prashantakerkar

http://en.wikipedia.org/wiki/Inertia
http://en.wikipedia.org/wiki/Newton's_laws_of_motion
http://muse.tau.ac.il/museum/galileo/the_law_of_inertia.html

Law of Inertia states "A body will preserve its velocity and direction so long as no force in its motion's direction acts on it."

Unit of Force : Newton or Kg meter/sec square.
Unit of Speed, Velocity : meter/sec
Unit of Acceleration : meter/sec square.
Unit of Momentum : kg meter/sec.

What is unit of Inertia ?.

Thanks & Regards,
Prashant S Akerkar
pmb
QUOTE (prashantakerkar+Jun 6 2012, 04:27 AM)
http://en.wikipedia.org/wiki/Inertia
http://en.wikipedia.org/wiki/Newton's_laws_of_motion
http://muse.tau.ac.il/museum/galileo/the_law_of_inertia.html

Law of Inertia states "A body will preserve its velocity and direction so long as no force in its motion's direction acts on it."

Unit of Force : Newton or Kg meter/sec square.
Unit of Speed, Velocity : meter/sec
Unit of Acceleration : meter/sec square.
Unit of Momentum : kg meter/sec.

What is unit of Inertia ?.

Thanks & Regards,
Prashant S Akerkar

Suggestion: You should use my webpage to your list. See
http://home.comcast.net/~peter.m.brown/sr/inertial_mass.htm

Inertia is the property of a body to resist changes in an object's quantity of motion. The term quantity of motion is the name usd by Newton for momentum. So the modern definition is as follows

Inertia is the property of a body to resist changes in an object's momentum. The dimension used for inertia is that of mass, i.e. [kg]
prashantakerkar

Thank you.

Thanks & Regards,
Prashant S Akerkar.
VernonNemitz
Hello. I'm aware of something that implies that "mass" cannot be the only factor involved in the definition of "inertia".

Background to a thought-experiment:
In the field of "seismology" it is widely known that when an earthquake happens, shock waves move away from the site at the speed of sound in the various substances of the Earth (different speeds in different substances, such as granite and sandstone).

For an object much smaller than the Earth, if a sudden force is applied to the surface of that object, it logically follows that a shock wave will traverse the object at the speed of sound in the substance of the object. Since the object is small and the speed of sound in most solid substances can easily be a few thousand meters per second, it is plain that the object can fully experience the applied force in a small fraction of a second, well below human sensitivity.

As a result, when Classical Mechanics employs the equation F=(m)(a), there is a hidden assumption that the entirety of the mass will instantly experience an externally applied force, and immediately begin accelerating. Yet we know that can't be correct, if for no other reason than because Einstein set a Maximum Speed Limit for ordinary things!

Now for the thought-experiment. It has two parts, the first of which is data-gathering.
(I) We start with two big chunks of steel, one shaped like a sphere and the other shaped like a long cylinder. Let's imagine this cylinder being 100 meters long, while the mass of both the sphere and the cylinder are a few metric tons, exactly equal to each other. Both objects are suspended off the ground with strong thin support wires, and are free to move somewhat like a pendulum.

At one place beside the sphere we hang a small steel ball. We hang it such that the ball physically contacts the sphere continuously, but it is also free to move, like a pendulum. If we went around to the other side of the large sphere and whacked it with a sledgehammer, we could be confident that a shock wave would be transmitted through the sphere and cause the smaller ball to move away from the large sphere. Things vaguely similar to that are common in the game of "croquet" and the toy "Netwon's Cradle".

We can also do the same thing with the long cylinder. We can hang a small steel ball next to one flat end of the cylinder, and go to the other end and whack it with a sledgehammer, and expect a shock wave to cause the small ball to move.

Now for the measurements. The sledgehammer is made of steel, as are the other objects mentioned. Let us set up an oscilloscope and connect a wire to the head of the sledgehammer, and another to the small steel ball. When the hammer impacts, an electric voltage can travel through the hammer and the large intermediary object and the small ball. When the shock wave reaches the small ball and makes it move, the electric circuit breaks, and the oscilloscope can tell us exactly how long it took the shock wave to traverse the large intermediary object, regardless of whether it was the large sphere or the long cylinder.

Does anyone here dare say the two traversal times, for the shock wave through the large sphere and the shock wave through the long cylinder, will be identical?

I didn't think so. We now remove the small balls and the oscilloscope from the experiment.
(II) When the sledgehammer hits either the large sphere or the long cylinder (with equal force, of course!), we can expect them to start moving, since they are hanging/suspended. However! We are now fully aware that the force of impact takes a certain amount of time to traverse the body of the sphere, and a rather longer time to traverse the length of the cylinder.

Therefore we should expect that the "far end" of each object (the other side from the point-of-hammer-strike), will not move in the slightest, until the shock wave arrives. The result: As a whole, the sphere will begin to move sooner than the cylinder. Because the far end of the cylinder has to wait longer, for the shock wave to arrive.

Now, "inertia" is the tendency for an object to keep moving-as-it-was, before a force is applied to it. In this case both the sphere and the cylinder are initially stationary. By the parameters of this thought-experiment, both have identical mass. Yet the sphere begins to move as a whole in less time than the cylinder requires. Obviously the sphere's tendency to as a whole remain stationary was less than that of the cylinder!

Therefore, logically, we should be able to say that mass alone cannot be the only relevant factor in the Scientifically Precise Definition of "inertia", when real-world objects are being described (not the simplified/perfect/ideal masses of Classical Mechanics). The propagation time of an externally applied force is a factor, too!

Okay? Or, if not, why not?
pmb
QUOTE (VernonNemitz+May 19 2013, 07:23 AM)
Therefore, logically, we should be able to say that mass alone cannot be the only relevant factor in the Scientifically Precise Definition of "inertia", when real-world objects are being described (not the simplified/perfect/ideal masses of Classical Mechanics). The propagation time of an externally applied force is a factor, too!

Okay? Or, if not, why not?

If you had read the link that I gave you then you'd have your answer. In my opinion Newton/Weyl's definition of mass is much better than the one you have in mind, which is Mach's definition. In the Newton/Weyl definition of mass its that which defines momentum and has nothing to do with acceleration
VernonNemitz
QUOTE
If you had read the link that I gave you then you'd have your answer. In my opinion Newton/Weyl's definition of mass is much better than the one you have in mind, which is Mach's definition. In the Newton/Weyl definition of mass its that which defines momentum and has nothing to do with acceleration

I think that the problem I posed, about the definition of "inertia", survives regardless of whether or not you define a force as the rate-of-change-of-momentum, or the rate-of-acceleration-of-a-mass. That's because, when an external impact-type force is applied to a mass-possessing object, if only part of that object immediately experiences the force (like the atoms and molecules at the surface of the object), then only part of the object's momentum is also changing at that instant. The force still has to propagate through the entirety of the object, for the whole of it mass, and for the whole of its momentum, to be affected.

Which means that the sphere still exhibits less tendency to stay stationary, than the long cylinder, despite having identical masses (and momenta, when the masses are stationary), in the thought-experiment I described.
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