Unknowable and Postulates

Reference: Course on Subject Clearing

(1) Unknowable simply means that you do not know everything in advance. You have certain observations, and among those observations there are many gaps of what you do not know.

(2) You postulate to fill these gaps. This may narrow the gap but some smaller gaps still remain. As you continue to postulate, you develop a system of postulates to explain what you do not know.

(3) Such a system of postulates must be consistent in itself to be able to predict consistently what you do not know. Everything that you know is based on this system of postulates.

(4) When you come across something that your system of postulates could not predict then you have an inconsistency in your system. You then have to recalibrate your system of postulates to be able to account for this new observation.

(5) Something unknowable still remains and it pulls you forward in developing your system of postulates. This continues on an individual basis life after life. It comes to be shared by others and starts to develop on a social basis.

(6) Ultimately, it has to become a universal system of postulates as inconsistencies continue to be resolved.

(7) The unknowable still remains as that which is yet to be explained fully by the universal system of postulates.

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November 24, 2022 – 7:51 AM Categories: Subject Clearing | Post a comment

Physics I: Chapter 6

Reference: Beginning Physics I

CHAPTER 6: WORK AND MECHANICAL ENERGY

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KEY WORD LIST

Work, Spring Force, Kinetic Energy, Work-Kinetic Energy Theorem, Gravitational Potential Energy, Work-Energy Theorem, Total Mechanical Energy, Conservation of Mechanical Energy, Energy Transfer, Conservative Force, Gravitational Potential away from Earth, Escape Velocity

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GLOSSARY

For details on the following concepts, please consult CHAPTER 6.

WORK
The work WF  due to a constant force F acting on an object while it moves through a displacement s is defined as the component of F along the s direction multiplied by the magnitude of s.

Even though the work involves two vector quantities F and s, it itself has no direction and is thus a scalar. The units of work are those of force times distance. The work is defined so that it can be positive, negative or zero, depending on whether the component of F along s is positive, negative or zero. Total work done is just the work by the resultant force.

SPRING FORCE
A stretched spring exerts a force whose magnitude is proportional to the length of the stretch. The proportionality constant k is called the spring constant:

Fsp = – kx;        F = kx

The work done by F in stretching the spring by a displacement x is

WF = ½ kx2

KINETIC ENERGY
The expression ½ mv2 is called the kinetic energy Ek of the mass m at velocity v. The kinetic energy has the units of work, and the SI units are Joules.

WORK-KINETIC ENERGY THEOREM
The work-kinetic energy theorem is expressed as follows.

Where WT is total work done; Ek is kinetic energy; and Ek is the change in kinetic energy in going from the initial to the final position.

It can be shown, using the calculus, that the work-kinetic energy theorem is still true for the most general possible situation. No matter how complicated the path of motion, and no matter how complicated and numerous the forces are acting on the object, the total work done on the object in any interval equals the final minus the initial kinetic energy for that interval.

GRAVITATIONAL POTENTIAL ENERGY
The expression mgy is called the gravitational potential energy Ep of the mass m at height y.

It can be shown that this equation is true for any path of an object near the earth’s surface. More generally,

WORK-ENERGY THEOREM
The work done by all forces other than gravity on an object equals the sum of the changes in the gravitational potential energy and kinetic energy of the object.

TOTAL MECHANICAL ENERGY
The sum of the potential and kinetic energies at any point is called the total mechanical energy (ET) at that point.

CONSERVATION OF MECHANICAL ENERGY
The total mechanical energy of an object stays constant (“is conserved”) throughout its motion if no forces other than gravity do work.

ENERGY TRANSFER
We can think of the work done by one system on another system as the mechanical transfer of energy between the systems.

CONSERVATIVE FORCE
Conservative force is any force that has the property that the work done by the force depends only on the starting and ending points, and not on what happened in between. The force of gravity near Earth’s surface is clearly such a force. The name “conservative” comes from the fact that if an object moves in a path that returns to the starting point, the total work done by such a force must be zero. We can define a potential energy for the conservative force. The spring force is also a conservative force.

NOTE: A conservative force of gravity is more like a force field in space that generates the same acceleration at all points in space.

GRAVITATIONAL POTENTIAL AWAY FROM EARTH
Gravitational force far from Earth’s surface is no longer constant, but it can be shown to be conservative. It thus has a potential energy. The gravitational potential energy is determined as,

ESCAPE VELOCITY
The escape velocity is the smallest burnout velocity for the rocket for no return. It is equal to

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November 23, 2022 – 5:44 AM Categories: Science | Post a comment

The Postulate of Eternal Being and God

The starting postulate of “Eternal Being” means that there is something existing without any change. We notice that every part of the universe is changing, but the idea of the universe itself is not. The idea of the universe is that of WHOLENESS or ONENESS. Therefore, the postulate of Eternal Being, simply translates as the postulate of ONENESS of existence.

In philosophy, the postulate of eternal being translates into the continuity, consistency and harmony of the system of postulates. But there is another aspect to this postulate—it is the aspect of aliveness. There is aliveness because there is the ability to postulate and the ability to ensure that all postulates are consistent. Thus, all subsequent postulates build up on these starting postulates in a consistent fashion.

The starting postulates are:

  1. There is the ability to postulate.
  2. This ability keeps all postulates consistent.
  3. The system of postulate generated is continuous, consistent and harmonious.

Therefore, any inconsistency in a system of postulates is an aberration. In order to predict or conclude correctly all inconsistencies must be resolved.

To believe in a human-like intelligence right from the beginning of the universe is an error. Human-like intelligence evolves from the starting postulates outlined above. It is therefore important to interpret the concept of God correctly.

There are warnings in the scriptures about misinterpreting the concept of God. The name of God in the Jewish Scriptures is an enigmatic mystery. People often pronounce the four Hebrew letters (YHWH) as “Yahweh” or “Jehovah”, but the truth is that we don’t really know how to say it. Jewish people, by and large, prefer to avoid using any name of God.

In Islam, God is never portrayed in any image. This is because human bias can easily be projected into one’s view of God.

The starting postulates above are the closest approach to the concept of God.

To give God superhuman type of attributes is an error that comes from the human-centric viewpoint. The human-centric viewpoint is a narrow viewpoint that leads to beliefs, such as, the earth is the center of the universe, the sun revolves around the earth, and the earth is flat. Superhuman attributes may come about with further evolution of humans. But that is something that lies in the future. It has not been realized yet in a consistent fashion.

In Christianity, God is portrayed with human-like images. The Bible portrays God as giving out the commandments in human voice. But these are poetic renditions of God. The actual understanding of God goes much deeper.

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November 22, 2022 – 9:09 AM Categories: Religion | Post a comment

Physics I: Chapter 5

Reference: Beginning Physics I

CHAPTER 5: NEWTON’S SECOND LAW

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KEY WORD LIST

Resultant Force and Acceleration, Newton’s Second Law, Mass, Inertia, Weight, Centripetal Force, Banking Equation, Newton’s Law of Gravitation

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GLOSSARY

For details on the following concepts, please consult CHAPTER 5.

RESULTANT FORCE AND ACCELERATION
The unbalanced force on an object causes its acceleration until it comes into balance. The acceleration continues with velocity increasing if the force is non-zero. When the unbalanced force vanishes, so does the acceleration, but the higher velocity continues at a constant rate unless some other resistance or counter force comes into play.

NEWTON’S SECOND LAW
When a nonzero resultant force F acts on a given object, the consequent acceleration a always points in the direction of F. Also, for a given magnitude of F, the magnitude of a is the same no matter what the direction of the force. On the other hand, if the magnitude of F doubles, the magnitude of a doubles; if the magnitude of F triples, the magnitude of a triples; etc. Thus, the magnitude of a is proportional to the magnitude of F. The proportionality constant is called the mass m of the object. This is expressed as the equation,

F = ma.

This equation is the mathematical statement of Newton’s second law.

MASS
The mass controls the response of the object to a given magnitude force. A small mass means a large acceleration, a large mass means a small acceleration. In a sense, the mass is a measure of the resistance of an object to having its velocity changed. This resistance is referred to as the inertia of the object. The relative magnitude of different masses can easily be established by applying the same magnitude force to different objects and measuring their accelerations. Then

The mass is an indestructible and unchanging property of any object that stays with the object even when it is combined into larger units. In the same way, when an object is broken into smaller parts, the sum of masses of the parts equals the original mass.

Units of mass: Kilogram; 1 lbm = 0.45359 kg; 1 slug = 32.2 lbm = 14.7 kg

INERTIA
Inertia is the resistance of an object to having its velocity changed. The inertia is exhibited while the velocity is changing. It vanishes when the velocity settles back to a higher constant value. At higher velocity, the mass of the object reduces (per the theory of relativity) by the amount of inertia overcome by the force. But this reduction in mass is infinitesimal and ignored in mathematical calculations at the level of matter. The mass reduces to almost zero when the speed of light is reached.

WEIGHT
The pull of gravity on an object is commonly called its weight. Weight and mass are proportional at a given point on earth’s surface.

CENTRIPETAL FORCE
When an object moves in uniform circular motion, it happens because it is continually being drawn toward the center of that path. The force drawing the object toward the center is called the centripetal force.

F = mv2/r

BANKING EQUATION
The banking equation gives the general relation among  (the banking angle), v (the velocity) and r (the radius of the curved path) that must hold in order to go around the curve, without the need for any frictional force. Note that the mass of vehicle does not enter the equation:

NEWTON’S LAW OF GRAVITATION

Newton’s Law of universal gravitation states that every particle of matter in the universe attracts every other particle of matter in the universe with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. If we assume the proportional constant is G, the magnitude of this force is then

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November 21, 2022 – 6:10 PM Categories: Science | Post a comment

Physics I: Chapter 4

Reference: Beginning Physics I

CHAPTER 4: FORCES IN EQUILIBRIUM

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KEY WORD LIST

Force, Resultant Force, Line of Action, Rigid Body, Translational Motion, Center of Mass, Uniform Translational Motion, Rotational Motion, Translational Equilibrium, Rotational Equilibrium, Frame of Reference, Inertial Frame of Reference, Newton’s First Law, Law of Equilibrium, Collinear Forces, Concurrent Forces, Body Diagram, Newton’s Third Law, Friction, Normal Force, Static Friction, Kinetic Friction

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GLOSSARY

For details on the following concepts, please consult CHAPTER 4.

FORCE
A force is a mechanical effect of the environment on an object. It is either a push or a pull that manifests either as motion or as distortion of the object. Force may be applied through direct contact or from a distance, such as, the magnetic force. Mathematically, a force can be represented by a vector as it has both a magnitude and a direction. Coplanar forces are “forces” that are acting in the same plane.

RESULTANT FORCE
The vector sum of the forces acting on a particle is called the resultant force on that particle. The forces acting on a particle may be replaced by their resultant, and it will have the same effect.

LINE OF ACTION
The line of action of a force is an imaginary line parallel to the force and drawn through the point at which the force is acting. A force acting on a rigid body can be applied anywhere along its line of action and still have exactly the same effect.

RIGID BODY
A rigid body refers to an object that doesn’t change its shape when forces act on it. No real object is truly rigid, but the concept is a good approximation for stiff objects

TRANSLATIONAL MOTION
Translational motion is the motion of an object as a whole, through space, without regard to how it spins on itself. The translational motion of a very small object, idealized as a particle, is just the motion of the particle along its path.

CENTER OF MASS
The center of mass is a special point of an object, whose translational motion represents the translational motion of the object as a whole, through space, without regard to how it spins on itself. For simple uniform symmetric objects, such as a disk, a sphere, a rod, or a rectangular solid, the center of mass is at the geometric center of the object.

UNIFORM TRANSLATIONAL MOTION
Uniform translational motion means that the center of mass of the object is either at rest or moving at constant speed in a straight line.

ROTATIONAL MOTION
Rotational motion is the spinning motion of an object about a fixed axis, such as the spinning of a wheel on a shaft, but it can also refer to the spinning of an object on itself as the object moves through space. Rotational motion is the change in the angular orientation of the object.

TRANSLATIONAL EQUILIBRIUM
Translational equilibrium means that the object as a whole, aside from rotation, has uniform translational motion. This is the case when the forces acting on an object add up to zero.

ROTATIONAL EQUILIBRIUM
Rotational equilibrium means that the object—whether it is undergoing translational motion or not—is either not spinning or it is spinning in a uniform fashion. For simple symmetric objects it means spinning at a constant rate about a fixed direction.

FRAME OF REFERENCE
A Frame of Reference refers to the “framework” that defines the coordinate system in which one’s measurements and observations are made. If a coordinate system is fixed to the earth and another one is fixed to a rotating merry-go-round, one is going to observe things differently in each. Each of these coordinate systems is fixed in a different frame of reference.

INERTIAL FRAME OF REFERENCE
An inertial frame of reference is a frame of reference in which a completely isolated object (no forces) will appear to be in both translational and rotational equilibrium. For most purposes the earth can be considered an inertial frame. The importance of inertial frame is that Newton’s laws hold only in such frames, and most of the other laws of physics take on simpler form when described in such frames.

NEWTON’S FIRST LAW
Newton’s first law is the condition that the center of mass of the object is either at rest or moving at constant speed in a straight line. Here the vector sum of all forces acting on the object is zero.

LAW OF EQUILIBRIUM
See Newton’s first law.

COLLINEAR FORCES
Two forces are collinear when they act along a common line of action.

CONCURRENT FORCES
Three forces are concurrent when their lines of action pass through a common point.

BODY DIAGRAM
Body diagram, as drawn, consists of the isolated object with only the forces acting on it.

NEWTON’S THIRD LAW
This law, otherwise known as the law of action and reaction, states that if some object exerts a force on another object, then the other object exerts a force back that is equal in magnitude and opposite in direction. The law holds   both for contact forces and for action-at-a-distance forces.

FRICTION
Friction is the rubbing force between two objects whose surfaces are in contact. The force of friction always acts parallel to the touching surfaces. The magnitude of the frictional force exerted by each surface on the other depends on how tightly the two surfaces are pressed together.

NORMAL FORCE
The force responsible for two surfaces pressing together is called the normal force because it acts perpendicular to the two surfaces. By Newton’s third law each surface exerts a normal force that is equal in magnitude and opposite in direction to that exerted by the other.

STATIC FRICTION
When two surfaces are at rest with respect to one another, the frictional force each exerts on the other always opposes any tendency to relative motion. The frictional force on an object adjusts itself in magnitude and direction to oppose and counterbalance any other forces on the object that would tend to make the object start to slide, as needed, from zero magnitude up to some maximum value to stop such slippage. The maximum static friction force that one surface can exert on another is proportional to the normal force, and the proportionality constant is called the coefficient of static friction. This coefficient depends on the nature of the two surfaces.

KINETIC FRICTION
Once two surfaces are in motion relative to one another, the frictional force, now called kinetic friction, acting on a surface is always in a direction opposed to the velocity of that surface. Its magnitude is independent of the magnitude of the velocity. The coefficient of kinetic friction is equal to or smaller than the coefficient of static friction for any given pair of surfaces.

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November 19, 2022 – 9:12 PM Categories: Science | Post a comment