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Relativity-I think

  1. May 16, 2009 #1
    Relativity-I think!!

    Hi,
    I'm new here,so I'm kinda nervous.

    Anyway,I have a big question(big to me atleast!) about inertia.

    I've been pondering what exactly this thing inertia is-why does a body have inertia just because it has a mass? What capability does "matter" in an object have to try and prevent external forces from acting on it?????

    I thought that Einstein's E=mcsquared might help-saying that mass has a certain amount of energy may mean that it has energy to oppose external forces--I'm not really sure.

    On the moon where the gravitational forces are a lot weaker,its easier to lift an object,does it mean that it has less inertia. If it does, inertia is supposed to depend on mass only,so gravitational forces aren't supposed to affect it!!!

    Please help!!
     
  2. jcsd
  3. May 16, 2009 #2

    Cyosis

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    Re: Relativity-I think!!

    Inertia is the resistance of an object to a change in motion. Why do objects have inertia? I don't think anyone really knows that. Inertia of an object doesn't change on the moon though. You will still need to apply the same force to give it a certain acceleration as you had to on earth.
     
  4. May 16, 2009 #3
    Re: Relativity-I think!!

    If your car (mass 1000 Kg) is coasting on level ground at 10 meters per sec, it has momentum or inertia of 10,000 Kg-m/sec. It will continue to coast (no friction) at 10 mps until it interacts with something (another car?) that absorbs some or all of the inertia. It does not have inertia just because it has mass. It has inertia because it resists changing its velocity. It has nothing to do with gravity and weight, altough a falling object of mass m has velocity v and therefore has inertia of mv. Also, a spinning wheel on your car has rotational inertia, because it has a moment of inertia I (approximately 1/2 mR2) and a rotational angular velocity w so the rotational inertia = Iw.
     
  5. May 16, 2009 #4

    Cyosis

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    Re: Relativity-I think!!

    Absorbing inertia seems to be a strange concept. It would imply that it is easier to change the car's speed after the collision than it was before the collision (not counting the car being torn apart and reduced in mass).
     
  6. May 16, 2009 #5

    atyy

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    Re: Relativity-I think!!

    Consider two particles with a property called "electric charge". This property results in an electric force between them, causing them to accelerate toward each other: "inertial mass" is defined as property that says how the electric force is related to the acceleration.

    Now consider two particles with a property called "gravitational charge". This property results in an gravitational force between them, causing them to accelerate toward from each other: "inertial mass" is defined as a property that says how the gravitational force is related to the acceleration.

    So "gravitational charge" is just a property like "electric charge" that produces forces between particles - it is a distinct concept from "inertial mass" which is defined as a property that tells us how forces and accelerations are related.

    Experimentally, "gravitational charge" is always proportional to "inertial mass" even though they are different concepts. Because of this constant relationship between "gravitational charge" and "inertial mass", "gravitational charge" is usually called "gravitational mass".
     
  7. May 16, 2009 #6

    atyy

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    Re: Relativity-I think!!

    The moon has less gravitational mass/inertial mass than the earth. Even though the mass of a small particle is the same on the earth and the moon, the gravitational force on the small particle is less on the moon than on the earth because the mass of the moon is less than that of the earth.
     
  8. May 16, 2009 #7
    Re: Relativity-I think!!

    Actually,if we define momentum as a form of inertia, then massless photons qualify. If a photon has energy hv, then its momentum is hv/c. A properly designed radiometer operating in a vacuum can demonstrate the force from sunlight (about 0.1 watts/cm2) striking a vane (about 1 x 10-4 dynes). So maybe having mass is not a requirement for having inertia.
     
  9. May 16, 2009 #8
    Re: Relativity-I think!!

    Hi,
    thanks for the threads. They were really helpful.

    However no-one really said anything bout the relativity concept.

    I think that Bob s's remark about car absorbing inertia kind of agrees with this concept of E=mcsquared. It seems the car 'absorbs' inertia because it has velocity.We also know that inertia increases with the velocity of a body,in a way that means the greater energy,the greater inertia.So inertia is a form of energy stored up on an object-the energy which thus helps it to prevent any change in its state of motion
    Again,I come back to a slight confusion-- as we know,all motion is relativistic. Hence looking at it in that angle, a body at rest w.r.t to me hasis supposed to have inertia because of energy stored inside it--but since it is at rest,it doesn't have energy(neglecting gravitational effects,since it dosn't have any effect on inertia)!!! How do I explain that?
     
    Last edited: May 16, 2009
  10. May 17, 2009 #9

    Dale

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    Re: Relativity-I think!!

    I vaguely remember reading somewhere that a container of hot gas has more inertia than the same container with the same amount of cold gas. So that would imply that energy has inertia. Which would explain why mass has inertia, but then begs the obvious question about why energy has inertia.
     
  11. May 17, 2009 #10
    Re: Relativity-I think!!

    All motion is relative, but rarely relativistic, meaning it satisfies Newton's equations but not necessarily special relativity equations. If I were driving along a deserted desert road on a moonless night, and I suddenly saw your car come up and hit me. I would tell my insurance company that I saw your car hit mine. You would tell your insurance company my car hit yours. So which car had more inertia? But wait. If you were driving a pickup, and I a VW bug, which car had more inertia? In this case, for Newtonian mechanics, inertia means resistance to change in velocity (I think), and not specifically resistance to change in momentum. So inertia has to refer to mass. My college mechanics book (Becker, Theoretical Mechanics) states:
    "Inertia is the property of a body by means of which the body resists a change in its motion. The term is a qualitative one, and is conventionally employed in a qualitative sense. The quantitative measure of inertia is mass....."
     
  12. May 17, 2009 #11

    diazona

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    Re: Relativity-I think!!

    What you're describing there is momentum, not inertia - they are different concepts. Admittedly inertia isn't defined quantitatively the way momentum is (unless you consider mass = inertia), but I'm pretty sure it's not something that jumps around from object to object, that can be gained or lost in a simple collision.
     
  13. May 17, 2009 #12
    Re: Relativity-I think!!

    While I think it is ok to talk about the momentum of a photon (planck constant/wavelength) I am not convinced that you can talk sensibly about the inertia of a photon.

    The reason for this is that (according to wikipedia) "inertia is the resistance of an object to a change in its state of motion".

    On creation, a photon goes from not existing to existing and travelling at c and after that resists all changes to its state of motion (it's complicated to think that the path of a photon can be bent by gravity but the photon itself does not change its state of motion, because it is space itself which is bent - but that's the way it is).

    So it would seem that, apart from the moment of creation, the inertia of a photon is infinite (or "capped" as in you can't get more resistance to change than "impossible to change").

    Or is there another way to look at it?

    I note that inertia seems to be qualitive rather than quantative - there is no actual equation for how much inertia something has.

    cheers,

    neopolitan
     
  14. May 17, 2009 #13
    Re: Relativity-I think!!


    I got a little confused with this part-please could someone clarify this for me.

    Again,the last 3 threads each seem to be going in different directions-I request you to please sum it up for me. Thankyou so much for your help.I really appreciate it.
     
  15. May 18, 2009 #14
    Re: Relativity-I think!!

    You might want to ignore my post, I was just pondering about how inertia and momentum are not the same thing (because you can sensibly talk about the momentum of a photon but maybe not the inertia of a photon).

    That might say more about the nature of a photon than the nature of inertia and momentum.

    cheers,

    neopolitan
     
  16. May 18, 2009 #15
    Re: Relativity-I think!!

    To clarify a point, momentum is not inertia.
     
  17. May 18, 2009 #16

    Cyosis

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    Re: Relativity-I think!!

    I agree to this. In one of the posts it was stated that an object can transfer some or all of its inertia. If we combine this with the definition of inertia, that is the object's resistance to change in motion.This would imply that if an object has transferred all of its inertia it does no longer resist a change in motion. This just doesn't happen in nature. Imagine you're playing a game of pool and you strike one ball in such a way that after it hits another ball it stops. It would have transferred all of its inertia after which the slightest touch would cause it to accelerate indefinitely. Yet I am pretty confident that unless the ball's mass has been reduced a force F would cause the same acceleration to the ball regardless whether I strike it before or after the collision.
     
  18. May 20, 2009 #17
    Re: Relativity-I think!!

    please give me a sum up all your statements. It seems that it is difficult to answer my original question (of what exactly inertia is and how mass enables an object to resist eternal forces),without taking momentum into consideration.but I'm still messed up.
     
  19. May 21, 2009 #18
    Re: Relativity-I think!!

    In physics, inertia is "the tendency of a body to maintain its state of rest or uniform motion unless acted upon by an external force".

    In common parlance, inertia is conflated with:
    • mass (more strictly "inertial mass" which is defined as "the resistance of the matter to acceleration or deceleration, as given by the factor m in Newton's 2nd law F = ma"), and
    • momentum (strictly "the product of a body's mass and its velocity" but more loosely "an impelling force")

    Mass is certainly something that has inertia, but as DaleSpam pointed out, that is not the whole story, since a container of hot gas has more inertia than a container containing the same amount of cold gas. So the heat itself may have inertia - I say this because the behaviour of hot gas is largely kinetic in nature - I'd more interested to hear whether a hot solid has more inertia than a cold solid.

    If heat conveys inertia, then we can say that energy is the deciding factor, not just mass.

    Anyway, to better understand, I think it might be worthwhile to do a thought experiment in which there was no inertia. If nothing "resisted" forces on them, everything would be spinning around the universe at maximum speed (because a photon hitting the Earth would be enough to send the Earth off at light speed). That sort of shows that inertia is not something odd, but something completely necessary.

    Also, I would have thought that inertia derives directly from the laws of thermodynamics - the energy of a system remains constant, so if you have a small object hit and merge with a large object then the energy ends up distributed across the new system comprising of both merged, the inertia of the now slightly larger large object just reflects the fact that much more energy than exists in the system is required to give it the same velocity that the small object had before the collision.

    cheers,

    neopolitan

    PS About the moon, you're not just talking about the inertia of the object, but also the fact that there is a lesser force already acting on the object you are trying to lift. To lift an object on the Earth you have to overcome not only the inertia of the object but also the force of gravity acting on it - on the Earth that is 9.8 newtons per kg and on the moon that is 1.6 newtons per kg. So to give your 10kg object 2m/s2 acceleration on the Earth, you need to apply (9.8 + 2) * 10 = 118 newtons. On the moon, that will be (1.6 + 2)* 10 = 36 newtons. You could, in a rough sort of way, say that the inertia you are overcoming is represented by the 2 * 10 = 20 newtons - a figure which is, as you say, unaffected by gravity. A problem that would experience on the moon that we don't have so much on the Earth is stopping the thing you are lifting from continuing its upwards motion.
     
    Last edited: May 21, 2009
  20. Jun 29, 2009 #19
    Re: Relativity-I think!!

    In broad terms you can think of inertia as a property of an object that measures a certain cause-effect relationship. In the case of mechanical inertia, it is a measure of the effect that a change in the mechanical energy of an object has upon its motion, in particular upon its velocity (eg. the bigger the mass of the object, the more mechanical energy it must absorb for the same linear velocity increase). Or think of thermal inertia (or heat capacity), which is a measure of the amount of thermal energy a body must absorb to undergo a certain temperature increase. Mass, moment of inertia (with respect to an axis), and heat capacity are all measures of types of inertia, and as others have pointed out, are inherent properties of a given object.

    The bigger the respective inertia, the less senstive the object is to changing its state, be it its state of motion, or temperature, or whatever, to variations in the amount of energy it possesses.

    Sorry but I don't know about special relativity :> (that is my pursed beak-face:P)
     
  21. Jun 29, 2009 #20
    Re: Relativity-I think!!

    Um, heat is a mechanism of transfer of energy, and temperature is a measure of internal energy (okay, microscopically you can say that all forms of energy a body possesses boil down to the kinetic energy of its constitutive molecules, but macroscopically we quantify random motion that doesn't contribute to advection as internal energy) . . . anyhow . . . heat does not "have" inertia. As far as I know only material objects can have inertia. A body has more or less energy, which is manisfested as kinetic energy (speed, be it linear or angular), or temperature. A hot body has more internal energy than a cold body of equal mass. Inertia measures the relation between the increment in energy content that the body possesses to the external manifestation of that increment in energy (linear speed, angular speed, temperature..)
     
    Last edited: Jun 29, 2009
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