Is it related to mass or to spacetime? What is the origin of inertia? Would the Higgs boson help to explain it? What is the difference between inertia and momentum? Please Register or Log in to view the hidden image!
Momentum is a gain in speed. Momentum was not present after the rider left the seat of the motorcycle, inertia was. What is the difference between inertia and momentum - I guess a way to look at it is inertia can be used to describe things that are not self powered\powered artificially or even naturally, as in a gust of wind. Once under the effect of the wind then momentum can be a factor, but not inertia.
Inertia is connected to mass and reflects the state of a system before any force is applied, which can be in motion or at rest. Momentum is mass times velocity, which can be a state of inertia , but inertia can have no momentum. At object at rest tends to stay at rest, while an object in motion tends to stay in motion is about inertia, with momentum only the second case.
Inertia is, to all intent and purpose, the same as mass, and is generally considered (iirc) the resistance of a body to changing velocity. Momentum is the inertial mass x velocity, so is a property of a body in motion (and is a conserved property in a closed system). Momentum is not "a gain in speed" as Stanley suggests, as a gain in speed (for a given mass) requires a force. Momentum is merely a property of a body in motion. Afaik there's no clear understanding of the source/cause of inertia, although the Higgs might be part of it... Inertia being the ease with which particles can travel through the Higgs fields, or some such, with that ease being determined by the Higgs boson. Although to be honest I'm way out on a limb here. Please Register or Log in to view the hidden image!
Inertia is essentially another word for mass, the resistance of an object to forces. An object with a large amount of mass (inertia) will not accelerate by a large amount under the application of force. Specifically, the quantities of force, mass (inertia), and acceleration are related by Newton's second law, F = ma. The mass (inertia) of fundamental particles, in general, is generated by the Higgs Mechanism. Normally, particles of matter (fermions) do not possess Lagrangians containing mass terms, as it is required to maintain gauge invariance. However, the mass term is essentially put in, but coupled (essentially, multiplied by) to the "value" of the Higgs field, the vacuum expectation value. In the early universe, the VEV becomes non-zero, generating mass terms and breaking the electroweak symmetry. This follows the process of electroweak symmetry breaking, during which the W and Z bosons acquire mass by absorbing additional degrees of freedom from the Higgs field. That leaves one degree of freedom, which then takes the form of a scalar field, the Higgs boson. Note that most of the mass of particles results from binding energy - for example, the mass of the neutron or proton is almost entirely due to the bonds holding the quarks together, not the masses of the quarks themselves, which are generated by the Higgs mechanism. Momentum is the mass of an object (its inertia) multiplied by its velocity. Changes in momentum are brought about by forces, resulting in another form of the second law, F = dp/dt. Most importantly, momentum is always conserved.
This is incorrect. Momentum is not a change in velocity, that would be acceleration (the rate of change of velocity with time). As mentioned in my post, momentum is the velocity multiplied by the mass of the object.
Tks everyone so far for your answers. Some more questions. Suppose I'm floating in space next to an anvil. Is the amount of force I need to exert on the anvil to get it to move a measure of the inertia or the mass? Or both? This resistance to force wouldn't be weight since there is no gravity. So it would be ? Also, does density effect inertia or mass? Say I take a clump of a billion atoms. Then I compress it to a 1/100 of its size. Wouldn't it have more mass since I have effectively squeezed most the empty space out of it? Matter -space = increase of mass? Does the matter of a neutron star have more mass than that of a regular star? Also, is it true a particle without mass will always go the speed of light? Why is this so? Please Register or Log in to view the hidden image!
Neither - in empty space, there is no friction, air drag, etc. and so the anvil will begin to move with any amount of force you apply. But the question is "how fast?". That's what mass determines (inertia and mass, as I said, are the same thing). For example, if you apply a force of 1 Newton onto an anvil of 1 kg for 1 s, the resulting velocity of the anvil will be 1 m/s. If the anvil has a mass of 10 kg, then the resulting velocity will by .1 m/s. For larger masses, less acceleration is produced by a force. However, no matter what the mass of the anvil, it will begin to move with any force - just at different velocities. For example, apply a force of 0.00000001 N onto an anvil of 10000000 kg in empty space for 1 s. The velocity of the anvil will be 1 X 10^-15 m/s. However, in everyday life, objects are subject to static friction that resists forces with its own force. You need to apply a significant amount of force on a cabinet to even get it moving, because you need to overcome to static friction between the cabinet and the ground. If the coefficient of static friction between the ground at the cabinet is u and gravitational acceleration g, then the force of static friction will be F = umg. In the absence of any external forces, the anvil will remain at that velocity forever (Newton's first law). On earth, however, air resistance and friction will slow it down quickly by applying their own forces. Just the resistance to force, that's all. Since the gravitational force is proportional to mass, mass determines weight in a gravitational field. It's a very strange notion that the mass that generates the gravitational force is the same as resistance to acceleration - it's a fact that led Einstein when developing GR. No, only the total mass matters. In most physics problems, you can actually take all of the mass of an object to be concentrated at one point, the center of mass, and then do your calculations. Density matters in other areas of physics, like chemistry, fluid dynamics, etc. but not kinematics. Yes, this is a consequence of special relativity. If a particle travels at the speed of light, then the Lorentz transformations dictate that all observers will measure that this particle travels at that velocity. For example, light. Therefore, the particle is can never be at rest in any frame of reference, and therefore has no rest mass. In other words, particles travelling at the speed of light are massless, and the LTs keep a particle travelling at c in one frame travelling at c in all frames (see "Relativistic velocity composition").
More precisely, only massless particles can travel at c. The proof is pretty simple: \(E=\frac{m_0c^2}{\sqrt{1-(v/c)^2}}\) \(E\)=particle energy in a certain frame of reference \(m_0\)=particle rest mass \(v\)=particle speed wrt. the respective frame of reference From the above: \(\frac{v^2}{c^2}=1-(\frac{m_0c^2}{E})^2\) This means that for all particles with rest mass \(m_0>0\) \(v<c\) (in ANY frame). Only for particles with \(m_0=0\) , \(v=c\)
It's all so...beautifully mathematical! Does that ever put you in awe? I was thinking for example what if the anvil and I were actually moving in space at the same speed. Then the force I apply to the anvil would actually be making it slow down. Here we observe the equivalence of the inertia/mass between moving and resting states. I'm assuming the force needed to slow down the anvil exactly matches the force needed to move it. I also assume my pushing on the anvil will speed me up considerably. Is there a mathematical relationship expressing the change in these two velocities? But the gravitational force of the anvil would seem to be minute compared to its resistance to acceleration. Why this huge disparity in expressions of the common mass. If scientists one day could manipulate the Higgs field to remove mass from matter, do you think they could achieve light speed?
Yes. People oft think that scientists/mathematicians and the ilk lack the ability to find things beautiful or awe-inspiring, or just simply beautiful... Yet we can find that in the simplicity of equations, the way the complex universe could be guided by such simple relationships such as E=mc^2 etc. Yes, there is a relationship and it's called the conservation of momentum. Assuming that you and the anvil are a closed system, then the combined momentum you have before any interaction will equal the sum of your individual momentum afterward. So assuming you are holding on to the anvil, and that you have mass Mr and the anvil has mass Ma, and you are travelling at velocity V, then your combined momentum is (Ma + Mr) * Vc After your interaction (you pushing on the anvil), you have velocity Vr and the anvil has velocity Va. Your momentum will be Mr * Vr, and the anvil will have Ma * Va. The relationship is that (Ma + Mr) * Vc = Mr*Vr + Ma*Va. I.e. momentum is conserved. I hope this is what you meant, otherwise I may have just taught a grandmother to suck eggs! Please Register or Log in to view the hidden image!
Yes. Let's say that your mass is m, the anvil's mass is mₐ, and the force you apply is F. Now, the force applied onto the anvil produces an acceleration, so that F = mₐaₐ, where aₐ is the acceleration of the anvil. Since acceleration is the change in velocity divided by the interval of time t (a = Δv/t), we can write that F = -mₐΔvₐ/t, or that Δvₐ = -Ft/mₐ. Note that your force is against the direction of motion of the anvil, producing a negative acceleration, slowing it down. So, we put a negative sign in to indicate this fact. The quantity Ft is called "impulse". What is it? Well, from that equation it's mΔv, or the mass multiplied by the change in velocity. Since momentum is mass times velocity, the mass times the change in velocity should be the change in momentum. Therefore, impulse is the change in momentum. Just an interesting side note. Anyways, that yields the change in velocity of the anvil. Next, invoke Newton's third law: the force you apply on the anvil will result in a an equal and opposite force applied to you. So, for you, Δv = Ft/m. Therefore, we can divide your change in velocity by that of the anvil: Δv/Δvₐ = -mₐ/m Which is independent of the force, and is the expression you wanted. Multiplying through by the denominators: mₐΔvₐ = -mΔv So, the total change in momentum of the entire system is mₐΔvₐ + mΔv = -mΔv + mΔv = 0 None. This is the conservation of momentum. The expression for the strength of the gravitational for between two objects, M and m, separated by a distance r, is given by \(F = \frac{GMm}{r^{2}}\) The constant G is Newton's constant, and it's equal to 6.67384 × 10^-11 m^3 kg^-1 s^-2. Obviously, it is very, very small. So even a large mass produces very little gravitational force. EDIT: I've been ninja'd by Sarkus! Sorry for the essentially redundant post, I was still typing when his was posted.
Mass. According to Einstein, it is rest-energy of the mass. YES. Momentum is inertia multiplied by the velocity of the mass.
This is a 'fun' thread to read. Magical Realist is asking some 'interesting' fundamental questions and your answers are excellent in content and composition.
