________
heedm
>" Dave, pick a reference point as one of the planets. That planet requires no centripetal acceleration in that reference frame."<
Fair enough. Your point is accepted. However, don't you think that this frame of reference may be too restrictive? Shouldn't Newton's third law be included? This conjures up the concept of opposing centripetal forces. This should also facilitate the understanding of rotor induced vibrations.
[ 22 December 2001: Message edited by: Dave Jackson]
Edited again to try and give a more intelligent response.
[ 22 December 2001: Message edited by: Dave Jackson ]</p>
Oops! Sorry, the Leonard comment did not come across as desired.
Lu had questioned the need to use higher levels of science. By way of a questioning example, I was trying to show that Newton's laws do not make Leonardo wrong. Newton allows for a deeper understanding of rotorcraft, but Leonardo's explanation is absolutely correct, from a very simplistic perspective.
In fact, Leonardo's description of operation is too advanced for someone who has no conceptualization of the screw and thread. <img src="eek.gif" border="0">
_______________
heedm
>" Dave, pick a reference point as one of the planets. That planet requires no centripetal acceleration in that reference frame."<
Fair enough. Your point is accepted. However, don't you think that this frame of reference may be too restrictive? Shouldn't Newton's third law be included? This conjures up the concept of opposing centripetal forces. This should also facilitate the understanding of rotor induced vibrations.
[ 22 December 2001: Message edited by: Dave Jackson]
Edited again to try and give a more intelligent response.
[ 22 December 2001: Message edited by: Dave Jackson ]</p>
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To all, sorry I haven't had time to respond before now.
I've done a little reading and have to admit there's some confusion about centripetal vs centrifugal forces, even among those who claim to know. Whether the "centrifugal" force is actually a force or not, seems to be more of a philosophical point rather than a scientifically observational or mathematical one. However I'm convinced that a purely centripetal force in NOT an acceleration force (though some claim it to be), as it does NOT alter the momentum of a rotating object, but only changes its direction. To blend these forces is a mistake.
From all of the posted comments, it seems that there are 2 basic questions that need to be addressed, namely that acceleration and centripetal forces are separate forces, and that velocity (or speed) is relative.
First the relative nature of speed, and for this I’ll go back to the van and roller-skate example. Let’s suppose that the van accelerates to 15mph (relative to the fixed spot over the road that you first occupied) before the back doors meet up with you. Suppose the latch on the back doors is fairly weak, and when the doors contact you, you are accelerated to only 5mph (relative to the road surface) before the doors open and you fall out landing on your feet. At the moment you exit, the van is traveling 15mph relative to the road surface, 10 mph relative to you, and you are traveling 5mph relative to the road surface. All are familiar with the idea that IAS, true airspeed, and true ground speed are speeds relative to an airframe and different external reference points.
Momentum is a product of mass and velocity (M = m * v), where M = momentum, m = mass, and v = velocity (or speed). Just as speed is relative to other objects, momentum is relative to other objects. Momentum changes when speed changes, which happens when acceleration forces are applied.
The centripetal force is a product of the mass and velocity squared over the radius, expressed as F = m * v2 (v squared) / R, where F = centripetal force, m = mass, v = velocity, and R = radius. The velocity here is relative to the center of rotation. Centrifugal force (and I’m convinced it’s a real force) opposes the centripetal force with the same (though opposite) magnitude.
Normal momentum is linear, but with a rotating object it’s angular. Newton’s first law states that once an object is in motion, it will remain in motion unless an external force is applied to it. Since speed and momentum are relative to other objects, for an object’s momentum to change relative to another object, its speed must change relative to that object (assuming we are not changing masses). For a rotating object, speed must change relative to the center of rotation.
For the next part of this discussion we need a pair of examples. For the first example, we’ll use a 5lb steel ball attached to a rope that can be swung around be an electric motor. The second example is not perfect, but should help to make my point that the centripetal force is NOT normally an acceleration force (exceptions like gravity will be covered). At this point we also have to make distinctions between centripetal forces that are exerted mechanically (like our first example) and those that are not, such as gravity and the electrical force of orbiting electrons in atoms. So the following example will work for mechanical means of exerting centripetal force, and will also work for gravity (with a strict limitation to purely circular orbits).
In the second example suppose you have a board that’s a 2x4 about 8 feet high, with one end embedded in concrete in the ground, and the other end sticking straight up. Let’s assume the wood is of high quality with the following properties: no matter how much the 2x4 is bent it will not break, it’s perfectly resilient so it won’t bend or crack and springs back straight, and it’s quite stiff. In this example we’ll use a rope attached to the top of the 2x4 to bend it.
Now lets start the motor and get the ball rotating at 120 rpm. Remember the formula for the centripetal force is F = m * v2 (v squared) / R, and momentum is M = mv. At 120 rpm we know the mass is 5lbs, and if we knew the length of the rope (to the center of the ball) we would know the radius, thus we could calculate the velocity from the radius and the rpm. We could then derive the centripetal force being exerted by the rope on the steel ball. This would also be the value of the centrifugal force being exerted by the steel ball on the rope. I think you can see that the centrifugal force is real as the rope is being pulled on both ends, or else the ball and rope would not be in the air spinning around.
The momentum (now angular momentum) of the steel ball is its mass times its velocity. According to Newton’s first law, all objects in motion want to travel in a straight line until acted on by an external force and this property is established by its momentum. The stiffness of the 2x4 represents the momentum of an object (the steel ball) and its tendency to want to travel in a straight line. Pulling on the rope to bend the 2x4 is equivalent to pulling the motion of an object into an arc around a center, which represents the centripetal force. Notice the 2x4 exerts no force at all on the rope, unless the rope is used to bend the 2x4, then the stiffness of the 2x4 starts exerting a force opposite the pull of the rope. This is how the centrifugal force works in that the force does not exist unless a centripetal force is being exerted.
Now lets change the rotation rate to 150rpm but reduce the length of the rope so that the steel ball continues to travel at the same velocity (relative to the center of rotation) in feet/sec or whatever our unit of measure is. By using the same velocity we maintain the same momentum (M = m * v) as in the 120rpm example. So now lets look at the formula for the centripetal force again, which is F = m * v2 (v squared) / R. Notice what has happened to the centripetal force. The numerator has not changed since mass and velocity have not changed but the radius is now smaller, so you can see that the centripetal force has increased.
Hmmm…the mass is still the same, the velocity is still the same, so therefore the momentum is still the same. Only the radius and rotation rate have changed. Why then has the centripetal force increased? This is due to the fact that the steel ball is now being pulled into a tighter arc, which is farther away from the straight line that it wants to travel in. This can be expressed in degrees per second change based on the steel ball traveling around the circumference of rotation. The 120rpm example will have fewer degrees per second change compared to the 150rpm example. This is equivalent to bending the 2x4 more by pulling harder on the rope, while the stiffness of the 2x4 exerts a harder counterforce to the bending. The only possible explanation for the increase in the centripetal force, is the increase in the centrifugal force, which in the 150rpm example, more strongly resists divergence from travel in a straight line.
Increasing the mass will also increase the centripetal force, but increasing the velocity produces a much stronger increase in the centripetal force, since it’s the only term in the formula being squared. Any increase in the velocity increases the degrees per second rate of change from straight-line travel (assuming the radius stays the same).
I’m going to skip the gravity example for now, as I’m tired. Also, there are no acceleration forces being used in these examples (once rpm was established), therefore the centripetal force CANNOT be an acceleration force, since there are no momentum changes in these examples. Acceleration changes momentum, the centripetal force causes divergence from straight-line motion.
I’ll stop here.
(edited for typos)
[ 23 December 2001: Message edited by: Flight Safety ]
[ 23 December 2001: Message edited by: Flight Safety ]</p>
I've done a little reading and have to admit there's some confusion about centripetal vs centrifugal forces, even among those who claim to know. Whether the "centrifugal" force is actually a force or not, seems to be more of a philosophical point rather than a scientifically observational or mathematical one. However I'm convinced that a purely centripetal force in NOT an acceleration force (though some claim it to be), as it does NOT alter the momentum of a rotating object, but only changes its direction. To blend these forces is a mistake.
From all of the posted comments, it seems that there are 2 basic questions that need to be addressed, namely that acceleration and centripetal forces are separate forces, and that velocity (or speed) is relative.
First the relative nature of speed, and for this I’ll go back to the van and roller-skate example. Let’s suppose that the van accelerates to 15mph (relative to the fixed spot over the road that you first occupied) before the back doors meet up with you. Suppose the latch on the back doors is fairly weak, and when the doors contact you, you are accelerated to only 5mph (relative to the road surface) before the doors open and you fall out landing on your feet. At the moment you exit, the van is traveling 15mph relative to the road surface, 10 mph relative to you, and you are traveling 5mph relative to the road surface. All are familiar with the idea that IAS, true airspeed, and true ground speed are speeds relative to an airframe and different external reference points.
Momentum is a product of mass and velocity (M = m * v), where M = momentum, m = mass, and v = velocity (or speed). Just as speed is relative to other objects, momentum is relative to other objects. Momentum changes when speed changes, which happens when acceleration forces are applied.
The centripetal force is a product of the mass and velocity squared over the radius, expressed as F = m * v2 (v squared) / R, where F = centripetal force, m = mass, v = velocity, and R = radius. The velocity here is relative to the center of rotation. Centrifugal force (and I’m convinced it’s a real force) opposes the centripetal force with the same (though opposite) magnitude.
Normal momentum is linear, but with a rotating object it’s angular. Newton’s first law states that once an object is in motion, it will remain in motion unless an external force is applied to it. Since speed and momentum are relative to other objects, for an object’s momentum to change relative to another object, its speed must change relative to that object (assuming we are not changing masses). For a rotating object, speed must change relative to the center of rotation.
For the next part of this discussion we need a pair of examples. For the first example, we’ll use a 5lb steel ball attached to a rope that can be swung around be an electric motor. The second example is not perfect, but should help to make my point that the centripetal force is NOT normally an acceleration force (exceptions like gravity will be covered). At this point we also have to make distinctions between centripetal forces that are exerted mechanically (like our first example) and those that are not, such as gravity and the electrical force of orbiting electrons in atoms. So the following example will work for mechanical means of exerting centripetal force, and will also work for gravity (with a strict limitation to purely circular orbits).
In the second example suppose you have a board that’s a 2x4 about 8 feet high, with one end embedded in concrete in the ground, and the other end sticking straight up. Let’s assume the wood is of high quality with the following properties: no matter how much the 2x4 is bent it will not break, it’s perfectly resilient so it won’t bend or crack and springs back straight, and it’s quite stiff. In this example we’ll use a rope attached to the top of the 2x4 to bend it.
Now lets start the motor and get the ball rotating at 120 rpm. Remember the formula for the centripetal force is F = m * v2 (v squared) / R, and momentum is M = mv. At 120 rpm we know the mass is 5lbs, and if we knew the length of the rope (to the center of the ball) we would know the radius, thus we could calculate the velocity from the radius and the rpm. We could then derive the centripetal force being exerted by the rope on the steel ball. This would also be the value of the centrifugal force being exerted by the steel ball on the rope. I think you can see that the centrifugal force is real as the rope is being pulled on both ends, or else the ball and rope would not be in the air spinning around.
The momentum (now angular momentum) of the steel ball is its mass times its velocity. According to Newton’s first law, all objects in motion want to travel in a straight line until acted on by an external force and this property is established by its momentum. The stiffness of the 2x4 represents the momentum of an object (the steel ball) and its tendency to want to travel in a straight line. Pulling on the rope to bend the 2x4 is equivalent to pulling the motion of an object into an arc around a center, which represents the centripetal force. Notice the 2x4 exerts no force at all on the rope, unless the rope is used to bend the 2x4, then the stiffness of the 2x4 starts exerting a force opposite the pull of the rope. This is how the centrifugal force works in that the force does not exist unless a centripetal force is being exerted.
Now lets change the rotation rate to 150rpm but reduce the length of the rope so that the steel ball continues to travel at the same velocity (relative to the center of rotation) in feet/sec or whatever our unit of measure is. By using the same velocity we maintain the same momentum (M = m * v) as in the 120rpm example. So now lets look at the formula for the centripetal force again, which is F = m * v2 (v squared) / R. Notice what has happened to the centripetal force. The numerator has not changed since mass and velocity have not changed but the radius is now smaller, so you can see that the centripetal force has increased.
Hmmm…the mass is still the same, the velocity is still the same, so therefore the momentum is still the same. Only the radius and rotation rate have changed. Why then has the centripetal force increased? This is due to the fact that the steel ball is now being pulled into a tighter arc, which is farther away from the straight line that it wants to travel in. This can be expressed in degrees per second change based on the steel ball traveling around the circumference of rotation. The 120rpm example will have fewer degrees per second change compared to the 150rpm example. This is equivalent to bending the 2x4 more by pulling harder on the rope, while the stiffness of the 2x4 exerts a harder counterforce to the bending. The only possible explanation for the increase in the centripetal force, is the increase in the centrifugal force, which in the 150rpm example, more strongly resists divergence from travel in a straight line.
Increasing the mass will also increase the centripetal force, but increasing the velocity produces a much stronger increase in the centripetal force, since it’s the only term in the formula being squared. Any increase in the velocity increases the degrees per second rate of change from straight-line travel (assuming the radius stays the same).
I’m going to skip the gravity example for now, as I’m tired. Also, there are no acceleration forces being used in these examples (once rpm was established), therefore the centripetal force CANNOT be an acceleration force, since there are no momentum changes in these examples. Acceleration changes momentum, the centripetal force causes divergence from straight-line motion.
I’ll stop here.
(edited for typos)
[ 23 December 2001: Message edited by: Flight Safety ]
[ 23 December 2001: Message edited by: Flight Safety ]</p>
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Flight Safety, you're wrong. Very wrong.
You call the ball's momentum angular momentum but you use a formula for linear momentum.
You claim the ball is not accelerating even though it's velocity is changing. The speed may be constant, but the velocity is a vector, it changes in direction. Any change in velocity is brought about by an acceleration.
"The stiffness of the 2x4 represents the momentum of an object...". Not even close.
"Hmmm…the mass is still the same, the velocity is still the same, so therefore the momentum is still the same." The velocity and linear momentum are constantly changing. They can't be the same. The angular velocity has changed. You haven't once calculated the angular momentum. What exactly are you saying here?
The stick bends because the ball wants to travel in a straight line, but is restricted by the length of the rope and the bend in the stick. When the rope is tight enough then the stick will bend and the rope will exert a force on the ball that is the required centripetal force to get the ball to travel in a circle. Look at that, everything explained without using the word centrifugal.
___________________
Everyone, don't get bent out of shape on this real and apparent terminology. A real force is created with effort. An apparent force is a by product of motion when you're in an accelerating or rotating reference frame.
[ 23 December 2001: Message edited by: heedm ]</p>
You call the ball's momentum angular momentum but you use a formula for linear momentum.
You claim the ball is not accelerating even though it's velocity is changing. The speed may be constant, but the velocity is a vector, it changes in direction. Any change in velocity is brought about by an acceleration.
"The stiffness of the 2x4 represents the momentum of an object...". Not even close.
"Hmmm…the mass is still the same, the velocity is still the same, so therefore the momentum is still the same." The velocity and linear momentum are constantly changing. They can't be the same. The angular velocity has changed. You haven't once calculated the angular momentum. What exactly are you saying here?
The stick bends because the ball wants to travel in a straight line, but is restricted by the length of the rope and the bend in the stick. When the rope is tight enough then the stick will bend and the rope will exert a force on the ball that is the required centripetal force to get the ball to travel in a circle. Look at that, everything explained without using the word centrifugal.
___________________
Everyone, don't get bent out of shape on this real and apparent terminology. A real force is created with effort. An apparent force is a by product of motion when you're in an accelerating or rotating reference frame.
[ 23 December 2001: Message edited by: heedm ]</p>
Iconoclast
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Regarding the above posts regarding the tractor / stump and the weight on the end of the rope there is a fatal flaw that can be corrected by further explanation.
Tractor / tree stump: If the tractor drives in a circle and is held in that path by a rope tied to the stump, then the tractor will travel in ever decreasing circles unless there is some provision to keep the tractor rotating in relation to the center of the stump. That provision being a shaft that either can rotate with the tractor or, a metal eye braided into the rope with the eye rotating about the shaft.
Weight at the end of a rope: This condition is similar to the above tractor example in that when the shaft starts to rotate the weight will be drawn to the shaft as the rope winds around the shaft. There is no means to transmit the movement of the shaft to the weight through the rope and keeping the rope taut. Once the rope is wound around the shaft there is no way to get the weight to move outward as to do so it would have to move faster than the shaft.
I realize there are explanations that can account for these anomalies but when you speak about anything using analogies then someone will find fault or possibly not understand when the only thing they know is that rotorblades are made to spin because they are attached to the rotorhead.
Tractor / tree stump: If the tractor drives in a circle and is held in that path by a rope tied to the stump, then the tractor will travel in ever decreasing circles unless there is some provision to keep the tractor rotating in relation to the center of the stump. That provision being a shaft that either can rotate with the tractor or, a metal eye braided into the rope with the eye rotating about the shaft.
Weight at the end of a rope: This condition is similar to the above tractor example in that when the shaft starts to rotate the weight will be drawn to the shaft as the rope winds around the shaft. There is no means to transmit the movement of the shaft to the weight through the rope and keeping the rope taut. Once the rope is wound around the shaft there is no way to get the weight to move outward as to do so it would have to move faster than the shaft.
I realize there are explanations that can account for these anomalies but when you speak about anything using analogies then someone will find fault or possibly not understand when the only thing they know is that rotorblades are made to spin because they are attached to the rotorhead.
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Rotorheads aren't the only ones struggling with 'centrifugal force'.
<a href="http://www-rocq.inria.fr/SB/Dialog/Centrifuge00.html" target="_blank">http://www-rocq.inria.fr/SB/Dialog/Centrifuge00.html</a>
<img src="smile.gif" border="0">
<a href="http://www-rocq.inria.fr/SB/Dialog/Centrifuge00.html" target="_blank">http://www-rocq.inria.fr/SB/Dialog/Centrifuge00.html</a>
<img src="smile.gif" border="0">
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heedm, wow...
1) If you're going to quote me, as least do it correctly...The stiffness of the 2x4 represents the momentum of an object (the steel ball) and its tendency to want to travel in a straight line.
2) I don't know how the steel ball got attached to the 2x4, as that was never in my examples. You blended the 2 examples somehow.
3) I could have included the formula for angular momentum (L = I * w) expressed in rads and kgs/m2 (m squared)/s, included the necessary values and then performed the calculations for comparison, but that seemed like unecessary complexity for the point being made.
4) I don't see why anyone would think that a basic mechanically exerted centripetal force could cause acceleration. Any force producing acceleration must also transfer energy. In the steel ball and electric motor example, the electric motor supplies the acceleration force to get the steel ball up to speed, after that however it only supplies the force necessary to overcome the friction and drag in the system. The example could have been a frictionless system so no motor would have been needed at all after the system was spun up to speed, but since frictionless systems don't really exist...
The rope is what supplies the centripetal force, not the electic motor. What energy is the rope using to hold the ball traveling in the arc? Please understand that accleration CAN be imparted through the rope to the steel ball to speed it up, but my example is a constant speed system (after spin up). However the spin up accelerating force would be a separate force from the purely centripetal force exerted by the rope.
Really, a purely centripetal force is more like a tension (or pressure) force rather than an acceleration force. If I lean against a wall, I'm exerting pressure (or tension) on the wall, but I'm not transferring any energy to it (unless the wall moves). Similarly, the "tension" in the centripetal/centrifugal system is the tendency of a body in motion to travel in a straight line.
Pulling a moving object into an arc is similar to pulling a rubber band, and to stretch the rubber band further, requires that more tension force be applied. In the same way, pulling a moving object into a tighter arc also requires more centripetal force (assuming momentum stays the same). If you let go of the rubber band it will return to its normal length. Let go of a moving object traveling in an arc, and it will return to traveling in a straight line without any change in its momentum.
This is why I believe that the centrifugal force is as real as the centripetal force. They are both "tension" forces, and neither is an acceleration force. The purpose of the 2x4 in the previous post was to illustrate the "tension" in the centripetal/centrifugal system.
(edited for additional clarity)
[ 24 December 2001: Message edited by: Flight Safety ]</p>
1) If you're going to quote me, as least do it correctly...The stiffness of the 2x4 represents the momentum of an object (the steel ball) and its tendency to want to travel in a straight line.
2) I don't know how the steel ball got attached to the 2x4, as that was never in my examples. You blended the 2 examples somehow.
3) I could have included the formula for angular momentum (L = I * w) expressed in rads and kgs/m2 (m squared)/s, included the necessary values and then performed the calculations for comparison, but that seemed like unecessary complexity for the point being made.
4) I don't see why anyone would think that a basic mechanically exerted centripetal force could cause acceleration. Any force producing acceleration must also transfer energy. In the steel ball and electric motor example, the electric motor supplies the acceleration force to get the steel ball up to speed, after that however it only supplies the force necessary to overcome the friction and drag in the system. The example could have been a frictionless system so no motor would have been needed at all after the system was spun up to speed, but since frictionless systems don't really exist...
The rope is what supplies the centripetal force, not the electic motor. What energy is the rope using to hold the ball traveling in the arc? Please understand that accleration CAN be imparted through the rope to the steel ball to speed it up, but my example is a constant speed system (after spin up). However the spin up accelerating force would be a separate force from the purely centripetal force exerted by the rope.
Really, a purely centripetal force is more like a tension (or pressure) force rather than an acceleration force. If I lean against a wall, I'm exerting pressure (or tension) on the wall, but I'm not transferring any energy to it (unless the wall moves). Similarly, the "tension" in the centripetal/centrifugal system is the tendency of a body in motion to travel in a straight line.
Pulling a moving object into an arc is similar to pulling a rubber band, and to stretch the rubber band further, requires that more tension force be applied. In the same way, pulling a moving object into a tighter arc also requires more centripetal force (assuming momentum stays the same). If you let go of the rubber band it will return to its normal length. Let go of a moving object traveling in an arc, and it will return to traveling in a straight line without any change in its momentum.
This is why I believe that the centrifugal force is as real as the centripetal force. They are both "tension" forces, and neither is an acceleration force. The purpose of the 2x4 in the previous post was to illustrate the "tension" in the centripetal/centrifugal system.
(edited for additional clarity)
[ 24 December 2001: Message edited by: Flight Safety ]</p>
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Flight Safety, I did get the two examples mixed up. I now see what you were comparing with the 2x4 analogy.
The steel ball travelling in a circle at a constant speed is continually accelerating. You must accept that to see why centrifugal forces are considered apparent forces.
Because the ball is accelerating, the net force on it must be non-zero, in fact it must be pointing towards the center of the circle with a magnitude of m v^2 / r (usual variable defs). That force is the required centripetal force. It is real. It is created mechanically through tensile forces in the string.
The stationary observer sees no effect of a force exerted on the ball oriented outwards. The only way that such a force can be observed is by putting yourself on the ball and ignoring the motion of the ball. In this case you feel a force that is magically pushing you away from the rope. In fact there is no force directed outwards at all, that is merely an explanation for what you observe in that rotating reference frame. It is not a force, it is just your body wanting to go in a straight line. When you counter that force by holding on to the ball, you are accelerating yourself towards the center of the circle.
___________________
When you lean on a wall, you do transmit energy to the wall. To make it simple, consider instead the ideal gas law, PV=nRT. Increase pressure and temperature (average kinetic energy) increases. The same is true with liquids and solids.
The steel ball travelling in a circle at a constant speed is continually accelerating. You must accept that to see why centrifugal forces are considered apparent forces.
Because the ball is accelerating, the net force on it must be non-zero, in fact it must be pointing towards the center of the circle with a magnitude of m v^2 / r (usual variable defs). That force is the required centripetal force. It is real. It is created mechanically through tensile forces in the string.
The stationary observer sees no effect of a force exerted on the ball oriented outwards. The only way that such a force can be observed is by putting yourself on the ball and ignoring the motion of the ball. In this case you feel a force that is magically pushing you away from the rope. In fact there is no force directed outwards at all, that is merely an explanation for what you observe in that rotating reference frame. It is not a force, it is just your body wanting to go in a straight line. When you counter that force by holding on to the ball, you are accelerating yourself towards the center of the circle.
___________________
When you lean on a wall, you do transmit energy to the wall. To make it simple, consider instead the ideal gas law, PV=nRT. Increase pressure and temperature (average kinetic energy) increases. The same is true with liquids and solids.
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heedm, I basically agree with your comments that "tension" forces produce "stored" kenetic energy. You mentioned heating and cooling gases, liquids, and solids as examples of storing (and releasing) this energy.
However there's also "stored" kenetic energy in mechanical processes that involve "tension" forces(you mentioned leaning against the wall), but this would include the rubber band, springs, bending the 2x4, lifting a hammer, and a host of other examples.
On the face of it, this also appears to be the case in the centripetal/centrifugal example. It "appears" as though pulling a moving object into an arc (against the tendency to travel in a straight line), "stores" the energy to return back to straight-line travel, once the centripetal force is released. Again, it seems to "appear" that way.
The fundamental difficulty that I have with "seeing" an object moving around in an arc as being under constant acceleration, in that there appears to be no energy being applied to the object in motion. Granted the "torque" force (rotational acceleration) speeds up or slows down a rotating system, but in a constant speed system, what energy in being transferred to the system to cause "continual acceleration" of the moving object around the arc? I just can't see the "acceleration" in this. How can there be "continual acceleration" of the object in motion without any momentum changes (assuming constant speed)?
(edited for typos)
[ 24 December 2001: Message edited by: Flight Safety ]</p>
However there's also "stored" kenetic energy in mechanical processes that involve "tension" forces(you mentioned leaning against the wall), but this would include the rubber band, springs, bending the 2x4, lifting a hammer, and a host of other examples.
On the face of it, this also appears to be the case in the centripetal/centrifugal example. It "appears" as though pulling a moving object into an arc (against the tendency to travel in a straight line), "stores" the energy to return back to straight-line travel, once the centripetal force is released. Again, it seems to "appear" that way.
The fundamental difficulty that I have with "seeing" an object moving around in an arc as being under constant acceleration, in that there appears to be no energy being applied to the object in motion. Granted the "torque" force (rotational acceleration) speeds up or slows down a rotating system, but in a constant speed system, what energy in being transferred to the system to cause "continual acceleration" of the moving object around the arc? I just can't see the "acceleration" in this. How can there be "continual acceleration" of the object in motion without any momentum changes (assuming constant speed)?
(edited for typos)
[ 24 December 2001: Message edited by: Flight Safety ]</p>
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Dave Jackson posted a listing of explanations of centripetal and centrifugal forces made by various Scientists and much of it was beyond my limited comprehension. However there was one among several that justified the consideration of centrifugal force as a necessary force to balance out the mathematical equation. One of the explanations is provided below. You might note that he references a free body diagram which was a part of the response from Sikorsky when I posed my question to them regarding the use of centrifugal force in calculating loads on the rotorhead (centripetal force). One detractor indicated that the use of a free body diagram was an incorrect form in which to calculate these forces.
“In mechanics, when all forces and moments acting on a body are shown (i.e. the "free body diagram"), it is customary to use "inertia forces" to ensure equilibrium. An inertia force is a force equal and opposite to the net acceleration multiplied by the mass of the body. That is, it is equal and opposite of the external force acting on the body. For an object to move on a curved path, an acceleration directed towards the center of rotation is necessary (otherwise the object will maintain a straight-line path). This acceleration is one of the "normal" components of acceleration (the other normal component is the "coriolis" acceleration). The "centrifugal force" is the inertia force corresponding to this normal component of acceleration. It may be an imaginary force, if you like, - but an absolutely necessary one if the equilibrium equations are to be valid”.
Necip Berme, Ph.D. Professor, Mechanical Engineering The Ohio State University 206 W 18th Avenue Columbus OH 43210 Phone: 614 292-0859 Fax: 614 430-5425 E-mail: [email protected]
I would suggest that you all read the various descriptions of the two forces and you will see that there is a great deal of disagreement in the scientific community. Once reading those descriptions it will be abundantly clear why members of this forum including myself cannot agree on the same subject.
“In mechanics, when all forces and moments acting on a body are shown (i.e. the "free body diagram"), it is customary to use "inertia forces" to ensure equilibrium. An inertia force is a force equal and opposite to the net acceleration multiplied by the mass of the body. That is, it is equal and opposite of the external force acting on the body. For an object to move on a curved path, an acceleration directed towards the center of rotation is necessary (otherwise the object will maintain a straight-line path). This acceleration is one of the "normal" components of acceleration (the other normal component is the "coriolis" acceleration). The "centrifugal force" is the inertia force corresponding to this normal component of acceleration. It may be an imaginary force, if you like, - but an absolutely necessary one if the equilibrium equations are to be valid”.
Necip Berme, Ph.D. Professor, Mechanical Engineering The Ohio State University 206 W 18th Avenue Columbus OH 43210 Phone: 614 292-0859 Fax: 614 430-5425 E-mail: [email protected]
I would suggest that you all read the various descriptions of the two forces and you will see that there is a great deal of disagreement in the scientific community. Once reading those descriptions it will be abundantly clear why members of this forum including myself cannot agree on the same subject.
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heedm
>"The steel ball travelling in a circle at a constant speed is continually accelerating."<
Won't continual acceleration require an infinite source of energy (even if it is between the atoms of the string)?
>"The steel ball travelling in a circle at a constant speed is continually accelerating."<
Won't continual acceleration require an infinite source of energy (even if it is between the atoms of the string)?
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Lu, "inertia force" is another way of referring to an "apparent force". You quoted Prof. Berme as saying that the "inertia" force is added to ensure equilibrium. If you consider an object moving in a circular path to be in equilibrium, then you are using a rotating reference frame. This is precisely the same as every argument I've given.
Physicists don't disagree on this. If physicists disagreed with biologists on the name of something smelly and slimy, would that mean that the biologists are wrong? NO. Trust those whose expertise is the field you're arguing.
____________________
Flight Safety there's no stored energy in the way which you are referring on an object moving in a circular path. You can apply an accelerating force to a moving object without changing the object's kinetic energy. Consider a hockey puck moving north. Apply a force of the appropriate magnitude to the southwest and you can get the puck moving west and the same speed. You can't disagree that smacking a puck with a hockey stick causes an 'accelerating' force. Oh, you live in Dallas. Oops.
You asked, "How can there be "continual acceleration" of the object in motion without any momentum changes (assuming constant speed)?"
There are momentum changes. Momentum is a vector. A change in the magnitude, the direction, or both is caused by an acceleration. In the case of uniform circular motion, the magnitude of momemtum doesn't change, but the direction does.
No Work is being done on the object because it's motion is perpindicular to the applied force.
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Dave, you're having too much fun with this one. <img src="smile.gif" border="0"> The string won't last forever so the experiment is finite. Besides, the net energy change is zero.
[ 24 December 2001: Message edited by: heedm ]</p>
Physicists don't disagree on this. If physicists disagreed with biologists on the name of something smelly and slimy, would that mean that the biologists are wrong? NO. Trust those whose expertise is the field you're arguing.
____________________
Flight Safety there's no stored energy in the way which you are referring on an object moving in a circular path. You can apply an accelerating force to a moving object without changing the object's kinetic energy. Consider a hockey puck moving north. Apply a force of the appropriate magnitude to the southwest and you can get the puck moving west and the same speed. You can't disagree that smacking a puck with a hockey stick causes an 'accelerating' force. Oh, you live in Dallas. Oops.
You asked, "How can there be "continual acceleration" of the object in motion without any momentum changes (assuming constant speed)?"
There are momentum changes. Momentum is a vector. A change in the magnitude, the direction, or both is caused by an acceleration. In the case of uniform circular motion, the magnitude of momemtum doesn't change, but the direction does.
No Work is being done on the object because it's motion is perpindicular to the applied force.
__________________
Dave, you're having too much fun with this one. <img src="smile.gif" border="0"> The string won't last forever so the experiment is finite. Besides, the net energy change is zero.
[ 24 December 2001: Message edited by: heedm ]</p>
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This just reminds why i HATE! it when I have to teach groundschool to a bunch of engineers. They never seem to be able to just say, "it works", and go fly the damm thing.
But it does pass the time (when one has it).
Merry X-Mas
But it does pass the time (when one has it).
Merry X-Mas
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heedm
You may not have seen Newton's 4th law.
It's the application of the variable-constant 'ff'. He applied it to his previous three laws, to tie-in a few lose ends, which he was unable to explain.
Oh! by the way ~ 'ff' stands for fudge factor.
just joking
You may not have seen Newton's 4th law.
It's the application of the variable-constant 'ff'. He applied it to his previous three laws, to tie-in a few lose ends, which he was unable to explain.
Oh! by the way ~ 'ff' stands for fudge factor.
just joking
Happy Christmas all!
I am convinced that we are trying to grapple with complex "end state" examples whilst we have not sorted the basics out. If we agree on the basic rules, then we can agree on explanations for the following examples that we have thus far discussed without solution:
1. David with his rock in a sling Vs Goliath.
2. A girl holding a chain on a merry go round.
3. A marble on a rotating disc.
4. An Alcohol pump.
5. Droop stops on a rotor disc.
6. A car going around a round about.
7. A steel ball on a chain.
8. A tractor on a chain around a stump.
9. Liquid dye on a rotating disc.
10. Sattelites and orbits.
Thats a lot considering we have not progressed at all.
Here is my suggestion:
A. we stop introducing yet another example, they are all the same (gravity excluded). Let us just use the last one: a steel ball on a chain.
B. We start with basics first.
I think there are some critical steps in the basics that, if we sort out, will lead us to explanations of the more complex issues. I am in agreement with heedm and FS that the first sticking point is acceleration. The first question is then:
1. Is velocity directional?
If so, then any change in direction is a change in velocity. And an acceleration IS a change in velocity. Thus a change in direction requires an acceleration.
Any disagreements with this so far?
<img src="smile.gif" border="0">
I am convinced that we are trying to grapple with complex "end state" examples whilst we have not sorted the basics out. If we agree on the basic rules, then we can agree on explanations for the following examples that we have thus far discussed without solution:
1. David with his rock in a sling Vs Goliath.
2. A girl holding a chain on a merry go round.
3. A marble on a rotating disc.
4. An Alcohol pump.
5. Droop stops on a rotor disc.
6. A car going around a round about.
7. A steel ball on a chain.
8. A tractor on a chain around a stump.
9. Liquid dye on a rotating disc.
10. Sattelites and orbits.
Thats a lot considering we have not progressed at all.
Here is my suggestion:
A. we stop introducing yet another example, they are all the same (gravity excluded). Let us just use the last one: a steel ball on a chain.
B. We start with basics first.
I think there are some critical steps in the basics that, if we sort out, will lead us to explanations of the more complex issues. I am in agreement with heedm and FS that the first sticking point is acceleration. The first question is then:
1. Is velocity directional?
If so, then any change in direction is a change in velocity. And an acceleration IS a change in velocity. Thus a change in direction requires an acceleration.
Any disagreements with this so far?
<img src="smile.gif" border="0">
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Let’s add a bit of realism to this thread where all answers are straight forward and do not depend on analogies to an unrelated matter that uses the same applied mathematical theory.
Question 1) On most dairy farms the farmer uses a “Centrifuge” to separate the milk from the cream. What principles are involved in this process?
Question 2) In many medical laboratories they use a “Centrifuge” to separate the various elements of fluids such as blood. What scientific principles are involved in the separation process?
Question 3) In several labs run by the USAF and NASA they use a “Centrifuge” to test pilots relative to their being able to resist G LOC. It can be easily demonstrated that centripetal forces are in play to keep the pilot from flying out of his seat if he is kept in a normal seated position with his butt towards the earth. On other “Centrifuges" the pilot is oriented with his body in a tilted position with one side down and his butt facing outward and his head towards the center of rotation. In either case, what forces are involved in causing the pilots blood to rush to his abdomen causing G LOC?
[ 28 December 2001: Message edited by: Lu Zuckerman ]
[ 28 December 2001: Message edited by: Lu Zuckerman ]</p>
Question 1) On most dairy farms the farmer uses a “Centrifuge” to separate the milk from the cream. What principles are involved in this process?
Question 2) In many medical laboratories they use a “Centrifuge” to separate the various elements of fluids such as blood. What scientific principles are involved in the separation process?
Question 3) In several labs run by the USAF and NASA they use a “Centrifuge” to test pilots relative to their being able to resist G LOC. It can be easily demonstrated that centripetal forces are in play to keep the pilot from flying out of his seat if he is kept in a normal seated position with his butt towards the earth. On other “Centrifuges" the pilot is oriented with his body in a tilted position with one side down and his butt facing outward and his head towards the center of rotation. In either case, what forces are involved in causing the pilots blood to rush to his abdomen causing G LOC?
[ 28 December 2001: Message edited by: Lu Zuckerman ]
[ 28 December 2001: Message edited by: Lu Zuckerman ]</p>