Gravity is the reason a mass is moving under these conditions.
1. Gravity pulls all objects no matter how much they weigh at the same rate of acceleration. Gravity is the fulcrum that all these observations are made under.
2. Since all objects travel at the same rate of acceleration, a mass that reaches it's bottom first has a greater frequency, not a greater speed, provided both masses are dropped at the same time and at the same angle.
3. Since gravity pulls objects at the same rate of acceleration, the only reason one object would have a greater frequency than another is because it has less distance to travel, which means it's mass has traveled less.
A perfect sphere's mass is measured from it's exact center. Has there been a test done to show that two fixes spheres with the same distances from their centers to the pivot point having different frequencies?
Center of Gyration
Moderator: scott
re: Center of Gyration
Feltcher, Jim and Michael.
Doing my best to stay on track here but I need some help.
Inertia is what wants to keep a stopped mass stopped.
Inertia is what wants to keep a mass in motion in motion.
So when Fletcher writes:
Ralph
Doing my best to stay on track here but I need some help.
Inertia is what wants to keep a stopped mass stopped.
Inertia is what wants to keep a mass in motion in motion.
So when Fletcher writes:
Is the inertial resistance mentioned that of a moving body or a stopped body, or can it be both?If dropped from the same height they both show different inertia & acceleration characteristics. The freely pivoted bob gives least inertial resistance IIRC.
Ralph
re: Center of Gyration
Hi Ralph,
Inertia is inertia. It's what pushes back when an object has been made to have a change in velocity. Fletcher is saying one weight on that pendulum set up has a greater frequency but that can only be because it's mass has actually traveled a lesser amount, so you see inertia has stayed constant and conservative as it should.
Inertia is inertia. It's what pushes back when an object has been made to have a change in velocity. Fletcher is saying one weight on that pendulum set up has a greater frequency but that can only be because it's mass has actually traveled a lesser amount, so you see inertia has stayed constant and conservative as it should.
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ken_behrendt
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re: Center of Gyration
Ralph...
Think of "inertia" as the tendency of an object to resist changes in motion. The higher the inertia, the more sluggish the object becomes. For a given force, if stationary, a high inertia object resists moving...and, if in motion, a high inertia object resists being accelerated or decelerated.
As far as using a pendulum whose weight can rotate freely as it swings, I would suspect that this would eliminate any change in period due to a radius of gyration different from the length of the suspension arm. Thus, in this situation, one could treat the pendulum as though it was a point mass. In my WM2D models, my weights usually are attached to the massless rods and free to rotate about their attachment points so I am not going to worry about the effect.
Jim wrote:
Aside from this, however, I don't see how the concept could be used in the construction of such a wheel especially if it must be able to start from a standstill.
ken
Think of "inertia" as the tendency of an object to resist changes in motion. The higher the inertia, the more sluggish the object becomes. For a given force, if stationary, a high inertia object resists moving...and, if in motion, a high inertia object resists being accelerated or decelerated.
As far as using a pendulum whose weight can rotate freely as it swings, I would suspect that this would eliminate any change in period due to a radius of gyration different from the length of the suspension arm. Thus, in this situation, one could treat the pendulum as though it was a point mass. In my WM2D models, my weights usually are attached to the massless rods and free to rotate about their attachment points so I am not going to worry about the effect.
Jim wrote:
Well, initially, Bessler's one-directional wheels must have had a lot of inertia to overcome as they started up from a standstill. That emplies to me that their maximum torque occurred when they were stationary. Later on, when they finally achieved their maximum terminal velocity, they would still have had the same amount of inertia, but, due to the rotation, it would have been storing a lot of energy as would any flywheel. I keep remembering that mention in some witness' letter about how if a man were to suddenly grab the rim of a moving two-directional wheel, it would, while braking, lift him off of the floor!I have a strong feeling that inertia plays a big role in a working PM wheel.
Aside from this, however, I don't see how the concept could be used in the construction of such a wheel especially if it must be able to start from a standstill.
ken
On 7/6/06, I found, in any overbalanced gravity wheel with rotation rate, ω, axle to CG distance d, and CG dip angle φ, the average vertical velocity of its drive weights is downward and given by:
Vaver = -2(√2)πdωcosφ
Vaver = -2(√2)πdωcosφ
re: Center of Gyration
Michael,
You seem to be having great difficulty in understanding the concept of "Radius of Gyration". The center of mass of any symmetrical object (including a sphere) is at the center point. But view the attached drawing that shows what happens when an object swings around a pivot. Notice that the arc does not split the circle into two equal halves. The upper portion is smaller than the lower portion. Go back to page one and read again the definition "Radius of Gyration". The radius of gyration is that radius which DOES split the circle into two (almost) equal halves.
The 'almost' needs to be included because it is NOT just a matter of dividing up the object into equal masses on each side of the arc.
When an object is bigger than a point mass then the Radius of Gyration grows bigger due to the arc of the swing. Inertia is a point by point or atom by atom phenomina. Some atoms are closer to the pivot and some are farther away. The sum of the square of the radial distance of each atom on one side of the Radius of Gyration matches the sum of the square of the radial distance of each atom on other side.
Ken and Ralph,
A weight that is free to rotate at the end of a weightless rod will act like a point mass. The will be no Radius of Gyration.
You seem to be having great difficulty in understanding the concept of "Radius of Gyration". The center of mass of any symmetrical object (including a sphere) is at the center point. But view the attached drawing that shows what happens when an object swings around a pivot. Notice that the arc does not split the circle into two equal halves. The upper portion is smaller than the lower portion. Go back to page one and read again the definition "Radius of Gyration". The radius of gyration is that radius which DOES split the circle into two (almost) equal halves.
The 'almost' needs to be included because it is NOT just a matter of dividing up the object into equal masses on each side of the arc.
When an object is bigger than a point mass then the Radius of Gyration grows bigger due to the arc of the swing. Inertia is a point by point or atom by atom phenomina. Some atoms are closer to the pivot and some are farther away. The sum of the square of the radial distance of each atom on one side of the Radius of Gyration matches the sum of the square of the radial distance of each atom on other side.
Ken and Ralph,
A weight that is free to rotate at the end of a weightless rod will act like a point mass. The will be no Radius of Gyration.
- Attachments
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- Simple Pendulum
re: Center of Gyration
No Jim, I don't.
I should probably go back and take out the part I put in about the sphere but you'll find the terms and actions I stated in my last two posts are the correct ones. I should have clarified by saying a larger object that is fixed will have a greater inertia to overcome as it's mass is accelerated. I should have combined both of my previous letters on this page but they are there.
I should probably go back and take out the part I put in about the sphere but you'll find the terms and actions I stated in my last two posts are the correct ones. I should have clarified by saying a larger object that is fixed will have a greater inertia to overcome as it's mass is accelerated. I should have combined both of my previous letters on this page but they are there.
Last edited by Michael on Sun Jan 15, 2006 1:40 am, edited 8 times in total.
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ken_behrendt
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re: Center of Gyration
Maybe another way of understanding the radius of gyration is to say that we can consider any pendulum weight to actually be made up of many smaller pendula. The pendula closer to the composite pendulum's pivot will have shorter arms and the pendula farther from the composite pendulum's pivot will have longer arms. However, the composite pendulum can not oscillate with a wide variety of frequencies, it must have one frequency. Thus, we can calculate an "average" composite pendulum arm length based on the distribution of mass in the pendulum weight, which we are here calling the "radius of gyration", that will determine what the frequency of the composite pendulum will be when we take this mass distribution effect into consideration.
For pendulum weights whose radii are small compared to the length of their arms, the effect is small enough so that the radius of gyration is almost equal to the length of the pendulum arm. As the radius of the pendulum weight increases, the effect will become more pronounced and the radius of gyration will grow larger than the length of the pendulum arm. This will cause the frequency of the pendulum to be less than what we would expect if we simply treat the larger pendulum weight like a point mass.
ken
For pendulum weights whose radii are small compared to the length of their arms, the effect is small enough so that the radius of gyration is almost equal to the length of the pendulum arm. As the radius of the pendulum weight increases, the effect will become more pronounced and the radius of gyration will grow larger than the length of the pendulum arm. This will cause the frequency of the pendulum to be less than what we would expect if we simply treat the larger pendulum weight like a point mass.
ken
On 7/6/06, I found, in any overbalanced gravity wheel with rotation rate, ω, axle to CG distance d, and CG dip angle φ, the average vertical velocity of its drive weights is downward and given by:
Vaver = -2(√2)πdωcosφ
Vaver = -2(√2)πdωcosφ
re: Center of Gyration
TrueMichael wrote:1. Gravity pulls all objects no matter how much they weigh at the same rate of acceleration.
"Fulcrum" makes no sense in this sentence. Fulcrum means "the pivot about which a lever turns".Michael wrote:Gravity is the fulcrum that all these observations are made under.
Only when subjected to a same rate of force is this true. I must assume then that you mean gravitational acceleration.Michael wrote:2. Since all objects travel at the same rate of acceleration
Frequency makes no sense in this sentence. Frequency means "the number of occurrences within a given time period". I must assume that you are speaking about the swing of a pendulum and its frequency. The speed of a swinging pendulum must be measured relative to some location on the pendulum. This is what Center of Gyration is all about. It is about choosing an appropriate point to use for calculations involving the swinging of a pendulum.Michael wrote:a mass that reaches its bottom first has a greater frequency, not a greater speed
Understood.Michael wrote:provided both masses are dropped at the same time and at the same angle.
Not true. You are forgetting that a pendulum fixed to a rod has two inertial components that must be considered. One is the vertical (and horizontal when swinging on a rod) component of the weight being pulled downward by gravity. The other component is rotational inertia. Rotation inertia affects the swing rate because some of the atoms are closer to the pivot point and some are more distant. In real life they are never compressed into a theoretical point mass. When a small sphere and a large sphere swing on identical rods the small sphere is more like a point mass and swings faster. The larger sphere has more rotational inertia to overcome on each swing. It will swing slower. If you adjust the rod lengths to the Radius of Gyration then they will both swing the same frequency.Michael wrote:3. Since gravity pulls objects at the same rate of acceleration, the only reason one object would have a greater frequency than another is because it has less distance to travel, which means it's mass has traveled less.
This has been proven in many tests in university labs throughout the world. When their physical size and shape are different their center of mass swings at different frequencies.Michael wrote:A perfect sphere's mass is measured from its exact center. Has there been a test done to show that two fixes spheres with the same distances from their centers to the pivot point having different frequencies?
re: Center of Gyration
Michael wrote:
Gravity is the fulcrum that all these observations are made under.
"Fulcrum" makes no sense in this sentence. Fulcrum means "the pivot about which a lever turns".
It makes sense if you regard it in the metaphorical spirit in which it is made.
Michael wrote:
2. Since all objects travel at the same rate of acceleration
Only when subjected to a same rate of force is this true. I must assume then that you mean gravitational acceleration.
Jim, this is silly. I don't know if you are inspired to go gun slinging :) but obviously I meant gravitational acceleration. I headed the post I made with gravity, I stated gravity is what we are measuring all of this on.
Michael wrote:
a mass that reaches its bottom first has a greater frequency, not a greater speed
Frequency makes no sense in this sentence.
It makes sense but again Jim, as I said, I should have combined both my letters. In my first letter I wasn't regarding the masses inertia, in my second and third letters I did. Of course speed is relevent also, because of inertia. Put it this way, in my first letter I only covered half the bases, with one mistake at the bottom.
Michael wrote:
3. Since gravity pulls objects at the same rate of acceleration, the only reason one object would have a greater frequency than another is because it has less distance to travel, which means it's mass has traveled less.
Not true.
Actually it is true. I should explain myself better though. A mass (in these examples, under gravity) that has a greater frequency, or is moving faster, is doing so because it's mass has traveled less. This might sound like goobaldygook but if you sum the masses complete travel, you'll see that it is less compared to the one moving slower. It's the exact same thing as you saying rotational inertia.
You are forgetting that a pendulum fixed to a rod has two inertial components that must be considered. One is the vertical (and horizontal when swinging on a rod) component of the weight being pulled downward by gravity. The other component is rotational inertia.
Not true at all, hopefully clarified above and again, it's in the second and third letter on this page. Again, also, I should have combined it with my first letter.
Michael wrote:
A perfect sphere's mass is measured from its exact center. Has there been a test done to show that two fixes spheres with the same distances from their centers to the pivot point having different frequencies?
This has been proven in many tests in university labs throughout the world. When their physical size and shape are different their center of mass swings at different frequencies.
As I said Jim, I should have taken that out. I left it in so others will know what is being talked about here.
Gravity is the fulcrum that all these observations are made under.
"Fulcrum" makes no sense in this sentence. Fulcrum means "the pivot about which a lever turns".
It makes sense if you regard it in the metaphorical spirit in which it is made.
Michael wrote:
2. Since all objects travel at the same rate of acceleration
Only when subjected to a same rate of force is this true. I must assume then that you mean gravitational acceleration.
Jim, this is silly. I don't know if you are inspired to go gun slinging :) but obviously I meant gravitational acceleration. I headed the post I made with gravity, I stated gravity is what we are measuring all of this on.
Michael wrote:
a mass that reaches its bottom first has a greater frequency, not a greater speed
Frequency makes no sense in this sentence.
It makes sense but again Jim, as I said, I should have combined both my letters. In my first letter I wasn't regarding the masses inertia, in my second and third letters I did. Of course speed is relevent also, because of inertia. Put it this way, in my first letter I only covered half the bases, with one mistake at the bottom.
Michael wrote:
3. Since gravity pulls objects at the same rate of acceleration, the only reason one object would have a greater frequency than another is because it has less distance to travel, which means it's mass has traveled less.
Not true.
Actually it is true. I should explain myself better though. A mass (in these examples, under gravity) that has a greater frequency, or is moving faster, is doing so because it's mass has traveled less. This might sound like goobaldygook but if you sum the masses complete travel, you'll see that it is less compared to the one moving slower. It's the exact same thing as you saying rotational inertia.
You are forgetting that a pendulum fixed to a rod has two inertial components that must be considered. One is the vertical (and horizontal when swinging on a rod) component of the weight being pulled downward by gravity. The other component is rotational inertia.
Not true at all, hopefully clarified above and again, it's in the second and third letter on this page. Again, also, I should have combined it with my first letter.
Michael wrote:
A perfect sphere's mass is measured from its exact center. Has there been a test done to show that two fixes spheres with the same distances from their centers to the pivot point having different frequencies?
This has been proven in many tests in university labs throughout the world. When their physical size and shape are different their center of mass swings at different frequencies.
As I said Jim, I should have taken that out. I left it in so others will know what is being talked about here.
re: Center of Gyration
So Michael, I'm supposed to know what you mean to say, rather than what you actually say at the time you say it? :))
I see you edited your post eight times. I guess the last one is what you meant to say and the other posts had strings attached to your words so you could reel them back in? :))
Someone once said to engage brain before opening mouth.
Now, back to the subject...
Can this little difference between "Pendulum Radius" and "Radius of Gyration" be made to turn a wheel? The Radius of Gyration (RoG) of a group of weights acting together can be changed by shifting the weights around within the group. The Center of Gravity (CoG) can be kept the same while the RoG is changed. That is what I showed here. I would think the reverse might be true (I've not tried yet) where the RoG might stay the same while the CoG changes. Whenever I've tried to move weights in or out inertia always mucked things up. If the RoG stays fixed then the group's inertia should not affect the wheel.
Remember that Bessler's wheels did not have a great amount of torque. The difference between Cog and RoG is in about the same range.
I see you edited your post eight times. I guess the last one is what you meant to say and the other posts had strings attached to your words so you could reel them back in? :))
Someone once said to engage brain before opening mouth.
Now, back to the subject...
Can this little difference between "Pendulum Radius" and "Radius of Gyration" be made to turn a wheel? The Radius of Gyration (RoG) of a group of weights acting together can be changed by shifting the weights around within the group. The Center of Gravity (CoG) can be kept the same while the RoG is changed. That is what I showed here. I would think the reverse might be true (I've not tried yet) where the RoG might stay the same while the CoG changes. Whenever I've tried to move weights in or out inertia always mucked things up. If the RoG stays fixed then the group's inertia should not affect the wheel.
Remember that Bessler's wheels did not have a great amount of torque. The difference between Cog and RoG is in about the same range.
re: Center of Gyration
I think the biggest problem that exists with wheel dynamics, is that too many people focus on shifting the "COG" of a wheel.. A wheel is rotated by the forces that act upon it. Not so much as where the weights are positioned within the wheel.
A pivoted, levered weight within a wheel will rotate about it's fulcrum, but the effect of that weight acting downwards, with gravity, will result in the forces acting on the wheel being directed at the pivot point.
A falling weight esssentialy has hardly any effects on the turning moment of a wheel. And it's weight will momentarily disappear from that part of the wheel as it is "free falling".
So, my main point here, is look at where the weights are directing their forces within the wheel. Don't always rely on Shifting the COG of it. Sometimes there is a direct relationship but other times there isn't!
A pivoted, levered weight within a wheel will rotate about it's fulcrum, but the effect of that weight acting downwards, with gravity, will result in the forces acting on the wheel being directed at the pivot point.
A falling weight esssentialy has hardly any effects on the turning moment of a wheel. And it's weight will momentarily disappear from that part of the wheel as it is "free falling".
So, my main point here, is look at where the weights are directing their forces within the wheel. Don't always rely on Shifting the COG of it. Sometimes there is a direct relationship but other times there isn't!
The limits of the possible can only be defined by going beyond them into the impossible.
re: Center of Gyration
That is very true!
Re: re: Center of Gyration
The post where I admitted what I should have done? It was edited to make it more plain Jim. Nice to see you've kept your new years resolution.
re: Center of Gyration
>I would think the reverse might be true (I've not tried yet) where the RoG might stay the same while the CoG changes.<
I've posted about that before, the centrifugal force eliminator.
I've posted about that before, the centrifugal force eliminator.
Disclaimer: I reserve the right not to know what I'm talking about and not to mention this possibility in my posts. This disclaimer also applies to sentences I claim are quotes from anybody, including me.
re: Center of Gyration
Jonathan,
Now that you mention it, I remember you posting that.
I tried but failed to find your centrifugal force eliminator post. Do you remember when it was posted or under what topic? TIA
Now that you mention it, I remember you posting that.
I tried but failed to find your centrifugal force eliminator post. Do you remember when it was posted or under what topic? TIA