I have searched the internet for the definition of mass when looking up about the difference mass vs inertia. There are two definitions of mass the I see: "Mass is the quantity of matter in an object," and "It is the measure of an object's resistance to acceleration." Which of these definitions is the correct? Or are they both correct and mean the same thing?
73279
I have learned in my physics classes about five different types of  and I am confused about the differences between them.  What's the difference between the five masses:    inertial mass,  gravitational mass, rest mass, invariant mass, relativistic mass?
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I've read a number of the helpful Q&amp;As on photons that mention the mass/mass-less issue. Do I understand correctly that the idea of mass-less (a rest mass of 0) may be just a convention to make the equations work?  From a layperson's view, it's difficult to understand how a particle of light (photon) can be mass-less. A physical object (everyday world-large or quantum-small) must have a mass. Yet, if my understanding is correct, the mass of a moving object/particle increases in proportion to its speed/velocity...so that at the speed of light, its mass would be infinite. A photon travels at the speed of light, but it obviously doesn't have infinite mass, right? Can someone formulate a practical explanation that can be understood by middle-school to high school kids? Much thanks for the help.    Wow--your answers to my original Q below clear up much of my confusion. I now have the daunting task of going over these nuggets and working up an equation-less (hopefully) explanation of the mass-less photon for non-physicist types.  Yes, from a layperson's view, it does seem remarkable that an existing piece of matter-- which has to be made of physical substance--could have zero mass at rest (though a photon is never at rest). It would be almost understandable if a piece of matter made of nothing had zero mass, but that  seems to be an oxymoron, and "nothing" would equate to nonexistent, right?  In case you might find it interesting: I'm working on a writing project that posits we inhabit a universe that consists of matter (physical stuff) only, and that the NON-physical (aka supernatural) does not (and cannot) exist. For instance, if a purported supernatural phenomenon is found to actually exist, then by definition, its existence is proof that it is mundane/natural. All it would take to disprove this premise is reliable proof that ONE supernatural event has occurred. Despite thousands of such claims, that's never yet happened.  Who else better than physicists to confirm my premise? However, I do wish the TV physicists would explain the terms they throw about, some of which mislead/confuse their lay viewers. Case in point: "The universe is made up of matter and energy" (without properly defining the term "energy" as a property of matter).  The result is that laypersons are left with the impression that energy must therefore be something apart from or independent of matter (ie, nonphysical). Their use of the term "pure energy" without specifying exactly what that means adds to the confusion. (Thanks to your replies on this forum, I now understand that "pure energy" refers to photon particles.) However, "psychics" and other charlatans take advantage of such confusion by hijacking terms like energy (as in "psychic energy"), frequencies, vibrations, etc to give perceived scientific legitimacy to their claims that a supernatural spirit world, etc., exists. As you may realize, the majority of people in the US (per 2009 Harris Poll) and around the world believe in the existence of nonphysical/supernatural stuff such as ghosts and spirits.  My purpose is to give laypersons the information they need to distinguish what's real from what's not.  Thanks so much for help...And, PLEASE, add any further comments you think might be helpful/insightful to better inform laypersons.
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Some people say that mass increases with speed, some people say that the mass of an object is independent of its speed.  I understand how some (though not many) things in physics are a matter of interpretation based on one's definitions. But I can't get my head around how both can be 'true' is any sense of the word.  Either mass increases or it doesn't, right?  Can't we just measure it, and find out which 'interpretation' is right? e.g.: (in some sophisticated way) heat up some particles in a box and measure their weight?  ------------------------------  UPDATE  Right, so I've got two identical containers, each with identical amounts of water, each on identical weighing scales, and each in the same g field. If one container has hotter water, will the reading on its scale be larger than the other? If the answer is yes, and g is constant, does this mean that the m in w=mg has got bigger?
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I thought this would be a particularly simple problem but it is turning out to be quite the opposite. I am sure I am doing a very simple mistake.   The problem statement is that there is a mass which is just barely kept on the spring (help by the force equal to the weight of the spring) such that the spring is uncompressed. As soon as I let the object go, it will compress the spring and come to rest at some height. The energy stored in the spring will be equal to the difference in the potential energy at the two height of the spring (compressed and uncompressed),  $$mgh_i -mgh_f= 1/2 kx^2$$ Furthermore, the compression of the spring would just be the difference in the $h_f -h_i$. This gives me two roots for compression,  $$ x=0 $$ And the second would be, $$ mg=1/2kx $$ But then by this, $kx=2mg$ and $kx$ is force by Hooks law, but then does it means that the force compressing the spring is twice the weight of the object? That sounds odd. I was expecting I would just recover Hooks law but I guess I am doing something wrong here. But I am not sure what that is.   Any help will be much appreciated.  P.S. This is not a homework problem. We are designing a project for our school.  Thanks for your time.
51551
Since Newtonian gravity is analogous to electrostatics shouldn't there be something called negative mass? Also, a moving charge generates electric field, but why doesn't a moving mass generate some other field?
1722
Some basic Physics books are often misguiding in the sense that they don't make clear whether something is a primitive concept, a law, a definition or a theorem. This is often a little confusing. I've asked here some moments ago if there's a definition of force, and I've been redirected to a question about whether Newton's Laws are laws or definitions of mass and force.  This is just an example, but there are many others, like for instance, the conservation of energy, which some books present as a theorem, and some places says that this is a law of Physics. Time on the other hand, is something that according to Feynman's lectures on Physics, cannot be defined, so we just say how to measure it and leave it as a primitive concept.  In this context: how in general can we identify whether something is a primitive concept, a fundamental law of Physics, a definition or a theorem?
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I've just learned about moments of inertia in my physics I class, $I=\int{r^2dm}$. The math involving moments of inertia in relation to torque and angular momentum is clear to me. I'm looking for some intuition towards where the definition/idea of moments of inertia comes from? Where do we obtain that the moment of inertia of a point mass $I=mr^2$?  I'm interested in the logical development of these ideas.
27899
What is the difference between  in thermodynamics and  in mechanics?
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Why is force = mass $\times$ acceleration? I have searched in many sites but didn't actually get at it. Simply I want to know that if a mass in space moves (gains velocity thus further accelerates), how can I think, postulate and further believe that force = multiplication  of mass and its acceleration ?
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I'm far from being a physics expert and figured this would be a good place to ask a beginner question that has been confusing me for some time.  According to Galileo, two bodies of different masses, dropped from the same height, will touch the floor at the same time in the absence of air resistance.  BUT Newton's second law states that $a = F/m$, with $a$ the acceleration of a particle, $m$ its mass and $F$ the sum of forces applied to it.  I understand that acceleration represents a variation of velocity and velocity represents a variation of position. I don't comprehend why the mass, which is seemingly affecting the acceleration, does not affect the "time of impact".  Can someone explain this to me? I feel pretty dumb right now :)
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Possible Duplicate:          Today we were in our Literature class talking about the Renaissance and the Enlightement and our teacher also said that scientific experiments were being conducted, and she gave as an example the experiment in which they dropped objects with different mass from a tower to see which object would land first. She then said that she herself didn't know the outcome and since I'm known in my class as the #1, they asked me and I said that they landed at the same time (to my shock many classmates even disagreed with me about this fact). The teacher asked me to explain why and we haven't had anything about inertia in our physics class, so I was forced to use my own self-thought knowledge of physics: I said gravity does pull harder on heavier objects, but heavier objects have more resistance to move, in other words, they have more inertia. The entire class except for the teacher disagreed with me even though they usually don't. One fairly annoying kid asked me to explain why a feather falls way slower than a bowling ball, and I explained why and I also made the claim that in a vacuum they would fall at the same rate. Was I right or my class? Of course I know my explanation is lacking, but it has truth to it, right?
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Do massless particles have a meaning in Newtonian mechanics? Do they have a physical interpretation? Because we don't have an equation of motion for massless particles, we don't have a gravitational potential. We could have electric potential but then we lack the equation of motion. I don't see how they can be a physical object, but I would love to hear from you about this.
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I'm looking to get rigorous definitions on which to base the important quantities in classical mechanics.  To me a "rigorous" physical definition is an operational definition -- that is one in which we define how to measure the quantity over the course of an experiment -- or a definition in terms of other quantities which are operationally defined.  Time can be measured (at least in classical theory) arbitrarily well with clocks.  Whether or not we can actually build a clock with the necessary accuracy is not important for this definition as long as we can conceive of one being built.  Position can be measured arbitrarily well with measuring sticks.  Using these two quantities above we could conceive of strategically placing an array of measuring sticks and clocks (that is building a reference frame from them) so as to entirely measure the motion -- position, velocity, acceleration, etc as a function of time -- of any object we care to.  Now I turn my attention to the most important equation in Newtonian mechanics: $F=ma$ (or $F=\dot p$ it doesn't really matter in this case).  For this equation to make any physical sense we need to be able to measure the mass and/ or force (and/ or momentum) of an object during any experiment arbitrarily well.  How can we define force or mass (or momentum) in such a way that in the midst of some complicated motion -- possibly involving losing/gaining mass, etc -- we can still be certain that we can measure values for these quantities?  One note on this: I would prefer not to assume the equivalence principle as a way of measuring mass.  Let's just pretend that inertia mass and gravitational mass are not the same because, as far as I can tell, in classical mechanics there is no strong reason to believe the equivalence principle holds based solely on Newton's laws (and other equally important "first principles" like the conservation laws).  Of course, there's empirical evidence, but again let's just ignore this for now and see if we can find another way of measuring mass (or force or momentum or kinetic energy or any other thing which as allow us to obtain a measurement of mass indirectly).    EDIT: This will be a response to the  (admittedly a similar question) detailing why I find the answers therein unsatisfactory.  My hope is that either someone can give a new answer or can assuage my uneasiness about one or more of those answers to the linked question.  The top answer is by joshphysics.  The part about forces (and masses) is his statement of the third law: " If any two objects are being observed in a local inertial frame, then their accelerations will be opposite in direction, and the ratio of their accelerations will be constant."  Here he implicitly assumes that two objects in an inertial frame will be accelerating.  So I think he just forgot to add that there must also be so interaction (force) between the two objects.  If we assume that there is an interaction between the two objects then this is just Newton's regular old third law (pretty much).  However, this definition only provides a means of measuring mass if the accelerations of the two bodies are completely due to the single interaction between the two objects.  I'm not entirely sure I understand his second law and so let's move on.  The second answer is by Cleonis.  His second law is the standard second law.  Cleonis claims that he's defining force and mass but he doesn't (well he does seem to imply that given a known force that mass is just a constant of proportionality in the last sentence of his third-to-last paragraph before the additional remarks -- but without a way of measuring force, it's not useful) -- so that's a bit disappointing.  Constantine then defines force as the time derivative of momentum.  Even if we leave force as a primitive we still need a method of measuring the mass of an object in any given system.  His method of defining it in a system of two particles doesn't work if we have more than two particles so it has a very limited applicability.
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What is the meaning of ? I'm little confused about the word as there are some terms like moment of momentum, moment of mass, moment of force, etc. I want to know what exactly is meant by the word "moment".
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I'm in a mechanical physics class, and I'm having a hard time understanding what the quantity of work represents. How can I understand it conceptually?
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As a layman, i can calculate approx "displacement" just by observing the moving object. And accurately by using a simple "scale". Similarly, again, I can calculate angle from origin by using displacement in $x$ and $y$ dimensions. Similarly I can use a stopwatch and scale to understand velocity.  But when I read about , first of all it confuses with the english word "force", we use in real life. To some extent I am sure, it has nothing to do with that. So exactly what is it in the real sense. How can a layman, see force as, just like he can see displacement or angle? Or force is just a quantity defined by physicists to simplify the combinations of $ma$, they might be facing every time. And thus came up with term "force" ( which is similar in spelling to english word in oxford dictionary). And lastly, why not force has just been called as something proportional to mass and it's displacement or velocity. Why something at the level of change of velocity has been used to define it.
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I learned today in class that photons and light are quantized.  I also remember that electric charge is quantized as well.  I was thinking about these implications, and I was wondering if (rest) mass was similarly quantized.  That is, if we describe certain finite irreducible masses $x$, $y$, $z$, etc., then all masses are integer multiples of these irreducible masses.  Or do masses exist along a continuum, as charge and light were thought to exist on before the discovery of photons and electrons?  (I'm only referring to invariant/rest mass.)